[{"date_created":"2024-02-14T12:16:17Z","date_published":"2024-02-05T00:00:00Z","doi":"10.1093/imrn/rnae005","year":"2024","publication":"International Mathematics Research Notices","day":"05","oa":1,"publisher":"Oxford University Press","quality_controlled":"1","acknowledgement":"This work was supported by the NSF [DMS-1502125to S.S.]; and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement [101034413 to S.S.].\r\nI would like to thank my advisor Tom Nevins for many helpful discussions on this subject and for his comments on this paper. I would like to thank Christopher Dodd, Michael Groechenig, and Tamas Hausel for helpful conversations. I would like to thank Tsao-Hsien Chen for useful comments on an earlier version of this paper.","external_id":{"arxiv":["1810.12491"]},"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Shen","full_name":"Shen, Shiyu","first_name":"Shiyu","id":"544cccd3-9005-11ec-87bc-94aef1c5b814"}],"title":"Tamely ramified geometric Langlands correspondence in positive characteristic","citation":{"mla":"Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices, Oxford University Press, 2024, doi:10.1093/imrn/rnae005.","apa":"Shen, S. (2024). Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae005","ama":"Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024. doi:10.1093/imrn/rnae005","short":"S. Shen, International Mathematics Research Notices (2024).","ieee":"S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,” International Mathematics Research Notices. Oxford University Press, 2024.","chicago":"Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae005.","ista":"Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"ec_funded":1,"publication_status":"epub_ahead","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.1093/imrn/rnae005","open_access":"1"}],"month":"02","abstract":[{"text":"We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k). Let k be an algebraically closed field of characteristic p>n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bunn,P the moduli stack of (quasi-)parabolic vector bundles on X, and by Locn,P the moduli stack of parabolic flat connections such that the residue is nilpotent with respect to the parabolic reduction at each marked point. We construct an equivalence between the bounded derived category Db(Qcoh(Loc0n,P)) of quasi-coherent sheaves on an open substack Loc0n,P⊂Locn,P, and the bounded derived category Db(D0Bunn,P-mod) of D0Bunn,P-modules, where D0Bunn,P is a localization of DBunn,P the sheaf of crystalline differential operators on Bunn,P. Thus we extend the work of Bezrukavnikov-Braverman to the tamely ramified case. We also prove a correspondence between flat connections on X with regular singularities and meromorphic Higgs bundles on the Frobenius twist X(1) of X with first order poles .","lang":"eng"}],"oa_version":"Published Version","department":[{"_id":"TaHa"}],"date_updated":"2024-02-19T10:22:44Z","article_type":"original","type":"journal_article","keyword":["General Mathematics"],"status":"public","_id":"14986"},{"date_updated":"2023-08-01T13:11:30Z","department":[{"_id":"UlWa"}],"_id":"12563","status":"public","keyword":["General Mathematics","General Computer Science"],"article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"publication_status":"published","volume":52,"issue":"1","ec_funded":1,"oa_version":"Preprint","abstract":[{"text":"he approximate graph coloring problem, whose complexity is unresolved in most cases, concerns finding a c-coloring of a graph that is promised to be k-colorable, where c≥k. This problem naturally generalizes to promise graph homomorphism problems and further to promise constraint satisfaction problems. The complexity of these problems has recently been studied through an algebraic approach. In this paper, we introduce two new techniques to analyze the complexity of promise CSPs: one is based on topology and the other on adjunction. We apply these techniques, together with the previously introduced algebraic approach, to obtain new unconditional NP-hardness results for a significant class of approximate graph coloring and promise graph homomorphism problems.","lang":"eng"}],"month":"01","intvolume":" 52","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2003.11351"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Krokhin, Andrei, et al. “Topology and Adjunction in Promise Constraint Satisfaction.” SIAM Journal on Computing, vol. 52, no. 1, Society for Industrial & Applied Mathematics, 2023, pp. 38–79, doi:10.1137/20m1378223.","ama":"Krokhin A, Opršal J, Wrochna M, Živný S. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 2023;52(1):38-79. doi:10.1137/20m1378223","apa":"Krokhin, A., Opršal, J., Wrochna, M., & Živný, S. (2023). Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/20m1378223","ieee":"A. Krokhin, J. Opršal, M. Wrochna, and S. Živný, “Topology and adjunction in promise constraint satisfaction,” SIAM Journal on Computing, vol. 52, no. 1. Society for Industrial & Applied Mathematics, pp. 38–79, 2023.","short":"A. Krokhin, J. Opršal, M. Wrochna, S. Živný, SIAM Journal on Computing 52 (2023) 38–79.","chicago":"Krokhin, Andrei, Jakub Opršal, Marcin Wrochna, and Stanislav Živný. “Topology and Adjunction in Promise Constraint Satisfaction.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2023. https://doi.org/10.1137/20m1378223.","ista":"Krokhin A, Opršal J, Wrochna M, Živný S. 2023. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 52(1), 38–79."},"title":"Topology and adjunction in promise constraint satisfaction","author":[{"last_name":"Krokhin","full_name":"Krokhin, Andrei","first_name":"Andrei"},{"id":"ec596741-c539-11ec-b829-c79322a91242","first_name":"Jakub","full_name":"Opršal, Jakub","orcid":"0000-0003-1245-3456","last_name":"Opršal"},{"first_name":"Marcin","full_name":"Wrochna, Marcin","last_name":"Wrochna"},{"full_name":"Živný, Stanislav","last_name":"Živný","first_name":"Stanislav"}],"external_id":{"isi":["000955000000001"],"arxiv":["2003.11351"]},"article_processing_charge":"No","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"}],"day":"01","publication":"SIAM Journal on Computing","isi":1,"year":"2023","doi":"10.1137/20m1378223","date_published":"2023-01-01T00:00:00Z","date_created":"2023-02-16T07:03:52Z","page":"38-79","acknowledgement":"Andrei Krokhin and Jakub Opršal were supported by the UK EPSRC grant EP/R034516/1. Jakub Opršal has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413. Stanislav Živný was supported by a Royal Society University Research Fellowship. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper re\u001eects only the authors’ views and not the views of the ERC or the European Commission. ","quality_controlled":"1","publisher":"Society for Industrial & Applied Mathematics","oa":1},{"author":[{"first_name":"Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory","last_name":"Ivanov"},{"first_name":"Márton","full_name":"Naszódi, Márton","last_name":"Naszódi"}],"external_id":{"arxiv":["2212.11781"]},"article_processing_charge":"Yes (via OA deal)","title":"Functional John and Löwner conditions for pairs of log-concave functions","citation":{"short":"G. Ivanov, M. Naszódi, International Mathematics Research Notices 2023 (2023) 20613–20669.","ieee":"G. Ivanov and M. Naszódi, “Functional John and Löwner conditions for pairs of log-concave functions,” International Mathematics Research Notices, vol. 2023, no. 23. Oxford University Press, pp. 20613–20669, 2023.","ama":"Ivanov G, Naszódi M. Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. 2023;2023(23):20613-20669. doi:10.1093/imrn/rnad210","apa":"Ivanov, G., & Naszódi, M. (2023). Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnad210","mla":"Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” International Mathematics Research Notices, vol. 2023, no. 23, Oxford University Press, 2023, pp. 20613–69, doi:10.1093/imrn/rnad210.","ista":"Ivanov G, Naszódi M. 2023. Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. 2023(23), 20613–20669.","chicago":"Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” International Mathematics Research Notices. Oxford University Press, 2023. https://doi.org/10.1093/imrn/rnad210."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"20613-20669","date_published":"2023-12-01T00:00:00Z","doi":"10.1093/imrn/rnad210","date_created":"2024-01-08T09:48:56Z","has_accepted_license":"1","year":"2023","day":"01","publication":"International Mathematics Research Notices","quality_controlled":"1","publisher":"Oxford University Press","oa":1,"acknowledgement":"We thank Alexander Litvak for the many discussions on Theorem 1.1. Igor Tsiutsiurupa participated in the early stage of this project. To our deep regret, Igor chose another road for his life and stopped working with us.\r\nThis work was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences [to M.N.]; the National Research, Development, and Innovation Fund (NRDI) [K119670 and K131529 to M.N.]; and the ÚNKP-22-5 New National Excellence Program of the Ministry for Innovation and Technology from the source of the NRDI [to M.N.].","file_date_updated":"2024-01-08T09:53:09Z","department":[{"_id":"UlWa"}],"date_updated":"2024-01-08T09:57:25Z","ddc":["510"],"type":"journal_article","article_type":"original","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"status":"public","keyword":["General Mathematics"],"_id":"14737","volume":2023,"issue":"23","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"publication_status":"published","file":[{"date_created":"2024-01-08T09:53:09Z","file_name":"2023_IMRN_Ivanov.pdf","date_updated":"2024-01-08T09:53:09Z","file_size":815777,"creator":"dernst","file_id":"14738","checksum":"353666cea80633beb0f1ffd342dff6d4","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"month":"12","intvolume":" 2023","abstract":[{"text":"John’s fundamental theorem characterizing the largest volume ellipsoid contained in a convex body $K$ in $\\mathbb{R}^{d}$ has seen several generalizations and extensions. One direction, initiated by V. Milman is to replace ellipsoids by positions (affine images) of another body $L$. Another, more recent direction is to consider logarithmically concave functions on $\\mathbb{R}^{d}$ instead of convex bodies: we designate some special, radially symmetric log-concave function $g$ as the analogue of the Euclidean ball, and want to find its largest integral position under the constraint that it is pointwise below some given log-concave function $f$. We follow both directions simultaneously: we consider the functional question, and allow essentially any meaningful function to play the role of $g$ above. Our general theorems jointly extend known results in both directions. The dual problem in the setting of convex bodies asks for the smallest volume ellipsoid, called Löwner’s ellipsoid, containing $K$. We consider the analogous problem for functions: we characterize the solutions of the optimization problem of finding a smallest integral position of some log-concave function $g$ under the constraint that it is pointwise above $f$. It turns out that in the functional setting, the relationship between the John and the Löwner problems is more intricate than it is in the setting of convex bodies.","lang":"eng"}],"oa_version":"Published Version"},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","keyword":["General Physics and Astronomy","General Engineering","General Mathematics"],"status":"public","_id":"14754","department":[{"_id":"BjHo"}],"file_date_updated":"2024-01-09T09:13:53Z","date_updated":"2024-01-09T09:15:29Z","ddc":["530"],"scopus_import":"1","intvolume":" 381","month":"05","abstract":[{"text":"The large-scale laminar/turbulent spiral patterns that appear in the linearly unstable regime of counter-rotating Taylor–Couette flow are investigated from a statistical perspective by means of direct numerical simulation. Unlike the vast majority of previous numerical studies, we analyse the flow in periodic parallelogram-annular domains, following a coordinate change that aligns one of the parallelogram sides with the spiral pattern. The domain size, shape and spatial resolution have been varied and the results compared with those in a sufficiently large computational orthogonal domain with natural axial and azimuthal periodicity. We find that a minimal parallelogram of the right tilt significantly reduces the computational cost without notably compromising the statistical properties of the supercritical turbulent spiral. Its mean structure, obtained from extremely long time integrations in a co-rotating reference frame using the method of slices, bears remarkable similarity with the turbulent stripes observed in plane Couette flow, the centrifugal instability playing only a secondary role.","lang":"eng"}],"oa_version":"Submitted Version","pmid":1,"volume":381,"issue":"2246","publication_status":"published","publication_identifier":{"issn":["1364-503X"],"eissn":["1471-2962"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"1978d126c0ce2f47c22ac20107cc0106","file_id":"14763","success":1,"date_updated":"2024-01-09T09:13:53Z","file_size":6421086,"creator":"dernst","date_created":"2024-01-09T09:13:53Z","file_name":"2023_PhilTransactionsA_Wang_accepted.pdf"}],"article_number":"0112","article_processing_charge":"No","external_id":{"pmid":["36907214"]},"author":[{"first_name":"B.","full_name":"Wang, B.","last_name":"Wang"},{"full_name":"Mellibovsky, F.","last_name":"Mellibovsky","first_name":"F."},{"last_name":"Ayats López","full_name":"Ayats López, Roger","orcid":"0000-0001-6572-0621","first_name":"Roger","id":"ab77522d-073b-11ed-8aff-e71b39258362"},{"last_name":"Deguchi","full_name":"Deguchi, K.","first_name":"K."},{"full_name":"Meseguer, A.","last_name":"Meseguer","first_name":"A."}],"title":"Mean structure of the supercritical turbulent spiral in Taylor–Couette flow","citation":{"mla":"Wang, B., et al. “Mean Structure of the Supercritical Turbulent Spiral in Taylor–Couette Flow.” Philosophical Transactions of the Royal Society A, vol. 381, no. 2246, 0112, The Royal Society, 2023, doi:10.1098/rsta.2022.0112.","ieee":"B. Wang, F. Mellibovsky, R. Ayats López, K. Deguchi, and A. Meseguer, “Mean structure of the supercritical turbulent spiral in Taylor–Couette flow,” Philosophical Transactions of the Royal Society A, vol. 381, no. 2246. The Royal Society, 2023.","short":"B. Wang, F. Mellibovsky, R. Ayats López, K. Deguchi, A. Meseguer, Philosophical Transactions of the Royal Society A 381 (2023).","apa":"Wang, B., Mellibovsky, F., Ayats López, R., Deguchi, K., & Meseguer, A. (2023). Mean structure of the supercritical turbulent spiral in Taylor–Couette flow. Philosophical Transactions of the Royal Society A. The Royal Society. https://doi.org/10.1098/rsta.2022.0112","ama":"Wang B, Mellibovsky F, Ayats López R, Deguchi K, Meseguer A. Mean structure of the supercritical turbulent spiral in Taylor–Couette flow. Philosophical Transactions of the Royal Society A. 2023;381(2246). doi:10.1098/rsta.2022.0112","chicago":"Wang, B., F. Mellibovsky, Roger Ayats López, K. Deguchi, and A. Meseguer. “Mean Structure of the Supercritical Turbulent Spiral in Taylor–Couette Flow.” Philosophical Transactions of the Royal Society A. The Royal Society, 2023. https://doi.org/10.1098/rsta.2022.0112.","ista":"Wang B, Mellibovsky F, Ayats López R, Deguchi K, Meseguer A. 2023. Mean structure of the supercritical turbulent spiral in Taylor–Couette flow. Philosophical Transactions of the Royal Society A. 381(2246), 0112."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"quality_controlled":"1","publisher":"The Royal Society","acknowledgement":"K.D.’s research was supported by Australian Research Council Discovery Early Career Researcher Award (DE170100171). B.W., R.A., F.M. and A.M. research was supported by the Spanish Ministerio de Economía y Competitividad (grant nos. FIS2016-77849-R and FIS2017-85794-P) and Ministerio de Ciencia e Innovación (grant no. PID2020-114043GB-I00) and the Generalitat de Catalunya (grant no. 2017-SGR-785). B.W.’s research was also supported by the Chinese Scholarship Council (grant CSC no. 201806440152). F.M. is a Serra-Húnter Fellow.","date_created":"2024-01-08T13:11:45Z","doi":"10.1098/rsta.2022.0112","date_published":"2023-05-01T00:00:00Z","year":"2023","has_accepted_license":"1","publication":"Philosophical Transactions of the Royal Society A","day":"01"},{"department":[{"_id":"JuFi"}],"date_updated":"2024-01-09T09:22:16Z","type":"journal_article","article_type":"original","status":"public","keyword":["General Mathematics"],"_id":"14755","volume":131,"issue":"3-4","publication_identifier":{"issn":["0921-7134"],"eissn":["1875-8576"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.07100"}],"month":"02","intvolume":" 131","abstract":[{"text":"We consider the sharp interface limit for the scalar-valued and vector-valued Allen–Cahn equation with homogeneous Neumann boundary condition in a bounded smooth domain Ω of arbitrary dimension N ⩾ 2 in the situation when a two-phase diffuse interface has developed and intersects the boundary ∂ Ω. The limit problem is mean curvature flow with 90°-contact angle and we show convergence in strong norms for well-prepared initial data as long as a smooth solution to the limit problem exists. To this end we assume that the limit problem has a smooth solution on [ 0 , T ] for some time T > 0. Based on the latter we construct suitable curvilinear coordinates and set up an asymptotic expansion for the scalar-valued and the vector-valued Allen–Cahn equation. In order to estimate the difference of the exact and approximate solutions with a Gronwall-type argument, a spectral estimate for the linearized Allen–Cahn operator in both cases is required. The latter will be shown in a separate paper, cf. (Moser (2021)).","lang":"eng"}],"oa_version":"Preprint","author":[{"first_name":"Maximilian","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","last_name":"Moser","full_name":"Moser, Maximilian"}],"external_id":{"arxiv":["2105.07100"]},"article_processing_charge":"No","title":"Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result","citation":{"mla":"Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” Asymptotic Analysis, vol. 131, no. 3–4, IOS Press, 2023, pp. 297–383, doi:10.3233/asy-221775.","apa":"Moser, M. (2023). Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. IOS Press. https://doi.org/10.3233/asy-221775","ama":"Moser M. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. 2023;131(3-4):297-383. doi:10.3233/asy-221775","ieee":"M. Moser, “Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result,” Asymptotic Analysis, vol. 131, no. 3–4. IOS Press, pp. 297–383, 2023.","short":"M. Moser, Asymptotic Analysis 131 (2023) 297–383.","chicago":"Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” Asymptotic Analysis. IOS Press, 2023. https://doi.org/10.3233/asy-221775.","ista":"Moser M. 2023. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. 131(3–4), 297–383."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"297-383","doi":"10.3233/asy-221775","date_published":"2023-02-02T00:00:00Z","date_created":"2024-01-08T13:13:28Z","year":"2023","day":"02","publication":"Asymptotic Analysis","quality_controlled":"1","publisher":"IOS Press","oa":1,"acknowledgement":"The author gratefully acknowledges support through DFG, GRK 1692 “Curvature,\r\nCycles and Cohomology” during parts of the work."},{"publication":"PRIMUS","day":"28","year":"2022","date_created":"2023-01-16T10:07:21Z","doi":"10.1080/10511970.2021.1872750","date_published":"2022-05-28T00:00:00Z","page":"593-609","quality_controlled":"1","publisher":"Taylor & Francis","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Shipman, B. A., & Stephenson, E. R. (2022). Tangible topology through the lens of limits. PRIMUS. Taylor & Francis. https://doi.org/10.1080/10511970.2021.1872750","ama":"Shipman BA, Stephenson ER. Tangible topology through the lens of limits. PRIMUS. 2022;32(5):593-609. doi:10.1080/10511970.2021.1872750","short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.","ieee":"B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” PRIMUS, vol. 32, no. 5. Taylor & Francis, pp. 593–609, 2022.","mla":"Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS, vol. 32, no. 5, Taylor & Francis, 2022, pp. 593–609, doi:10.1080/10511970.2021.1872750.","ista":"Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609.","chicago":"Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS. Taylor & Francis, 2022. https://doi.org/10.1080/10511970.2021.1872750."},"title":"Tangible topology through the lens of limits","article_processing_charge":"No","author":[{"last_name":"Shipman","full_name":"Shipman, Barbara A.","first_name":"Barbara A."},{"last_name":"Stephenson","orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","first_name":"Elizabeth R"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["1935-4053"],"issn":["1051-1970"]},"volume":32,"issue":"5","oa_version":"None","abstract":[{"lang":"eng","text":"Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences."}],"intvolume":" 32","month":"05","scopus_import":"1","date_updated":"2023-01-30T13:02:30Z","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"_id":"12307","keyword":["Education","General Mathematics"],"status":"public","type":"journal_article","article_type":"original"},{"project":[{"call_identifier":"H2020","_id":"26580278-B435-11E9-9278-68D0E5697425","grant_number":"771209","name":"Characterizing the fitness landscape on population and global scales"},{"name":"Evolutionary analysis of gene regulation","grant_number":"I05127","_id":"c098eddd-5a5b-11eb-8a69-abe27170a68f"}],"article_number":"74","title":"Relation between the number of peaks and the number of reciprocal sign epistatic interactions","external_id":{"isi":["000812509800001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Raimundo J","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","orcid":"0000-0001-5103-038X","full_name":"Saona Urmeneta, Raimundo J","last_name":"Saona Urmeneta"},{"full_name":"Kondrashov, Fyodor","orcid":"0000-0001-8243-4694","last_name":"Kondrashov","first_name":"Fyodor","id":"44FDEF62-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Khudiakova","full_name":"Khudiakova, Kseniia","orcid":"0000-0002-6246-1465","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","first_name":"Kseniia"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Saona Urmeneta, Raimundo J, Fyodor Kondrashov, and Kseniia Khudiakova. “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.” Bulletin of Mathematical Biology. Springer Nature, 2022. https://doi.org/10.1007/s11538-022-01029-z.","ista":"Saona Urmeneta RJ, Kondrashov F, Khudiakova K. 2022. Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. 84(8), 74.","mla":"Saona Urmeneta, Raimundo J., et al. “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.” Bulletin of Mathematical Biology, vol. 84, no. 8, 74, Springer Nature, 2022, doi:10.1007/s11538-022-01029-z.","ieee":"R. J. Saona Urmeneta, F. Kondrashov, and K. Khudiakova, “Relation between the number of peaks and the number of reciprocal sign epistatic interactions,” Bulletin of Mathematical Biology, vol. 84, no. 8. Springer Nature, 2022.","short":"R.J. Saona Urmeneta, F. Kondrashov, K. Khudiakova, Bulletin of Mathematical Biology 84 (2022).","ama":"Saona Urmeneta RJ, Kondrashov F, Khudiakova K. Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. 2022;84(8). doi:10.1007/s11538-022-01029-z","apa":"Saona Urmeneta, R. J., Kondrashov, F., & Khudiakova, K. (2022). Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. Springer Nature. https://doi.org/10.1007/s11538-022-01029-z"},"oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"We are grateful to Herbert Edelsbrunner and Jeferson Zapata for helpful discussions. Open access funding provided by Austrian Science Fund (FWF). Partially supported by the ERC Consolidator (771209–CharFL) and the FWF Austrian Science Fund (I5127-B) grants to FAK.","date_created":"2022-06-17T16:16:15Z","date_published":"2022-06-17T00:00:00Z","doi":"10.1007/s11538-022-01029-z","publication":"Bulletin of Mathematical Biology","day":"17","year":"2022","has_accepted_license":"1","isi":1,"keyword":["Computational Theory and Mathematics","General Agricultural and Biological Sciences","Pharmacology","General Environmental Science","General Biochemistry","Genetics and Molecular Biology","General Mathematics","Immunology","General Neuroscience"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"11447","department":[{"_id":"GradSch"},{"_id":"NiBa"},{"_id":"JaMa"}],"file_date_updated":"2022-06-20T07:51:32Z","ddc":["510","570"],"date_updated":"2023-08-03T07:20:53Z","intvolume":" 84","month":"06","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Empirical essays of fitness landscapes suggest that they may be rugged, that is having multiple fitness peaks. Such fitness landscapes, those that have multiple peaks, necessarily have special local structures, called reciprocal sign epistasis (Poelwijk et al. in J Theor Biol 272:141–144, 2011). Here, we investigate the quantitative relationship between the number of fitness peaks and the number of reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk et al. in J Theor Biol 272:141–144, 2011) that pairwise reciprocal sign epistasis is a necessary but not sufficient condition for the existence of multiple peaks. Applying discrete Morse theory, which to our knowledge has never been used in this context, we extend this result by giving the minimal number of reciprocal sign epistatic interactions required to create a given number of peaks."}],"ec_funded":1,"issue":"8","volume":84,"related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1007/s11538-022-01118-z"}]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"05a1fe7d10914a00c2bca9b447993a65","file_id":"11455","success":1,"date_updated":"2022-06-20T07:51:32Z","file_size":463025,"creator":"dernst","date_created":"2022-06-20T07:51:32Z","file_name":"2022_BulletinMathBiology_Saona.pdf"}],"publication_status":"published","publication_identifier":{"issn":["0092-8240"],"eissn":["1522-9602"]}},{"_id":"11717","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["General Mathematics"],"date_updated":"2023-08-03T12:36:07Z","ddc":["510"],"department":[{"_id":"VaKa"}],"file_date_updated":"2023-02-02T07:39:09Z","abstract":[{"text":"We study rigidity of rational maps that come from Newton's root finding method for polynomials of arbitrary degrees. We establish dynamical rigidity of these maps: each point in the Julia set of a Newton map is either rigid (i.e. its orbit can be distinguished in combinatorial terms from all other orbits), or the orbit of this point eventually lands in the filled-in Julia set of a polynomial-like restriction of the original map. As a corollary, we show that the Julia sets of Newton maps in many non-trivial cases are locally connected; in particular, every cubic Newton map without Siegel points has locally connected Julia set.\r\nIn the parameter space of Newton maps of arbitrary degree we obtain the following rigidity result: any two combinatorially equivalent Newton maps are quasiconformally conjugate in a neighborhood of their Julia sets provided that they either non-renormalizable, or they are both renormalizable “in the same way”.\r\nOur main tool is a generalized renormalization concept called “complex box mappings” for which we extend a dynamical rigidity result by Kozlovski and van Strien so as to include irrationally indifferent and renormalizable situations.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"10","intvolume":" 408","publication_identifier":{"issn":["0001-8708"]},"publication_status":"published","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"2710e6f5820f8c20a676ddcbb30f0e8d","file_id":"12474","success":1,"creator":"dernst","date_updated":"2023-02-02T07:39:09Z","file_size":2164036,"date_created":"2023-02-02T07:39:09Z","file_name":"2022_AdvancesMathematics_Drach.pdf"}],"language":[{"iso":"eng"}],"issue":"Part A","volume":408,"ec_funded":1,"article_number":"108591","project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"citation":{"chicago":"Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” Advances in Mathematics. Elsevier, 2022. https://doi.org/10.1016/j.aim.2022.108591.","ista":"Drach K, Schleicher D. 2022. Rigidity of Newton dynamics. Advances in Mathematics. 408(Part A), 108591.","mla":"Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” Advances in Mathematics, vol. 408, no. Part A, 108591, Elsevier, 2022, doi:10.1016/j.aim.2022.108591.","short":"K. Drach, D. Schleicher, Advances in Mathematics 408 (2022).","ieee":"K. Drach and D. Schleicher, “Rigidity of Newton dynamics,” Advances in Mathematics, vol. 408, no. Part A. Elsevier, 2022.","apa":"Drach, K., & Schleicher, D. (2022). Rigidity of Newton dynamics. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2022.108591","ama":"Drach K, Schleicher D. Rigidity of Newton dynamics. Advances in Mathematics. 2022;408(Part A). doi:10.1016/j.aim.2022.108591"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Drach","orcid":"0000-0002-9156-8616","full_name":"Drach, Kostiantyn","first_name":"Kostiantyn","id":"fe8209e2-906f-11eb-847d-950f8fc09115"},{"first_name":"Dierk","last_name":"Schleicher","full_name":"Schleicher, Dierk"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000860924200005"]},"title":"Rigidity of Newton dynamics","acknowledgement":"We are grateful to a number of colleagues for helpful and inspiring discussions during the time when we worked on this project, in particular Dima Dudko, Misha Hlushchanka, John Hubbard, Misha Lyubich, Oleg Kozlovski, and Sebastian van Strien. Finally, we would like to thank our dynamics research group for numerous helpful and enjoyable discussions: Konstantin Bogdanov, Roman Chernov, Russell Lodge, Steffen Maaß, David Pfrang, Bernhard Reinke, Sergey Shemyakov, and Maik Sowinski. We gratefully acknowledge support by the Advanced Grant “HOLOGRAM” (#695 621) of the European Research Council (ERC), as well as hospitality of Cornell University in the spring of 2018 while much of this work was prepared. The first-named author also acknowledges the support of the ERC Advanced Grant “SPERIG” (#885 707).","publisher":"Elsevier","quality_controlled":"1","oa":1,"has_accepted_license":"1","isi":1,"year":"2022","day":"29","publication":"Advances in Mathematics","date_published":"2022-10-29T00:00:00Z","doi":"10.1016/j.aim.2022.108591","date_created":"2022-08-01T17:08:16Z"},{"oa_version":"Preprint","abstract":[{"lang":"eng","text":"The aim of this paper is to find new estimates for the norms of functions of a (minus) distinguished Laplace operator L on the ‘ax+b’ groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type ψ(L−−√)exp(itL−−√), with ψ∈C0(R). We show that for t→+∞, the convolution kernel kt of this operator satisfies\r\n∥kt∥1≍t,∥kt∥∞≍1,\r\nso that the upper estimates of D. Müller and C. Thiele (Studia Math., 2007) are sharp. As a necessary component, we recall the Plancherel density of L and spend certain time presenting and comparing different approaches to its calculation. Using its explicit form, we estimate uniform norms of several functions of the shifted Laplace-Beltrami operator Δ~, closely related to L. The functions include in particular exp(−tΔ~γ), t>0,γ>0, and (Δ~−z)s, with complex z, s."}],"intvolume":" 302","month":"12","main_file_link":[{"url":"https://arxiv.org/abs/2101.00584","open_access":"1"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]},"ec_funded":1,"issue":"4","volume":302,"_id":"12210","keyword":["General Mathematics"],"status":"public","type":"journal_article","article_type":"original","date_updated":"2023-08-04T09:22:14Z","department":[{"_id":"JaMa"}],"acknowledgement":"Yu. K. thanks Professor Waldemar Hebisch for valuable discussions on the general context of multipliers on Lie groups. This work was started during an ICL-CNRS fellowship of the second\r\nnamed author at the Imperial College London. Yu. K. is supported by the ANR-19-CE40-0002 grant of the French National Research Agency (ANR). H. Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. R. A. was supported by the EPSRC grant EP/R003025. M. R. is supported by the EPSRC grant EP/R003025/2 and by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","publication":"Mathematische Zeitschrift","day":"01","year":"2022","isi":1,"date_created":"2023-01-16T09:45:31Z","doi":"10.1007/s00209-022-03143-z","date_published":"2022-12-01T00:00:00Z","page":"2327-2352","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Akylzhanov, Rauan, Yulia Kuznetsova, Michael Ruzhansky, and Haonan Zhang. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” Mathematische Zeitschrift. Springer Nature, 2022. https://doi.org/10.1007/s00209-022-03143-z.","ista":"Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. 2022. Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. 302(4), 2327–2352.","mla":"Akylzhanov, Rauan, et al. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” Mathematische Zeitschrift, vol. 302, no. 4, Springer Nature, 2022, pp. 2327–52, doi:10.1007/s00209-022-03143-z.","apa":"Akylzhanov, R., Kuznetsova, Y., Ruzhansky, M., & Zhang, H. (2022). Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. Springer Nature. https://doi.org/10.1007/s00209-022-03143-z","ama":"Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. 2022;302(4):2327-2352. doi:10.1007/s00209-022-03143-z","short":"R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, H. Zhang, Mathematische Zeitschrift 302 (2022) 2327–2352.","ieee":"R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, and H. Zhang, “Norms of certain functions of a distinguished Laplacian on the ax + b groups,” Mathematische Zeitschrift, vol. 302, no. 4. Springer Nature, pp. 2327–2352, 2022."},"title":"Norms of certain functions of a distinguished Laplacian on the ax + b groups","article_processing_charge":"No","external_id":{"arxiv":["2101.00584"],"isi":["000859680700001"]},"author":[{"first_name":"Rauan","last_name":"Akylzhanov","full_name":"Akylzhanov, Rauan"},{"first_name":"Yulia","full_name":"Kuznetsova, Yulia","last_name":"Kuznetsova"},{"last_name":"Ruzhansky","full_name":"Ruzhansky, Michael","first_name":"Michael"},{"first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang","full_name":"Zhang, Haonan"}]},{"_id":"12214","article_type":"original","type":"journal_article","status":"public","keyword":["General Mathematics"],"date_updated":"2023-08-04T09:24:17Z","department":[{"_id":"LaEr"}],"abstract":[{"text":"Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0 < p < ∞ and for all separable real Hilbert spaces E. In particular, we show that Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is a consequence of our more general result: we prove that W1(X) is isometrically rigid if X is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence of mass-splitting isometries. ","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2102.02037"}],"month":"09","intvolume":" 106","publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"4","volume":106,"ec_funded":1,"project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society. Wiley, 2022. https://doi.org/10.1112/jlms.12676.","ista":"Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4), 3865–3894.","mla":"Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society, vol. 106, no. 4, Wiley, 2022, pp. 3865–94, doi:10.1112/jlms.12676.","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2022). The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12676","ama":"Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 2022;106(4):3865-3894. doi:10.1112/jlms.12676","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” Journal of the London Mathematical Society, vol. 106, no. 4. Wiley, pp. 3865–3894, 2022.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Gehér","full_name":"Gehér, György Pál","first_name":"György Pál"},{"first_name":"Tamás","last_name":"Titkos","full_name":"Titkos, Tamás"},{"last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"arxiv":["2102.02037"],"isi":["000854878500001"]},"title":"The isometry group of Wasserstein spaces: The Hilbertian case","acknowledgement":"Geher was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and no. KH129601). ","quality_controlled":"1","publisher":"Wiley","oa":1,"isi":1,"year":"2022","day":"18","publication":"Journal of the London Mathematical Society","page":"3865-3894","doi":"10.1112/jlms.12676","date_published":"2022-09-18T00:00:00Z","date_created":"2023-01-16T09:46:13Z"},{"acknowledgement":"This research is partially supported by University of Padova, BIRD grant “Ultracold atoms\r\nin curved geometries”. KF is supported by Fondazione CARIPARO with a PhD fellowship. AT is\r\npartially supported by French National Research Agency ANR Grant Droplets N. ANR-19-CE30-0003-02. LS thanks Herwig Ott and Sandro Wimberger for their kind invitation to the\r\nInternational Workshop “Quantum Transport with ultracold atoms” (2022).","publisher":"MDPI","quality_controlled":"1","oa":1,"day":"17","publication":"Symmetry","has_accepted_license":"1","isi":1,"year":"2022","doi":"10.3390/sym14102182","date_published":"2022-10-17T00:00:00Z","date_created":"2023-01-12T12:08:31Z","article_number":"2182","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Salasnich, Luca, Alberto Cappellaro, Koichiro Furutani, Andrea Tononi, and Giacomo Bighin. “First and Second Sound in Two-Dimensional Bosonic and Fermionic Superfluids.” Symmetry. MDPI, 2022. https://doi.org/10.3390/sym14102182.","ista":"Salasnich L, Cappellaro A, Furutani K, Tononi A, Bighin G. 2022. First and second sound in two-dimensional bosonic and fermionic superfluids. Symmetry. 14(10), 2182.","mla":"Salasnich, Luca, et al. “First and Second Sound in Two-Dimensional Bosonic and Fermionic Superfluids.” Symmetry, vol. 14, no. 10, 2182, MDPI, 2022, doi:10.3390/sym14102182.","ieee":"L. Salasnich, A. Cappellaro, K. Furutani, A. Tononi, and G. Bighin, “First and second sound in two-dimensional bosonic and fermionic superfluids,” Symmetry, vol. 14, no. 10. MDPI, 2022.","short":"L. Salasnich, A. Cappellaro, K. Furutani, A. Tononi, G. Bighin, Symmetry 14 (2022).","apa":"Salasnich, L., Cappellaro, A., Furutani, K., Tononi, A., & Bighin, G. (2022). First and second sound in two-dimensional bosonic and fermionic superfluids. Symmetry. MDPI. https://doi.org/10.3390/sym14102182","ama":"Salasnich L, Cappellaro A, Furutani K, Tononi A, Bighin G. First and second sound in two-dimensional bosonic and fermionic superfluids. Symmetry. 2022;14(10). doi:10.3390/sym14102182"},"title":"First and second sound in two-dimensional bosonic and fermionic superfluids","author":[{"first_name":"Luca","full_name":"Salasnich, Luca","last_name":"Salasnich"},{"orcid":"0000-0001-6110-2359","full_name":"Cappellaro, Alberto","last_name":"Cappellaro","id":"9d13b3cb-30a2-11eb-80dc-f772505e8660","first_name":"Alberto"},{"first_name":"Koichiro","full_name":"Furutani, Koichiro","last_name":"Furutani"},{"full_name":"Tononi, Andrea","last_name":"Tononi","first_name":"Andrea"},{"id":"4CA96FD4-F248-11E8-B48F-1D18A9856A87","first_name":"Giacomo","last_name":"Bighin","orcid":"0000-0001-8823-9777","full_name":"Bighin, Giacomo"}],"external_id":{"isi":["000875039200001"]},"article_processing_charge":"Yes","oa_version":"Published Version","abstract":[{"text":"We review our theoretical results of the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the U(1) symmetry, there is the coexistence of first and second sound. In the case of weakly-interacting repulsive bosons, we model the recent measurements of the sound velocities of 39K atoms in 2D obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless (BKT) superfluid-to-normal transition temperature. In particular, we perform a quite accurate computation of the superfluid density and show that it is reasonably consistent with the experimental results. For superfluid attractive fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover. In the low-temperature regime, we reproduce the recent measurements of first-sound speed with 6Li atoms. We also predict that there is mixing between sound modes only in the finite-temperature BEC regime.","lang":"eng"}],"month":"10","intvolume":" 14","scopus_import":"1","file":[{"file_size":843723,"date_updated":"2023-01-24T10:56:12Z","creator":"dernst","file_name":"2022_Symmetry_Salsnich.pdf","date_created":"2023-01-24T10:56:12Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"9b6bd0e484834dd76d7b26e3c5fba8bd","file_id":"12361"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2073-8994"]},"publication_status":"published","volume":14,"issue":"10","_id":"12154","status":"public","keyword":["Physics and Astronomy (miscellaneous)","General Mathematics","Chemistry (miscellaneous)","Computer Science (miscellaneous)"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["530"],"date_updated":"2023-08-09T10:13:17Z","file_date_updated":"2023-01-24T10:56:12Z","department":[{"_id":"MiLe"}]},{"page":"100-119","date_published":"2022-02-01T00:00:00Z","doi":"10.1287/moor.2020.1116","date_created":"2021-04-08T09:33:31Z","isi":1,"year":"2022","day":"01","publication":"Mathematics of Operations Research","quality_controlled":"1","publisher":"Institute for Operations Research and the Management Sciences","oa":1,"acknowledgement":"Partially supported by Austrian Science Fund (FWF) NFN Grant No RiSE/SHiNE S11407, by CONICYT Chile through grant PII 20150140, and by ECOS-CONICYT through grant C15E03.\r\n","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"first_name":"Raimundo J","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","full_name":"Saona Urmeneta, Raimundo J","orcid":"0000-0001-5103-038X","last_name":"Saona Urmeneta"},{"full_name":"Ziliotto, Bruno","last_name":"Ziliotto","first_name":"Bruno"}],"article_processing_charge":"No","external_id":{"isi":["000731918100001"],"arxiv":["1904.13360"]},"title":"Finite-memory strategies in POMDPs with long-run average objectives","citation":{"mla":"Chatterjee, Krishnendu, et al. “Finite-Memory Strategies in POMDPs with Long-Run Average Objectives.” Mathematics of Operations Research, vol. 47, no. 1, Institute for Operations Research and the Management Sciences, 2022, pp. 100–19, doi:10.1287/moor.2020.1116.","ieee":"K. Chatterjee, R. J. Saona Urmeneta, and B. Ziliotto, “Finite-memory strategies in POMDPs with long-run average objectives,” Mathematics of Operations Research, vol. 47, no. 1. Institute for Operations Research and the Management Sciences, pp. 100–119, 2022.","short":"K. Chatterjee, R.J. Saona Urmeneta, B. Ziliotto, Mathematics of Operations Research 47 (2022) 100–119.","apa":"Chatterjee, K., Saona Urmeneta, R. J., & Ziliotto, B. (2022). Finite-memory strategies in POMDPs with long-run average objectives. Mathematics of Operations Research. Institute for Operations Research and the Management Sciences. https://doi.org/10.1287/moor.2020.1116","ama":"Chatterjee K, Saona Urmeneta RJ, Ziliotto B. Finite-memory strategies in POMDPs with long-run average objectives. Mathematics of Operations Research. 2022;47(1):100-119. doi:10.1287/moor.2020.1116","chicago":"Chatterjee, Krishnendu, Raimundo J Saona Urmeneta, and Bruno Ziliotto. “Finite-Memory Strategies in POMDPs with Long-Run Average Objectives.” Mathematics of Operations Research. Institute for Operations Research and the Management Sciences, 2022. https://doi.org/10.1287/moor.2020.1116.","ista":"Chatterjee K, Saona Urmeneta RJ, Ziliotto B. 2022. Finite-memory strategies in POMDPs with long-run average objectives. Mathematics of Operations Research. 47(1), 100–119."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","name":"Game Theory"}],"issue":"1","volume":47,"publication_identifier":{"eissn":["1526-5471"],"issn":["0364-765X"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1904.13360"}],"month":"02","intvolume":" 47","abstract":[{"lang":"eng","text":"Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function. "}],"oa_version":"Preprint","department":[{"_id":"GradSch"},{"_id":"KrCh"}],"date_updated":"2023-09-05T13:16:11Z","article_type":"original","type":"journal_article","status":"public","keyword":["Management Science and Operations Research","General Mathematics","Computer Science Applications"],"_id":"9311"},{"ec_funded":1,"issue":"1","volume":149,"publication_status":"published","publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.08286"}],"intvolume":" 149","month":"01","abstract":[{"text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"date_updated":"2023-08-04T11:11:47Z","type":"journal_article","article_type":"original","keyword":["Applied Mathematics","General Mathematics"],"status":"public","_id":"8773","page":"37-52","date_created":"2020-11-19T10:17:40Z","doi":"10.1090/proc/15205","date_published":"2021-01-01T00:00:00Z","year":"2021","isi":1,"publication":"Proceedings of the American Mathematical Society","day":"01","oa":1,"quality_controlled":"1","publisher":"American Mathematical Society","acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","external_id":{"arxiv":["1910.08286"],"isi":["000600416300004"]},"article_processing_charge":"No","author":[{"last_name":"Brown","full_name":"Brown, Adam","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"first_name":"Anna","last_name":"Romanov","full_name":"Romanov, Anna"}],"title":"Contravariant forms on Whittaker modules","citation":{"chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/proc/15205.","ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","apa":"Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}]},{"article_number":"107595","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595.","apa":"Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595","ama":"Virosztek D. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595","short":"D. Virosztek, Advances in Mathematics 380 (2021).","ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021.","chicago":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595.","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595."},"title":"The metric property of the quantum Jensen-Shannon divergence","article_processing_charge":"No","external_id":{"isi":["000619676100035"],"arxiv":["1910.10447"]},"author":[{"first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511"}],"acknowledgement":"D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","oa":1,"publisher":"Elsevier","quality_controlled":"1","publication":"Advances in Mathematics","day":"26","year":"2021","isi":1,"date_created":"2021-01-22T17:55:17Z","doi":"10.1016/j.aim.2021.107595","date_published":"2021-03-26T00:00:00Z","_id":"9036","keyword":["General Mathematics"],"status":"public","article_type":"original","type":"journal_article","date_updated":"2023-08-07T13:34:48Z","department":[{"_id":"LaEr"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space."}],"intvolume":" 380","month":"03","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.10447"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0001-8708"]},"ec_funded":1,"volume":380,"issue":"3"},{"title":"Tight frames and related geometric problems","external_id":{"arxiv":["1804.10055"],"isi":["000730165300021"]},"article_processing_charge":"No","author":[{"first_name":"Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov","full_name":"Ivanov, Grigory"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ieee":"G. Ivanov, “Tight frames and related geometric problems,” Canadian Mathematical Bulletin, vol. 64, no. 4. Canadian Mathematical Society, pp. 942–963, 2021.","short":"G. Ivanov, Canadian Mathematical Bulletin 64 (2021) 942–963.","ama":"Ivanov G. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 2021;64(4):942-963. doi:10.4153/s000843952000096x","apa":"Ivanov, G. (2021). Tight frames and related geometric problems. Canadian Mathematical Bulletin. Canadian Mathematical Society. https://doi.org/10.4153/s000843952000096x","mla":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian Mathematical Bulletin, vol. 64, no. 4, Canadian Mathematical Society, 2021, pp. 942–63, doi:10.4153/s000843952000096x.","ista":"Ivanov G. 2021. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 64(4), 942–963.","chicago":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian Mathematical Bulletin. Canadian Mathematical Society, 2021. https://doi.org/10.4153/s000843952000096x."},"oa":1,"quality_controlled":"1","publisher":"Canadian Mathematical Society","acknowledgement":"The author was supported by the Swiss National Science Foundation grant 200021_179133. The author acknowledges the financial support from the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no. 075-15-2019-1926.","date_created":"2022-03-18T09:55:59Z","date_published":"2021-12-18T00:00:00Z","doi":"10.4153/s000843952000096x","page":"942-963","publication":"Canadian Mathematical Bulletin","day":"18","year":"2021","isi":1,"keyword":["General Mathematics","Tight frame","Grassmannian","zonotope"],"status":"public","type":"journal_article","article_type":"original","_id":"10860","department":[{"_id":"UlWa"}],"date_updated":"2023-09-05T12:43:09Z","intvolume":" 64","month":"12","main_file_link":[{"url":"https://arxiv.org/abs/1804.10055","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":"A tight frame is the orthogonal projection of some orthonormal basis of Rn onto Rk. We show that a set of vectors is a tight frame if and only if the set of all cross products of these vectors is a tight frame. We reformulate a range of problems on the volume of projections (or sections) of regular polytopes in terms of tight frames and write a first-order necessary condition for local extrema of these problems. As applications, we prove new results for the problem of maximization of the volume of zonotopes."}],"volume":64,"issue":"4","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0008-4395"],"eissn":["1496-4287"]}},{"department":[{"_id":"HeEd"}],"date_updated":"2023-08-24T14:19:55Z","article_type":"original","type":"journal_article","keyword":["General Mathematics"],"status":"public","_id":"10867","volume":2020,"issue":"3","publication_status":"published","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.07513"}],"scopus_import":"1","intvolume":" 2020","month":"02","abstract":[{"text":"In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces.","lang":"eng"}],"oa_version":"Preprint","article_processing_charge":"No","external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"title":"Waist of balls in hyperbolic and spherical spaces","citation":{"short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” International Mathematics Research Notices, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","apa":"Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny037","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037.","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny037."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"669-697","date_created":"2022-03-18T11:39:30Z","date_published":"2020-02-01T00:00:00Z","doi":"10.1093/imrn/rny037","year":"2020","isi":1,"publication":"International Mathematics Research Notices","day":"01","oa":1,"publisher":"Oxford University Press","quality_controlled":"1","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036."},{"author":[{"last_name":"Hensel","orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastian"},{"last_name":"Rosati","full_name":"Rosati, Tommaso","first_name":"Tommaso"}],"external_id":{"isi":["000558100500002"],"arxiv":["1709.05202"]},"article_processing_charge":"No","title":"Modelled distributions of Triebel–Lizorkin type","citation":{"mla":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica, vol. 252, no. 3, Instytut Matematyczny, 2020, pp. 251–97, doi:10.4064/sm180411-11-2.","ieee":"S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,” Studia Mathematica, vol. 252, no. 3. Instytut Matematyczny, pp. 251–297, 2020.","short":"S. Hensel, T. Rosati, Studia Mathematica 252 (2020) 251–297.","ama":"Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 2020;252(3):251-297. doi:10.4064/sm180411-11-2","apa":"Hensel, S., & Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. Instytut Matematyczny. https://doi.org/10.4064/sm180411-11-2","chicago":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica. Instytut Matematyczny, 2020. https://doi.org/10.4064/sm180411-11-2.","ista":"Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 252(3), 251–297."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"251-297","date_published":"2020-03-01T00:00:00Z","doi":"10.4064/sm180411-11-2","date_created":"2021-02-25T08:55:03Z","isi":1,"year":"2020","day":"01","publication":"Studia Mathematica","publisher":"Instytut Matematyczny","quality_controlled":"1","department":[{"_id":"JuFi"},{"_id":"GradSch"}],"date_updated":"2023-10-17T09:15:53Z","type":"journal_article","article_type":"original","status":"public","keyword":["General Mathematics"],"_id":"9196","issue":"3","volume":252,"publication_identifier":{"issn":["0039-3223"],"eissn":["1730-6337"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","month":"03","intvolume":" 252","abstract":[{"lang":"eng","text":"In order to provide a local description of a regular function in a small neighbourhood of a point x, it is sufficient by Taylor’s theorem to know the value of the function as well as all of its derivatives up to the required order at the point x itself. In other words, one could say that a regular function is locally modelled by the set of polynomials. The theory of regularity structures due to Hairer generalizes this observation and provides an abstract setup, which in the application to singular SPDE extends the set of polynomials by functionals constructed from, e.g., white noise. In this context, the notion of Taylor polynomials is lifted to the notion of so-called modelled distributions. The celebrated reconstruction theorem, which in turn was inspired by Gubinelli’s \\textit {sewing lemma}, is of paramount importance for the theory. It enables one to reconstruct a modelled distribution as a true distribution on Rd which is locally approximated by this extended set of models or “monomials”. In the original work of Hairer, the error is measured by means of Hölder norms. This was then generalized to the whole scale of Besov spaces by Hairer and Labbé. It is the aim of this work to adapt the analytic part of the theory of regularity structures to the scale of Triebel–Lizorkin spaces."}],"oa_version":"Preprint"},{"citation":{"chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica. EMS Press, 2020. https://doi.org/10.4171/dm/780.","ista":"Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica, vol. 25, EMS Press, 2020, pp. 1421–539, doi:10.4171/dm/780.","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2020). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. EMS Press. https://doi.org/10.4171/dm/780","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 2020;25:1421-1539. doi:10.4171/dm/780","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” Documenta Mathematica, vol. 25. EMS Press, pp. 1421–1539, 2020.","short":"J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes","external_id":{"arxiv":["1804.07752"]},"author":[{"full_name":"Alt, Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"}],"title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","oa":1,"publisher":"EMS Press","quality_controlled":"1","year":"2020","has_accepted_license":"1","publication":"Documenta Mathematica","day":"01","page":"1421-1539","date_created":"2023-12-18T10:37:43Z","date_published":"2020-09-01T00:00:00Z","doi":"10.4171/dm/780","_id":"14694","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","keyword":["General Mathematics"],"status":"public","date_updated":"2023-12-18T10:46:09Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2023-12-18T10:42:32Z","abstract":[{"lang":"eng","text":"We study the unique solution m of the Dyson equation \\( -m(z)^{-1} = z\\1 - a + S[m(z)] \\) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving linear operator on A. We show that m is the Stieltjes transform of a compactly supported A-valued measure on R. Under suitable assumptions, we establish that this measure has a uniformly 1/3-Hölder continuous density with respect to the Lebesgue measure, which is supported on finitely many intervals, called bands. In fact, the density is analytic inside the bands with a square-root growth at the edges and internal cubic root cusps whenever the gap between two bands vanishes. The shape of these singularities is universal and no other singularity may occur. We give a precise asymptotic description of m near the singular points. These asymptotics generalize the analysis at the regular edges given in the companion paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020; Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1, No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math. Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite dimensional band mass formula from [the first author et al., loc. cit.] to the von Neumann algebra setting by showing that the spectral mass of the bands is topologically rigid under deformations and we conclude that these masses are quantized in some important cases."}],"oa_version":"Published Version","intvolume":" 25","month":"09","publication_status":"published","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"14695","checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","success":1,"creator":"dernst","date_updated":"2023-12-18T10:42:32Z","file_size":1374708,"date_created":"2023-12-18T10:42:32Z","file_name":"2020_DocumentaMathematica_Alt.pdf"}],"related_material":{"record":[{"status":"public","id":"6183","relation":"earlier_version"}]},"volume":25},{"abstract":[{"lang":"eng","text":"In this survey, we provide a concise introduction to convex billiards and describe some recent results, obtained by the authors and collaborators, on the classification of integrable billiards, namely the so-called Birkhoff conjecture.\r\n\r\nThis article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’."}],"oa_version":"None","publisher":"The Royal Society","quality_controlled":"1","intvolume":" 376","month":"10","year":"2018","publication_status":"published","publication_identifier":{"issn":["1364-503X","1471-2962"]},"publication":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","language":[{"iso":"eng"}],"day":"28","date_created":"2020-09-17T10:42:01Z","issue":"2131","doi":"10.1098/rsta.2017.0419","volume":376,"date_published":"2018-10-28T00:00:00Z","_id":"8419","article_number":"20170419","type":"journal_article","article_type":"original","keyword":["General Engineering","General Physics and Astronomy","General Mathematics"],"status":"public","citation":{"chicago":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff Billiards.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. The Royal Society, 2018. https://doi.org/10.1098/rsta.2017.0419.","ista":"Kaloshin V, Sorrentino A. 2018. On the integrability of Birkhoff billiards. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376(2131), 20170419.","mla":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff Billiards.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 376, no. 2131, 20170419, The Royal Society, 2018, doi:10.1098/rsta.2017.0419.","ama":"Kaloshin V, Sorrentino A. On the integrability of Birkhoff billiards. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2018;376(2131). doi:10.1098/rsta.2017.0419","apa":"Kaloshin, V., & Sorrentino, A. (2018). On the integrability of Birkhoff billiards. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. The Royal Society. https://doi.org/10.1098/rsta.2017.0419","short":"V. Kaloshin, A. Sorrentino, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376 (2018).","ieee":"V. Kaloshin and A. Sorrentino, “On the integrability of Birkhoff billiards,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 376, no. 2131. The Royal Society, 2018."},"date_updated":"2021-01-12T08:19:09Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","article_processing_charge":"No","author":[{"last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim"},{"full_name":"Sorrentino, Alfonso","last_name":"Sorrentino","first_name":"Alfonso"}],"title":"On the integrability of Birkhoff billiards"},{"oa_version":"Preprint","abstract":[{"lang":"eng","text":"In this paper, we study small perturbations of a class of non-convex integrable Hamiltonians with two degrees of freedom, and we prove a result of diffusion for an open and dense set of perturbations, with an optimal time of diffusion which grows linearly with respect to the inverse of the size of the perturbation."}],"month":"04","intvolume":" 14","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1609-3321","1609-4514"]},"publication_status":"published","issue":"2","volume":14,"_id":"8501","status":"public","keyword":["General Mathematics"],"type":"journal_article","article_type":"original","extern":"1","date_updated":"2021-01-12T08:19:43Z","quality_controlled":"1","publisher":"Independent University of Moscow","day":"01","publication":"Moscow Mathematical Journal","year":"2014","date_published":"2014-04-01T00:00:00Z","doi":"10.17323/1609-4514-2014-14-2-181-203","date_created":"2020-09-18T10:47:09Z","page":"181-203","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Bounemoura A, Kaloshin V. Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom. Moscow Mathematical Journal. 2014;14(2):181-203. doi:10.17323/1609-4514-2014-14-2-181-203","apa":"Bounemoura, A., & Kaloshin, V. (2014). Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom. Moscow Mathematical Journal. Independent University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-2-181-203","short":"A. Bounemoura, V. Kaloshin, Moscow Mathematical Journal 14 (2014) 181–203.","ieee":"A. Bounemoura and V. Kaloshin, “Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom,” Moscow Mathematical Journal, vol. 14, no. 2. Independent University of Moscow, pp. 181–203, 2014.","mla":"Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class of Non-Convex Hamiltonians with Two Degrees of Freedom.” Moscow Mathematical Journal, vol. 14, no. 2, Independent University of Moscow, 2014, pp. 181–203, doi:10.17323/1609-4514-2014-14-2-181-203.","ista":"Bounemoura A, Kaloshin V. 2014. Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom. Moscow Mathematical Journal. 14(2), 181–203.","chicago":"Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class of Non-Convex Hamiltonians with Two Degrees of Freedom.” Moscow Mathematical Journal. Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-2-181-203."},"title":"Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom","author":[{"first_name":"Abed","last_name":"Bounemoura","full_name":"Bounemoura, Abed"},{"orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"article_processing_charge":"No","external_id":{"arxiv":["1304.3050"]}}]