[{"year":"2012","publication_status":"published","day":"23","publication":"Experimental Mathematics","page":"204 - 211","issue":"2","volume":21,"date_published":"2012-05-23T00:00:00Z","doi":"10.1080/10586458.2011.605733","date_created":"2018-12-11T11:45:23Z","abstract":[{"text":"We investigate the frequency of positive squareful numbers x, y, z≤B for which x+y=z and present a conjecture concerning its asymptotic behavior.","lang":"eng"}],"acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","publisher":"Taylor & Francis","quality_controlled":0,"month":"05","intvolume":" 21","citation":{"mla":"Browning, Timothy D., and K. Van Valckenborgh. “Sums of Three Squareful Numbers.” Experimental Mathematics, vol. 21, no. 2, Taylor & Francis, 2012, pp. 204–11, doi:10.1080/10586458.2011.605733.","short":"T.D. Browning, K.V. Valckenborgh, Experimental Mathematics 21 (2012) 204–211.","ieee":"T. D. Browning and K. V. Valckenborgh, “Sums of three squareful numbers,” Experimental Mathematics, vol. 21, no. 2. Taylor & Francis, pp. 204–211, 2012.","ama":"Browning TD, Valckenborgh KV. Sums of three squareful numbers. Experimental Mathematics. 2012;21(2):204-211. doi:10.1080/10586458.2011.605733","apa":"Browning, T. D., & Valckenborgh, K. V. (2012). Sums of three squareful numbers. Experimental Mathematics. Taylor & Francis. https://doi.org/10.1080/10586458.2011.605733","chicago":"Browning, Timothy D, and K Van Valckenborgh. “Sums of Three Squareful Numbers.” Experimental Mathematics. Taylor & Francis, 2012. https://doi.org/10.1080/10586458.2011.605733.","ista":"Browning TD, Valckenborgh KV. 2012. Sums of three squareful numbers. Experimental Mathematics. 21(2), 204–211."},"date_updated":"2021-01-12T06:57:15Z","extern":1,"publist_id":"7664","author":[{"orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Valckenborgh","full_name":"Valckenborgh, K Van","first_name":"K Van"}],"title":"Sums of three squareful numbers","_id":"240","type":"journal_article","status":"public"},{"year":"2012","publication_status":"published","publication":"Communications in Mathematical Physics","day":"01","page":"405 - 424","date_created":"2018-12-11T11:57:27Z","doi":"10.1007/s00220-012-1436-9","volume":313,"date_published":"2012-07-01T00:00:00Z","issue":"2","abstract":[{"lang":"eng","text":"If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2."}],"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1106.0729"}],"quality_controlled":0,"publisher":"Springer","intvolume":" 313","month":"07","date_updated":"2021-01-12T06:57:15Z","citation":{"chicago":"Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Binding of Polarons and Atoms at Threshold.” Communications in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1436-9.","ista":"Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 313(2), 405–424.","mla":"Frank, Rupert, et al. “Binding of Polarons and Atoms at Threshold.” Communications in Mathematical Physics, vol. 313, no. 2, Springer, 2012, pp. 405–24, doi:10.1007/s00220-012-1436-9.","ama":"Frank R, Lieb É, Seiringer R. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 2012;313(2):405-424. doi:10.1007/s00220-012-1436-9","apa":"Frank, R., Lieb, É., & Seiringer, R. (2012). Binding of polarons and atoms at threshold. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1436-9","ieee":"R. Frank, É. Lieb, and R. Seiringer, “Binding of polarons and atoms at threshold,” Communications in Mathematical Physics, vol. 313, no. 2. Springer, pp. 405–424, 2012.","short":"R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313 (2012) 405–424."},"extern":1,"publist_id":"4527","author":[{"last_name":"Frank","full_name":"Frank, Rupert L","first_name":"Rupert"},{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"title":"Binding of polarons and atoms at threshold","_id":"2400","type":"journal_article","status":"public"},{"date_published":"2012-11-01T00:00:00Z","issue":"11","doi":"10.1088/1742-5468/2012/11/P11007","volume":2012,"date_created":"2018-12-11T11:57:28Z","day":"01","publication":"Journal of Statistical Mechanics Theory and Experiment","year":"2012","publication_status":"published","month":"11","intvolume":" 2012","quality_controlled":0,"publisher":"IOP Publishing Ltd.","main_file_link":[{"url":"http://arxiv.org/abs/1207.7054","open_access":"1"}],"oa":1,"abstract":[{"lang":"eng","text":"We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose-Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval."}],"title":"Disordered Bose-Einstein condensates with interaction in one dimension","publist_id":"4523","author":[{"full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jakob","full_name":"Yngvason, Jakob","last_name":"Yngvason"},{"full_name":"Zagrebnov, Valentin A","last_name":"Zagrebnov","first_name":"Valentin"}],"extern":1,"citation":{"mla":"Seiringer, Robert, et al. “Disordered Bose-Einstein Condensates with Interaction in One Dimension.” Journal of Statistical Mechanics Theory and Experiment, vol. 2012, no. 11, IOP Publishing Ltd., 2012, doi:10.1088/1742-5468/2012/11/P11007.","ieee":"R. Seiringer, J. Yngvason, and V. Zagrebnov, “Disordered Bose-Einstein condensates with interaction in one dimension,” Journal of Statistical Mechanics Theory and Experiment, vol. 2012, no. 11. IOP Publishing Ltd., 2012.","short":"R. Seiringer, J. Yngvason, V. Zagrebnov, Journal of Statistical Mechanics Theory and Experiment 2012 (2012).","apa":"Seiringer, R., Yngvason, J., & Zagrebnov, V. (2012). Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. IOP Publishing Ltd. https://doi.org/10.1088/1742-5468/2012/11/P11007","ama":"Seiringer R, Yngvason J, Zagrebnov V. Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. 2012;2012(11). doi:10.1088/1742-5468/2012/11/P11007","chicago":"Seiringer, Robert, Jakob Yngvason, and Valentin Zagrebnov. “Disordered Bose-Einstein Condensates with Interaction in One Dimension.” Journal of Statistical Mechanics Theory and Experiment. IOP Publishing Ltd., 2012. https://doi.org/10.1088/1742-5468/2012/11/P11007.","ista":"Seiringer R, Yngvason J, Zagrebnov V. 2012. Disordered Bose-Einstein condensates with interaction in one dimension. Journal of Statistical Mechanics Theory and Experiment. 2012(11)."},"date_updated":"2021-01-12T06:57:16Z","status":"public","type":"journal_article","_id":"2403"},{"publist_id":"4524","author":[{"full_name":"Frank, Rupert L","last_name":"Frank","first_name":"Rupert"},{"last_name":"Seiringer","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"title":"Lieb-Thirring inequality for a model of particles with point interactions","date_updated":"2021-01-12T06:57:16Z","citation":{"ama":"Frank R, Seiringer R. Lieb-Thirring inequality for a model of particles with point interactions. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.3697416","apa":"Frank, R., & Seiringer, R. (2012). Lieb-Thirring inequality for a model of particles with point interactions. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.3697416","ieee":"R. Frank and R. Seiringer, “Lieb-Thirring inequality for a model of particles with point interactions,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012.","short":"R. Frank, R. Seiringer, Journal of Mathematical Physics 53 (2012).","mla":"Frank, Rupert, and Robert Seiringer. “Lieb-Thirring Inequality for a Model of Particles with Point Interactions.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute of Physics, 2012, doi:10.1063/1.3697416.","ista":"Frank R, Seiringer R. 2012. Lieb-Thirring inequality for a model of particles with point interactions. Journal of Mathematical Physics. 53(9).","chicago":"Frank, Rupert, and Robert Seiringer. “Lieb-Thirring Inequality for a Model of Particles with Point Interactions.” Journal of Mathematical Physics. American Institute of Physics, 2012. https://doi.org/10.1063/1.3697416."},"extern":1,"type":"journal_article","status":"public","_id":"2402","date_published":"2012-09-28T00:00:00Z","issue":"9","volume":53,"doi":"10.1063/1.3697416","date_created":"2018-12-11T11:57:27Z","publication_status":"published","year":"2012","day":"28","publication":"Journal of Mathematical Physics","publisher":"American Institute of Physics","quality_controlled":0,"oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1112.5617","open_access":"1"}],"month":"09","intvolume":" 53","abstract":[{"lang":"eng","text":"We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power."}]},{"abstract":[{"lang":"eng","text":"We find further implications of the BMV conjecture, which states that for hermitian matrices B≥0 and A, the function λ {mapping} Tr exp(A - λB) is the Laplace transform of a positive measure supported on [0,∞]."}],"month":"10","intvolume":" 149","publisher":"Springer","quality_controlled":0,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1206.0460"}],"oa":1,"day":"01","publication":"Journal of Statistical Physics","publication_status":"published","year":"2012","doi":"10.1007/s10955-012-0585-8","date_published":"2012-10-01T00:00:00Z","issue":"1","volume":149,"date_created":"2018-12-11T11:57:27Z","page":"86 - 91","_id":"2401","status":"public","type":"journal_article","extern":1,"date_updated":"2021-01-12T06:57:16Z","citation":{"mla":"Lieb, Élliott, and Robert Seiringer. “Further Implications of the Bessis-Moussa-Villani Conjecture.” Journal of Statistical Physics, vol. 149, no. 1, Springer, 2012, pp. 86–91, doi:10.1007/s10955-012-0585-8.","apa":"Lieb, É., & Seiringer, R. (2012). Further implications of the Bessis-Moussa-Villani conjecture. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-012-0585-8","ama":"Lieb É, Seiringer R. Further implications of the Bessis-Moussa-Villani conjecture. Journal of Statistical Physics. 2012;149(1):86-91. doi:10.1007/s10955-012-0585-8","ieee":"É. Lieb and R. Seiringer, “Further implications of the Bessis-Moussa-Villani conjecture,” Journal of Statistical Physics, vol. 149, no. 1. Springer, pp. 86–91, 2012.","short":"É. Lieb, R. Seiringer, Journal of Statistical Physics 149 (2012) 86–91.","chicago":"Lieb, Élliott, and Robert Seiringer. “Further Implications of the Bessis-Moussa-Villani Conjecture.” Journal of Statistical Physics. Springer, 2012. https://doi.org/10.1007/s10955-012-0585-8.","ista":"Lieb É, Seiringer R. 2012. Further implications of the Bessis-Moussa-Villani conjecture. Journal of Statistical Physics. 149(1), 86–91."},"title":"Further implications of the Bessis-Moussa-Villani conjecture","author":[{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott H"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"publist_id":"4525"},{"quality_controlled":"1","publisher":"Oxford University Press","oa":1,"page":"1319 - 1334","doi":"10.1093/molbev/msr285","date_published":"2012-05-01T00:00:00Z","date_created":"2018-12-11T11:57:30Z","has_accepted_license":"1","year":"2012","day":"01","publication":"Molecular Biology and Evolution","publist_id":"4515","author":[{"full_name":"Ebersberger, Ingo","last_name":"Ebersberger","first_name":"Ingo"},{"first_name":"Ricardo","last_name":"De Matos Simoes","full_name":"De Matos Simoes, Ricardo"},{"full_name":"Kupczok, Anne","last_name":"Kupczok","first_name":"Anne","id":"2BB22BC2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Matthias","full_name":"Gube, Matthias","last_name":"Gube"},{"full_name":"Kothe, Erika","last_name":"Kothe","first_name":"Erika"},{"last_name":"Voigt","full_name":"Voigt, Kerstin","first_name":"Kerstin"},{"first_name":"Arndt","last_name":"Von Haeseler","full_name":"Von Haeseler, Arndt"}],"title":"A consistent phylogenetic backbone for the fungi","citation":{"ista":"Ebersberger I, De Matos Simoes R, Kupczok A, Gube M, Kothe E, Voigt K, Von Haeseler A. 2012. A consistent phylogenetic backbone for the fungi. Molecular Biology and Evolution. 29(5), 1319–1334.","chicago":"Ebersberger, Ingo, Ricardo De Matos Simoes, Anne Kupczok, Matthias Gube, Erika Kothe, Kerstin Voigt, and Arndt Von Haeseler. “A Consistent Phylogenetic Backbone for the Fungi.” Molecular Biology and Evolution. Oxford University Press, 2012. https://doi.org/10.1093/molbev/msr285.","ama":"Ebersberger I, De Matos Simoes R, Kupczok A, et al. A consistent phylogenetic backbone for the fungi. Molecular Biology and Evolution. 2012;29(5):1319-1334. doi:10.1093/molbev/msr285","apa":"Ebersberger, I., De Matos Simoes, R., Kupczok, A., Gube, M., Kothe, E., Voigt, K., & Von Haeseler, A. (2012). A consistent phylogenetic backbone for the fungi. Molecular Biology and Evolution. Oxford University Press. https://doi.org/10.1093/molbev/msr285","short":"I. Ebersberger, R. De Matos Simoes, A. Kupczok, M. Gube, E. Kothe, K. Voigt, A. Von Haeseler, Molecular Biology and Evolution 29 (2012) 1319–1334.","ieee":"I. Ebersberger et al., “A consistent phylogenetic backbone for the fungi,” Molecular Biology and Evolution, vol. 29, no. 5. Oxford University Press, pp. 1319–1334, 2012.","mla":"Ebersberger, Ingo, et al. “A Consistent Phylogenetic Backbone for the Fungi.” Molecular Biology and Evolution, vol. 29, no. 5, Oxford University Press, 2012, pp. 1319–34, doi:10.1093/molbev/msr285."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"month":"05","intvolume":" 29","abstract":[{"text":"The kingdom of fungi provides model organisms for biotechnology, cell biology, genetics, and life sciences in general. Only when their phylogenetic relationships are stably resolved, can individual results from fungal research be integrated into a holistic picture of biology. However, and despite recent progress, many deep relationships within the fungi remain unclear. Here, we present the first phylogenomic study of an entire eukaryotic kingdom that uses a consistency criterion to strengthen phylogenetic conclusions. We reason that branches (splits) recovered with independent data and different tree reconstruction methods are likely to reflect true evolutionary relationships. Two complementary phylogenomic data sets based on 99 fungal genomes and 109 fungal expressed sequence tag (EST) sets analyzed with four different tree reconstruction methods shed light from different angles on the fungal tree of life. Eleven additional data sets address specifically the phylogenetic position of Blastocladiomycota, Ustilaginomycotina, and Dothideomycetes, respectively. The combined evidence from the resulting trees supports the deep-level stability of the fungal groups toward a comprehensive natural system of the fungi. In addition, our analysis reveals methodologically interesting aspects. Enrichment for EST encoded data-a common practice in phylogenomic analyses-introduces a strong bias toward slowly evolving and functionally correlated genes. Consequently, the generalization of phylogenomic data sets as collections of randomly selected genes cannot be taken for granted. A thorough characterization of the data to assess possible influences on the tree reconstruction should therefore become a standard in phylogenomic analyses.","lang":"eng"}],"oa_version":"Published Version","volume":29,"issue":"5","license":"https://creativecommons.org/licenses/by-nc/4.0/","publication_status":"published","file":[{"file_name":"IST-2015-384-v1+1_Mol_Biol_Evol-2012-Ebersberger-1319-34.pdf","date_created":"2018-12-12T10:13:30Z","file_size":754922,"date_updated":"2020-07-14T12:45:40Z","creator":"system","file_id":"5013","checksum":"d565dcac27d1736c0c378ea6fcf22d69","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)"},"status":"public","pubrep_id":"384","_id":"2411","file_date_updated":"2020-07-14T12:45:40Z","department":[{"_id":"JoBo"}],"date_updated":"2021-01-12T06:57:19Z","ddc":["570","576"]},{"publication":"Israel Journal of Mathematics","day":"28","publication_status":"published","year":"2012","date_created":"2018-12-11T11:45:23Z","doi":"10.1007/s11856-012-0019-y","issue":"2","volume":191,"date_published":"2012-02-28T00:00:00Z","page":"973 - 1012","abstract":[{"text":"The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Châtelet surfaces over ℚ.","lang":"eng"}],"intvolume":" 191","month":"02","publisher":"Springer","quality_controlled":0,"extern":1,"citation":{"mla":"De La Bretèche, Régis, and Timothy D. Browning. “Binary Forms as Sums of Two Squares and Châtelet Surfaces.” Israel Journal of Mathematics, vol. 191, no. 2, Springer, 2012, pp. 973–1012, doi:10.1007/s11856-012-0019-y.","short":"R. De La Bretèche, T.D. Browning, Israel Journal of Mathematics 191 (2012) 973–1012.","ieee":"R. De La Bretèche and T. D. Browning, “Binary forms as sums of two squares and Châtelet surfaces,” Israel Journal of Mathematics, vol. 191, no. 2. Springer, pp. 973–1012, 2012.","apa":"De La Bretèche, R., & Browning, T. D. (2012). Binary forms as sums of two squares and Châtelet surfaces. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-012-0019-y","ama":"De La Bretèche R, Browning TD. Binary forms as sums of two squares and Châtelet surfaces. Israel Journal of Mathematics. 2012;191(2):973-1012. doi:10.1007/s11856-012-0019-y","chicago":"De La Bretèche, Régis, and Timothy D Browning. “Binary Forms as Sums of Two Squares and Châtelet Surfaces.” Israel Journal of Mathematics. Springer, 2012. https://doi.org/10.1007/s11856-012-0019-y.","ista":"De La Bretèche R, Browning TD. 2012. Binary forms as sums of two squares and Châtelet surfaces. Israel Journal of Mathematics. 191(2), 973–1012."},"date_updated":"2021-01-12T06:57:19Z","title":"Binary forms as sums of two squares and Châtelet surfaces","author":[{"first_name":"Régis","last_name":"De La Bretèche","full_name":"de la Bretèche, Régis"},{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning"}],"publist_id":"7663","_id":"241","status":"public","type":"journal_article"},{"publisher":"Cambridge University Press","quality_controlled":0,"main_file_link":[{"url":"https://arxiv.org/abs/1101.5464","open_access":"1"}],"oa":1,"month":"10","intvolume":" 55","abstract":[{"lang":"eng","text":"We investigate the first and second moments of shifted convolutions of the generalized divisor function d 3(n)."}],"acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","page":"551 - 576","doi":"10.1017/S001309151100037X","date_published":"2012-10-01T00:00:00Z","issue":"3","volume":55,"date_created":"2018-12-11T11:45:23Z","year":"2012","publication_status":"published","day":"01","publication":"Proceedings of the Edinburgh Mathematical Society","type":"journal_article","status":"public","_id":"242","author":[{"full_name":"Baier, Stephan","last_name":"Baier","first_name":"Stephan"},{"orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"},{"first_name":"Gihan","full_name":"Marasingha, Gihan","last_name":"Marasingha"},{"first_name":"Liangyi","full_name":"Zhao, Liangyi","last_name":"Zhao"}],"publist_id":"7662","title":"Averages of shifted convolutions of d3 (n)","date_updated":"2021-01-12T06:57:23Z","citation":{"ista":"Baier S, Browning TD, Marasingha G, Zhao L. 2012. Averages of shifted convolutions of d3 (n). Proceedings of the Edinburgh Mathematical Society. 55(3), 551–576.","chicago":"Baier, Stephan, Timothy D Browning, Gihan Marasingha, and Liangyi Zhao. “Averages of Shifted Convolutions of D3 (N).” Proceedings of the Edinburgh Mathematical Society. Cambridge University Press, 2012. https://doi.org/10.1017/S001309151100037X.","apa":"Baier, S., Browning, T. D., Marasingha, G., & Zhao, L. (2012). Averages of shifted convolutions of d3 (n). Proceedings of the Edinburgh Mathematical Society. Cambridge University Press. https://doi.org/10.1017/S001309151100037X","ama":"Baier S, Browning TD, Marasingha G, Zhao L. Averages of shifted convolutions of d3 (n). Proceedings of the Edinburgh Mathematical Society. 2012;55(3):551-576. doi:10.1017/S001309151100037X","ieee":"S. Baier, T. D. Browning, G. Marasingha, and L. Zhao, “Averages of shifted convolutions of d3 (n),” Proceedings of the Edinburgh Mathematical Society, vol. 55, no. 3. Cambridge University Press, pp. 551–576, 2012.","short":"S. Baier, T.D. Browning, G. Marasingha, L. Zhao, Proceedings of the Edinburgh Mathematical Society 55 (2012) 551–576.","mla":"Baier, Stephan, et al. “Averages of Shifted Convolutions of D3 (N).” Proceedings of the Edinburgh Mathematical Society, vol. 55, no. 3, Cambridge University Press, 2012, pp. 551–76, doi:10.1017/S001309151100037X."},"extern":1},{"date_created":"2018-12-11T11:45:24Z","doi":"10.1007/s00039-012-0168-5","date_published":"2012-08-25T00:00:00Z","issue":"5","volume":22,"page":"1124 - 1190","publication":"Geometric and Functional Analysis","day":"25","publication_status":"published","year":"2012","intvolume":" 22","month":"08","publisher":"Springer Basel","quality_controlled":0,"abstract":[{"lang":"eng","text":"Let P(t) ∈ ℚ[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of ℚ containing the roots of P(t). Let N K/ℚ(X) be a full norm form for the extension K/ℚ. We show that the variety P(t) =N K/ℚ(X)≠ 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods."}],"title":"Quadratic polynomials represented by norm forms","publist_id":"7661","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning"},{"full_name":"Heath-Brown, Roger","last_name":"Heath Brown","first_name":"Roger"}],"extern":1,"date_updated":"2021-01-12T06:57:26Z","citation":{"ieee":"T. D. Browning and R. Heath Brown, “Quadratic polynomials represented by norm forms,” Geometric and Functional Analysis, vol. 22, no. 5. Springer Basel, pp. 1124–1190, 2012.","short":"T.D. Browning, R. Heath Brown, Geometric and Functional Analysis 22 (2012) 1124–1190.","ama":"Browning TD, Heath Brown R. Quadratic polynomials represented by norm forms. Geometric and Functional Analysis. 2012;22(5):1124-1190. doi:10.1007/s00039-012-0168-5","apa":"Browning, T. D., & Heath Brown, R. (2012). Quadratic polynomials represented by norm forms. Geometric and Functional Analysis. Springer Basel. https://doi.org/10.1007/s00039-012-0168-5","mla":"Browning, Timothy D., and Roger Heath Brown. “Quadratic Polynomials Represented by Norm Forms.” Geometric and Functional Analysis, vol. 22, no. 5, Springer Basel, 2012, pp. 1124–90, doi:10.1007/s00039-012-0168-5.","ista":"Browning TD, Heath Brown R. 2012. Quadratic polynomials represented by norm forms. Geometric and Functional Analysis. 22(5), 1124–1190.","chicago":"Browning, Timothy D, and Roger Heath Brown. “Quadratic Polynomials Represented by Norm Forms.” Geometric and Functional Analysis. Springer Basel, 2012. https://doi.org/10.1007/s00039-012-0168-5."},"status":"public","type":"journal_article","_id":"243"},{"_id":"2440","type":"conference","conference":{"name":"SODA: Symposium on Discrete Algorithms"},"status":"public","citation":{"mla":"Čadek, Martin, et al. Computing All Maps into a Sphere. SIAM, 2012, pp. 1–10.","ieee":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner, “Computing all maps into a sphere,” presented at the SODA: Symposium on Discrete Algorithms, 2012, pp. 1–10.","short":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, in:, SIAM, 2012, pp. 1–10.","apa":"Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner, U. (2012). Computing all maps into a sphere (pp. 1–10). Presented at the SODA: Symposium on Discrete Algorithms, SIAM.","ama":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing all maps into a sphere. In: SIAM; 2012:1-10.","chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek, and Uli Wagner. “Computing All Maps into a Sphere,” 1–10. SIAM, 2012.","ista":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2012. Computing all maps into a sphere. SODA: Symposium on Discrete Algorithms, 1–10."},"date_updated":"2021-01-12T06:57:30Z","extern":1,"publist_id":"4466","author":[{"first_name":"Martin","full_name":"Čadek, Martin","last_name":"Čadek"},{"first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","full_name":"Marek Krcál"},{"first_name":"Jiří","last_name":"Matoušek","full_name":"Matoušek, Jiří"},{"first_name":"Francis","last_name":"Sergeraert","full_name":"Sergeraert, Francis"},{"first_name":"Lukáš","full_name":"Vokřínek, Lukáš","last_name":"Vokřínek"},{"last_name":"Wagner","orcid":"0000-0002-1494-0568","full_name":"Uli Wagner","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"title":"Computing all maps into a sphere","abstract":[{"text":"We present an algorithm for computing [X, Y], i.e., all homotopy classes of continuous maps X → Y, where X, Y are topological spaces given as finite simplicial complexes, Y is (d - 1)-connected for some d ≥ 2 (for example, Y can be the d-dimensional sphere S d), and dim X ≤ 2d - 2. These conditions on X, Y guarantee that [X, Y] has a natural structure of a finitely generated Abelian group, and the algorithm finds generators and relations for it. We combine several tools and ideas from homotopy theory (such as Postnikov systems, simplicial sets, and obstruction theory) with algorithmic tools from effective algebraic topology (objects with effective homology). We hope that a further extension of the methods developed here will yield an algorithm for computing, in some cases of interest, the ℤ 2-index, which is a quantity playing a prominent role in Borsuk-Ulam style applications of topology in combinatorics and geometry, e.g., in topological lower bounds for the chromatic number of a graph. In a certain range of dimensions, deciding the embeddability of a simplicial complex into ℝ d also amounts to a ℤ 2-index computation. This is the main motivation of our work. We believe that investigating the computational complexity of questions in homotopy theory and similar areas presents a fascinating research area, and we hope that our work may help bridge the cultural gap between algebraic topology and theoretical computer science.","lang":"eng"}],"publisher":"SIAM","quality_controlled":0,"main_file_link":[{"open_access":"0","url":"http://arxiv.org/abs/1105.6257"}],"month":"01","publication_status":"published","year":"2012","day":"01","page":"1 - 10","date_published":"2012-01-01T00:00:00Z","date_created":"2018-12-11T11:57:40Z"}]