--- _id: '8182' abstract: - lang: eng text: "Suppose that $n\\neq p^k$ and $n\\neq 2p^k$ for all $k$ and all primes $p$. We prove that for any Hausdorff compactum $X$ with a free action of the symmetric group $\\mathfrak S_n$ there exists an $\\mathfrak S_n$-equivariant map $X \\to\r\n{\\mathbb R}^n$ whose image avoids the diagonal $\\{(x,x\\dots,x)\\in {\\mathbb R}^n|x\\in {\\mathbb R}\\}$.\r\n Previously, the special cases of this statement for certain $X$ were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We\r\ntake a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of $\\mathfrak S_n$-equivariant maps from the boundary\r\n$\\partial\\Delta^{n-1}$ of $(n-1)$-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser's conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem." article_number: '1910.12628' article_processing_charge: No author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Sergey full_name: Kudrya, Sergey id: ecf01965-d252-11ea-95a5-8ada5f6c6a67 last_name: Kudrya citation: ama: Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv. apa: Avvakumov, S., & Kudrya, S. (n.d.). Vanishing of all equivariant obstructions and the mapping degree. arXiv. arXiv. chicago: Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” ArXiv. arXiv, n.d. ieee: S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” arXiv. arXiv. ista: Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv, 1910.12628. mla: Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” ArXiv, 1910.12628, arXiv. short: S. Avvakumov, S. Kudrya, ArXiv (n.d.). date_created: 2020-07-30T10:45:08Z date_published: 2019-10-28T00:00:00Z date_updated: 2023-09-07T13:12:17Z day: '28' department: - _id: UlWa external_id: arxiv: - '1910.12628' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.12628 month: '10' oa: 1 oa_version: Preprint project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: arXiv publication_status: submitted publisher: arXiv related_material: record: - id: '11446' relation: later_version status: public - id: '8156' relation: dissertation_contains status: public status: public title: Vanishing of all equivariant obstructions and the mapping degree type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '8185' abstract: - lang: eng text: "In this paper we study envy-free division problems. The classical approach to some of such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions when this map hits the center of the simplex. The mere continuity is not sufficient for such a conclusion, the usual assumption (for example, in the Knaster--Kuratowski--Mazurkiewicz and the Gale theorem) is a certain boundary condition.\r\n We follow Erel Segal-Halevi, Fr\\'ed\\'eric Meunier, and Shira Zerbib, and replace the boundary condition by another assumption, which has the economic meaning of possibility for a player to prefer an empty part in the segment\r\npartition problem. We solve the problem positively when $n$, the number of players that divide the segment, is a prime power, and we provide counterexamples for every $n$ which is not a prime power. We also provide counterexamples relevant to a wider class of fair or envy-free partition problems when $n$ is odd and not a prime power." article_number: '1907.11183' article_processing_charge: No author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv. doi:10.48550/arXiv.1907.11183 apa: Avvakumov, S., & Karasev, R. (n.d.). Envy-free division using mapping degree. arXiv. https://doi.org/10.48550/arXiv.1907.11183 chicago: Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1907.11183. ieee: S. Avvakumov and R. Karasev, “Envy-free division using mapping degree,” arXiv. . ista: Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv, 1907.11183. mla: Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, 1907.11183, doi:10.48550/arXiv.1907.11183. short: S. Avvakumov, R. Karasev, ArXiv (n.d.). date_created: 2020-07-30T10:45:51Z date_published: 2019-07-25T00:00:00Z date_updated: 2023-09-07T13:12:17Z day: '25' department: - _id: UlWa doi: 10.48550/arXiv.1907.11183 external_id: arxiv: - '1907.11183' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1907.11183 month: '07' oa: 1 oa_version: Preprint project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: arXiv publication_status: submitted related_material: link: - relation: later_version url: https://doi.org/10.1112/mtk.12059 record: - id: '8156' relation: dissertation_contains status: public status: public title: Envy-free division using mapping degree type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '7524' abstract: - lang: eng text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\\rho$ and inverse temperature $\\beta$ differs from the one of the non-interacting system by the correction term $4 \\pi \\rho^2 |\\ln a^2 \\rho|^{-1} (2 - [1 - \\beta_{\\mathrm{c}}/\\beta]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\\cdot]_+ = \\max\\{ 0, \\cdot \\}$ and $\\beta_{\\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit\r\n$a^2\\rho \\ll 1$ and if $\\beta \\rho \\gtrsim 1$." article_processing_charge: No author: - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Simon full_name: Mayer, Simon id: 30C4630A-F248-11E8-B48F-1D18A9856A87 last_name: Mayer - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:191003372. apa: Deuchert, A., Mayer, S., & Seiringer, R. (n.d.). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372. ArXiv. chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372. ArXiv, n.d. ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” arXiv:1910.03372. ArXiv. ista: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372, . mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372, ArXiv. short: A. Deuchert, S. Mayer, R. Seiringer, ArXiv:1910.03372 (n.d.). date_created: 2020-02-26T08:46:40Z date_published: 2019-10-08T00:00:00Z date_updated: 2023-09-07T13:12:41Z day: '08' department: - _id: RoSe ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.03372 month: '10' oa: 1 oa_version: Preprint page: '61' project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: arXiv:1910.03372 publication_status: draft publisher: ArXiv related_material: record: - id: '7790' relation: later_version status: public - id: '7514' relation: dissertation_contains status: public scopus_import: 1 status: public title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '6608' abstract: - lang: eng text: We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Katharina full_name: Ölsböck, Katharina id: 4D4AA390-F248-11E8-B48F-1D18A9856A87 last_name: Ölsböck orcid: 0000-0002-4672-8297 citation: ama: Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003 apa: Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003 chicago: Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003. ieee: H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019. ista: Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15. mla: Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019, pp. 1–15, doi:10.1016/j.cagd.2019.06.003. short: H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15. date_created: 2019-07-07T21:59:20Z date_published: 2019-08-01T00:00:00Z date_updated: 2023-09-07T13:15:29Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.cagd.2019.06.003 ec_funded: 1 external_id: isi: - '000485207800001' file: - access_level: open_access checksum: 7c99be505dc7533257d42eb1830cef04 content_type: application/pdf creator: kschuh date_created: 2019-07-08T15:24:26Z date_updated: 2020-07-14T12:47:34Z file_id: '6624' file_name: Elsevier_2019_Edelsbrunner.pdf file_size: 2665013 relation: main_file file_date_updated: 2020-07-14T12:47:34Z has_accepted_license: '1' intvolume: ' 73' isi: 1 language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 1-15 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Computer Aided Geometric Design publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '7460' relation: dissertation_contains status: public scopus_import: '1' status: public title: Holes and dependences in an ordered complex tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 73 year: '2019' ... --- _id: '6677' abstract: - lang: eng text: "The Fiat-Shamir heuristic transforms a public-coin interactive proof into a non-interactive argument, by replacing the verifier with a cryptographic hash function that is applied to the protocol’s transcript. Constructing hash functions for which this transformation is sound is a central and long-standing open question in cryptography.\r\n\r\nWe show that solving the END−OF−METERED−LINE problem is no easier than breaking the soundness of the Fiat-Shamir transformation when applied to the sumcheck protocol. In particular, if the transformed protocol is sound, then any hard problem in #P gives rise to a hard distribution in the class CLS, which is contained in PPAD. Our result opens up the possibility of sampling moderately-sized games for which it is hard to find a Nash equilibrium, by reducing the inversion of appropriately chosen one-way functions to #SAT.\r\n\r\nOur main technical contribution is a stateful incrementally verifiable procedure that, given a SAT instance over n variables, counts the number of satisfying assignments. This is accomplished via an exponential sequence of small steps, each computable in time poly(n). Incremental verifiability means that each intermediate state includes a sumcheck-based proof of its correctness, and the proof can be updated and verified in time poly(n)." article_processing_charge: No author: - first_name: Arka Rai full_name: Choudhuri, Arka Rai last_name: Choudhuri - first_name: Pavel full_name: Hubáček, Pavel last_name: Hubáček - first_name: Chethan full_name: Kamath Hosdurg, Chethan id: 4BD3F30E-F248-11E8-B48F-1D18A9856A87 last_name: Kamath Hosdurg - first_name: Krzysztof Z full_name: Pietrzak, Krzysztof Z id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87 last_name: Pietrzak orcid: 0000-0002-9139-1654 - first_name: Alon full_name: Rosen, Alon last_name: Rosen - first_name: Guy N. full_name: Rothblum, Guy N. last_name: Rothblum citation: ama: 'Choudhuri AR, Hubáček P, Kamath Hosdurg C, Pietrzak KZ, Rosen A, Rothblum GN. Finding a Nash equilibrium is no easier than breaking Fiat-Shamir. In: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019. ACM Press; 2019:1103-1114. doi:10.1145/3313276.3316400' apa: 'Choudhuri, A. R., Hubáček, P., Kamath Hosdurg, C., Pietrzak, K. Z., Rosen, A., & Rothblum, G. N. (2019). Finding a Nash equilibrium is no easier than breaking Fiat-Shamir. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019 (pp. 1103–1114). Phoenix, AZ, United States: ACM Press. https://doi.org/10.1145/3313276.3316400' chicago: Choudhuri, Arka Rai, Pavel Hubáček, Chethan Kamath Hosdurg, Krzysztof Z Pietrzak, Alon Rosen, and Guy N. Rothblum. “Finding a Nash Equilibrium Is No Easier than Breaking Fiat-Shamir.” In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019, 1103–14. ACM Press, 2019. https://doi.org/10.1145/3313276.3316400. ieee: A. R. Choudhuri, P. Hubáček, C. Kamath Hosdurg, K. Z. Pietrzak, A. Rosen, and G. N. Rothblum, “Finding a Nash equilibrium is no easier than breaking Fiat-Shamir,” in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019, Phoenix, AZ, United States, 2019, pp. 1103–1114. ista: 'Choudhuri AR, Hubáček P, Kamath Hosdurg C, Pietrzak KZ, Rosen A, Rothblum GN. 2019. Finding a Nash equilibrium is no easier than breaking Fiat-Shamir. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019. STOC: Symposium on Theory of Computing, 1103–1114.' mla: Choudhuri, Arka Rai, et al. “Finding a Nash Equilibrium Is No Easier than Breaking Fiat-Shamir.” Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019, ACM Press, 2019, pp. 1103–14, doi:10.1145/3313276.3316400. short: A.R. Choudhuri, P. Hubáček, C. Kamath Hosdurg, K.Z. Pietrzak, A. Rosen, G.N. Rothblum, in:, Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019, ACM Press, 2019, pp. 1103–1114. conference: end_date: 2019-06-26 location: Phoenix, AZ, United States name: 'STOC: Symposium on Theory of Computing' start_date: 2019-06-23 date_created: 2019-07-24T09:20:53Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-09-07T13:15:55Z day: '01' department: - _id: KrPi doi: 10.1145/3313276.3316400 ec_funded: 1 external_id: isi: - '000523199100100' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://eprint.iacr.org/2019/549 month: '06' oa: 1 oa_version: Preprint page: 1103-1114 project: - _id: 258AA5B2-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '682815' name: Teaching Old Crypto New Tricks publication: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019 publication_identifier: isbn: - '9781450367059' publication_status: published publisher: ACM Press quality_controlled: '1' related_material: record: - id: '7896' relation: dissertation_contains status: public scopus_import: '1' status: public title: Finding a Nash equilibrium is no easier than breaking Fiat-Shamir type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2019' ...