[{"extern":"1","date_updated":"2023-02-23T13:26:41Z","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"status":"public","article_type":"original","type":"journal_article","_id":"11446","volume":66,"related_material":{"record":[{"status":"public","id":"8182","relation":"earlier_version"}]},"issue":"3","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"intvolume":" 66","month":"10","scopus_import":"1","oa_version":"Preprint","abstract":[{"text":"Suppose that n is not a prime power and not twice a prime power. We prove that for any Hausdorff compactum X with a free action of the symmetric group Sn, there exists an Sn-equivariant map X→Rn whose image avoids the diagonal {(x,x,…,x)∈Rn∣x∈R}. 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 take 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 Sn-equivariant maps from the boundary ∂Δn−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.","lang":"eng"}],"title":"Vanishing of all equivariant obstructions and the mapping degree","external_id":{"arxiv":["1910.12628"]},"article_processing_charge":"No","author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","full_name":"Avvakumov, Sergey","last_name":"Avvakumov"},{"id":"ecf01965-d252-11ea-95a5-8ada5f6c6a67","first_name":"Sergey","last_name":"Kudrya","full_name":"Kudrya, Sergey"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Avvakumov S, Kudrya S. 2021. Vanishing of all equivariant obstructions and the mapping degree. Discrete & Computational Geometry. 66(3), 1202–1216.","chicago":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-021-00299-z.","ama":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. Discrete & Computational Geometry. 2021;66(3):1202-1216. doi:10.1007/s00454-021-00299-z","apa":"Avvakumov, S., & Kudrya, S. (2021). Vanishing of all equivariant obstructions and the mapping degree. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00299-z","ieee":"S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” Discrete & Computational Geometry, vol. 66, no. 3. Springer Nature, pp. 1202–1216, 2021.","short":"S. Avvakumov, S. Kudrya, Discrete & Computational Geometry 66 (2021) 1202–1216.","mla":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” Discrete & Computational Geometry, vol. 66, no. 3, Springer Nature, 2021, pp. 1202–16, doi:10.1007/s00454-021-00299-z."},"date_created":"2022-06-17T08:45:15Z","doi":"10.1007/s00454-021-00299-z","date_published":"2021-10-01T00:00:00Z","page":"1202-1216","publication":"Discrete & Computational Geometry","day":"01","year":"2021","publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"S. Avvakumov has received funding from the European Research Council under the European Union’s Seventh Framework Programme ERC Grant agreement ERC StG 716424–CASe. S. Kudrya was supported by the Austrian Academic Exchange Service (OeAD), ICM-2019-13577."},{"citation":{"mla":"Avvakumov, Sergey, et al. “Eliminating Higher-Multiplicity Intersections. III. Codimension 2.” Israel Journal of Mathematics, vol. 245, Springer Nature, 2021, pp. 501–534, doi:10.1007/s11856-021-2216-z.","short":"S. Avvakumov, I. Mabillard, A.B. Skopenkov, U. Wagner, Israel Journal of Mathematics 245 (2021) 501–534.","ieee":"S. Avvakumov, I. Mabillard, A. B. Skopenkov, and U. Wagner, “Eliminating higher-multiplicity intersections. III. Codimension 2,” Israel Journal of Mathematics, vol. 245. Springer Nature, pp. 501–534, 2021.","apa":"Avvakumov, S., Mabillard, I., Skopenkov, A. B., & Wagner, U. (2021). Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s11856-021-2216-z","ama":"Avvakumov S, Mabillard I, Skopenkov AB, Wagner U. Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. 2021;245:501–534. doi:10.1007/s11856-021-2216-z","chicago":"Avvakumov, Sergey, Isaac Mabillard, Arkadiy B. Skopenkov, and Uli Wagner. “Eliminating Higher-Multiplicity Intersections. III. Codimension 2.” Israel Journal of Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s11856-021-2216-z.","ista":"Avvakumov S, Mabillard I, Skopenkov AB, Wagner U. 2021. Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. 245, 501–534."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Avvakumov, Sergey","last_name":"Avvakumov","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mabillard","full_name":"Mabillard, Isaac","first_name":"Isaac","id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Skopenkov","full_name":"Skopenkov, Arkadiy B.","first_name":"Arkadiy B."},{"first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner"}],"article_processing_charge":"No","external_id":{"arxiv":["1511.03501"],"isi":["000712942100013"]},"title":"Eliminating higher-multiplicity intersections. III. Codimension 2","project":[{"grant_number":"P31312","name":"Algorithms for Embeddings and Homotopy Theory","call_identifier":"FWF","_id":"26611F5C-B435-11E9-9278-68D0E5697425"}],"isi":1,"year":"2021","day":"30","publication":"Israel Journal of Mathematics","page":"501–534 ","doi":"10.1007/s11856-021-2216-z","date_published":"2021-10-30T00:00:00Z","date_created":"2021-11-07T23:01:24Z","acknowledgement":"Research supported by the Swiss National Science Foundation (Project SNSF-PP00P2-138948), by the Austrian Science Fund (FWF Project P31312-N35), by the Russian Foundation for Basic Research (Grants No. 15-01-06302 and 19-01-00169), by a Simons-IUM Fellowship, and by the D. Zimin Dynasty Foundation Grant. We would like to thank E. Alkin, A. Klyachko, V. Krushkal, S. Melikhov, M. Tancer, P. Teichner and anonymous referees for helpful comments and discussions.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"date_updated":"2023-08-14T11:43:55Z","department":[{"_id":"UlWa"}],"_id":"10220","type":"journal_article","article_type":"original","status":"public","publication_identifier":{"eissn":["1565-8511"],"issn":["0021-2172"]},"publication_status":"published","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","id":"8183","relation":"earlier_version"},{"relation":"earlier_version","status":"public","id":"9308"}]},"volume":245,"abstract":[{"text":"We study conditions under which a finite simplicial complex K can be mapped to ℝd without higher-multiplicity intersections. An almost r-embedding is a map f: K → ℝd such that the images of any r pairwise disjoint simplices of K do not have a common point. We show that if r is not a prime power and d ≥ 2r + 1, then there is a counterexample to the topological Tverberg conjecture, i.e., there is an almost r-embedding of the (d +1)(r − 1)-simplex in ℝd. This improves on previous constructions of counterexamples (for d ≥ 3r) based on a series of papers by M. Özaydin, M. Gromov, P. Blagojević, F. Frick, G. Ziegler, and the second and fourth present authors.\r\n\r\nThe counterexamples are obtained by proving the following algebraic criterion in codimension 2: If r ≥ 3 and if K is a finite 2(r − 1)-complex, then there exists an almost r-embedding K → ℝ2r if and only if there exists a general position PL map f: K → ℝ2r such that the algebraic intersection number of the f-images of any r pairwise disjoint simplices of K is zero. This result can be restated in terms of a cohomological obstruction and extends an analogous codimension 3 criterion by the second and fourth authors. As another application, we classify ornaments f: S3 ⊔ S3 ⊔ S3 → ℝ5 up to ornament concordance.\r\n\r\nIt follows from work of M. Freedman, V. Krushkal and P. Teichner that the analogous criterion for r = 2 is false. We prove a lemma on singular higher-dimensional Borromean rings, yielding an elementary proof of the counterexample.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1511.03501","open_access":"1"}],"month":"10","intvolume":" 245"},{"file_date_updated":"2020-07-14T12:48:06Z","department":[{"_id":"UlWa"}],"date_updated":"2021-01-12T08:16:23Z","ddc":["510"],"type":"conference","conference":{"location":"Zürich, Switzerland","end_date":"2020-06-26","start_date":"2020-06-22","name":"SoCG: Symposium on Computational Geometry"},"tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"status":"public","_id":"7991","volume":164,"license":"https://creativecommons.org/licenses/by/3.0/","publication_identifier":{"issn":["18688969"],"isbn":["9783959771436"]},"publication_status":"published","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"8007","checksum":"6872df6549142f709fb6354a1b2f2c06","creator":"dernst","file_size":575896,"date_updated":"2020-07-14T12:48:06Z","file_name":"2020_LIPIcsSoCG_Avvakumov.pdf","date_created":"2020-06-23T11:13:49Z"}],"language":[{"iso":"eng"}],"alternative_title":["LIPIcs"],"scopus_import":"1","month":"06","intvolume":" 164","abstract":[{"lang":"eng","text":"We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a set P⊂ ℝ² of point obstacles, and evolves in discrete steps, where each step consists of (1) taking shortcuts around the obstacles, and (2) reducing the curve to its shortest homotopic equivalent. We find experimentally that, if the initial curve is held fixed and P is chosen to be either a very fine regular grid or a uniformly random point set, then HCS behaves at the limit like the affine curve-shortening flow (ACSF). This connection between HCS and ACSF generalizes the link between \"grid peeling\" and the ACSF observed by Eppstein et al. (2017), which applied only to convex curves, and which was studied only for regular grids. We prove that HCS satisfies some properties analogous to those of ACSF: HCS is invariant under affine transformations, preserves convexity, and does not increase the total absolute curvature. Furthermore, the number of self-intersections of a curve, or intersections between two curves (appropriately defined), does not increase. Finally, if the initial curve is simple, then the number of inflection points (appropriately defined) does not increase."}],"oa_version":"Published Version","author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","last_name":"Avvakumov","full_name":"Avvakumov, Sergey"},{"first_name":"Gabriel","last_name":"Nivasch","full_name":"Nivasch, Gabriel"}],"article_processing_charge":"No","external_id":{"arxiv":["1909.00263"]},"title":"Homotopic curve shortening and the affine curve-shortening flow","citation":{"mla":"Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and the Affine Curve-Shortening Flow.” 36th International Symposium on Computational Geometry, vol. 164, 12:1-12:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.12.","ieee":"S. Avvakumov and G. Nivasch, “Homotopic curve shortening and the affine curve-shortening flow,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","short":"S. Avvakumov, G. Nivasch, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ama":"Avvakumov S, Nivasch G. Homotopic curve shortening and the affine curve-shortening flow. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.12","apa":"Avvakumov, S., & Nivasch, G. (2020). Homotopic curve shortening and the affine curve-shortening flow. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.12","chicago":"Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and the Affine Curve-Shortening Flow.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.12.","ista":"Avvakumov S, Nivasch G. 2020. Homotopic curve shortening and the affine curve-shortening flow. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 12:1-12:15."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"FWF","_id":"26611F5C-B435-11E9-9278-68D0E5697425","name":"Algorithms for Embeddings and Homotopy Theory","grant_number":"P31312"}],"article_number":"12:1 - 12:15","doi":"10.4230/LIPIcs.SoCG.2020.12","date_published":"2020-06-01T00:00:00Z","date_created":"2020-06-22T09:14:19Z","has_accepted_license":"1","year":"2020","day":"01","publication":"36th International Symposium on Computational Geometry","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1},{"_id":"9308","status":"public","article_type":"original","type":"journal_article","date_updated":"2023-08-14T11:43:54Z","department":[{"_id":"UlWa"}],"oa_version":"Preprint","month":"12","intvolume":" 75","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1511.03501","open_access":"1"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0036-0279"]},"publication_status":"published","issue":"6","related_material":{"record":[{"status":"public","id":"8183","relation":"earlier_version"},{"id":"10220","status":"public","relation":"later_version"}]},"volume":75,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Avvakumov S, Wagner U, Mabillard I, Skopenkov AB. 2020. Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. 75(6), 1156–1158.","chicago":"Avvakumov, Sergey, Uli Wagner, Isaac Mabillard, and A. B. Skopenkov. “Eliminating Higher-Multiplicity Intersections, III. Codimension 2.” Russian Mathematical Surveys. IOP Publishing, 2020. https://doi.org/10.1070/RM9943.","apa":"Avvakumov, S., Wagner, U., Mabillard, I., & Skopenkov, A. B. (2020). Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. IOP Publishing. https://doi.org/10.1070/RM9943","ama":"Avvakumov S, Wagner U, Mabillard I, Skopenkov AB. Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. 2020;75(6):1156-1158. doi:10.1070/RM9943","short":"S. Avvakumov, U. Wagner, I. Mabillard, A.B. Skopenkov, Russian Mathematical Surveys 75 (2020) 1156–1158.","ieee":"S. Avvakumov, U. Wagner, I. Mabillard, and A. B. Skopenkov, “Eliminating higher-multiplicity intersections, III. Codimension 2,” Russian Mathematical Surveys, vol. 75, no. 6. IOP Publishing, pp. 1156–1158, 2020.","mla":"Avvakumov, Sergey, et al. “Eliminating Higher-Multiplicity Intersections, III. Codimension 2.” Russian Mathematical Surveys, vol. 75, no. 6, IOP Publishing, 2020, pp. 1156–58, doi:10.1070/RM9943."},"title":"Eliminating higher-multiplicity intersections, III. Codimension 2","author":[{"first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey","last_name":"Avvakumov"},{"first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","last_name":"Wagner"},{"full_name":"Mabillard, Isaac","last_name":"Mabillard","id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87","first_name":"Isaac"},{"first_name":"A. B.","last_name":"Skopenkov","full_name":"Skopenkov, A. B."}],"external_id":{"arxiv":["1511.03501"],"isi":["000625983100001"]},"article_processing_charge":"No","acknowledgement":"This research was carried out with the support of the Russian Foundation for Basic Research(grant no. 19-01-00169)","quality_controlled":"1","publisher":"IOP Publishing","oa":1,"day":"01","publication":"Russian Mathematical Surveys","isi":1,"year":"2020","doi":"10.1070/RM9943","date_published":"2020-12-01T00:00:00Z","date_created":"2021-04-04T22:01:22Z","page":"1156-1158"},{"oa":1,"publisher":"Institute of Science and Technology Austria","day":"24","year":"2020","has_accepted_license":"1","date_created":"2020-07-23T09:51:29Z","doi":"10.15479/AT:ISTA:8156","date_published":"2020-07-24T00:00:00Z","page":"119","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Avvakumov S. 2020. Topological methods in geometry and discrete mathematics. Institute of Science and Technology Austria.","chicago":"Avvakumov, Sergey. “Topological Methods in Geometry and Discrete Mathematics.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:8156.","ieee":"S. Avvakumov, “Topological methods in geometry and discrete mathematics,” Institute of Science and Technology Austria, 2020.","short":"S. Avvakumov, Topological Methods in Geometry and Discrete Mathematics, Institute of Science and Technology Austria, 2020.","ama":"Avvakumov S. Topological methods in geometry and discrete mathematics. 2020. doi:10.15479/AT:ISTA:8156","apa":"Avvakumov, S. (2020). Topological methods in geometry and discrete mathematics. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:8156","mla":"Avvakumov, Sergey. Topological Methods in Geometry and Discrete Mathematics. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:8156."},"title":"Topological methods in geometry and discrete mathematics","article_processing_charge":"No","author":[{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We present solutions to several problems originating from geometry and discrete mathematics: existence of equipartitions, maps without Tverberg multiple points, and inscribing quadrilaterals. Equivariant obstruction theory is the natural topological approach to these type of questions. However, for the specific problems we consider it had yielded only partial or no results. We get our results by complementing equivariant obstruction theory with other techniques from topology and geometry."}],"month":"07","alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"file":[{"content_type":"application/zip","access_level":"closed","relation":"source_file","file_id":"8178","date_updated":"2020-07-27T12:44:51Z","file_size":1061740,"creator":"savvakum","date_created":"2020-07-27T12:44:51Z","file_name":"source.zip"},{"date_created":"2020-07-27T12:46:53Z","file_name":"thesis_pdfa.pdf","date_updated":"2020-07-27T12:46:53Z","file_size":1336501,"creator":"savvakum","file_id":"8179","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"related_material":{"record":[{"id":"8182","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"8183"},{"id":"8185","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"8184"},{"relation":"part_of_dissertation","id":"6355","status":"public"},{"status":"public","id":"75","relation":"part_of_dissertation"}]},"_id":"8156","status":"public","type":"dissertation","ddc":["514"],"date_updated":"2023-12-18T10:51:01Z","supervisor":[{"last_name":"Wagner","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"file_date_updated":"2020-07-27T12:46:53Z","department":[{"_id":"UlWa"}]},{"quality_controlled":"1","publisher":"Public Library of Science","oa":1,"doi":"10.1371/journal.pgen.1008079","date_published":"2019-04-10T00:00:00Z","date_created":"2019-05-13T07:58:38Z","isi":1,"has_accepted_license":"1","year":"2019","day":"10","publication":"PLoS Genetics","project":[{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"article_number":"e1008079","author":[{"first_name":"Victoria","id":"3184041C-F248-11E8-B48F-1D18A9856A87","last_name":"Pokusaeva","full_name":"Pokusaeva, Victoria","orcid":"0000-0001-7660-444X"},{"full_name":"Usmanova, Dinara R.","last_name":"Usmanova","first_name":"Dinara R."},{"full_name":"Putintseva, Ekaterina V.","last_name":"Putintseva","first_name":"Ekaterina V."},{"full_name":"Espinar, Lorena","last_name":"Espinar","first_name":"Lorena"},{"first_name":"Karen","id":"39A7BF80-F248-11E8-B48F-1D18A9856A87","last_name":"Sarkisyan","orcid":"0000-0002-5375-6341","full_name":"Sarkisyan, Karen"},{"first_name":"Alexander S.","full_name":"Mishin, Alexander S.","last_name":"Mishin"},{"last_name":"Bogatyreva","full_name":"Bogatyreva, Natalya S.","first_name":"Natalya S."},{"last_name":"Ivankov","full_name":"Ivankov, Dmitry","id":"49FF1036-F248-11E8-B48F-1D18A9856A87","first_name":"Dmitry"},{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Avvakumov, Sergey","last_name":"Avvakumov","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Povolotskaya, Inna S.","last_name":"Povolotskaya","first_name":"Inna S."},{"first_name":"Guillaume J.","full_name":"Filion, Guillaume J.","last_name":"Filion"},{"first_name":"Lucas B.","last_name":"Carey","full_name":"Carey, Lucas B."},{"id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","first_name":"Fyodor","full_name":"Kondrashov, Fyodor","orcid":"0000-0001-8243-4694","last_name":"Kondrashov"}],"external_id":{"isi":["000466866000029"]},"article_processing_charge":"No","title":"An experimental assay of the interactions of amino acids from orthologous sequences shaping a complex fitness landscape","citation":{"ista":"Pokusaeva V, Usmanova DR, Putintseva EV, Espinar L, Sarkisyan K, Mishin AS, Bogatyreva NS, Ivankov D, Akopyan A, Avvakumov S, Povolotskaya IS, Filion GJ, Carey LB, Kondrashov F. 2019. An experimental assay of the interactions of amino acids from orthologous sequences shaping a complex fitness landscape. PLoS Genetics. 15(4), e1008079.","chicago":"Pokusaeva, Victoria, Dinara R. Usmanova, Ekaterina V. Putintseva, Lorena Espinar, Karen Sarkisyan, Alexander S. Mishin, Natalya S. Bogatyreva, et al. “An Experimental Assay of the Interactions of Amino Acids from Orthologous Sequences Shaping a Complex Fitness Landscape.” PLoS Genetics. Public Library of Science, 2019. https://doi.org/10.1371/journal.pgen.1008079.","short":"V. Pokusaeva, D.R. Usmanova, E.V. Putintseva, L. Espinar, K. Sarkisyan, A.S. Mishin, N.S. Bogatyreva, D. Ivankov, A. Akopyan, S. Avvakumov, I.S. Povolotskaya, G.J. Filion, L.B. Carey, F. Kondrashov, PLoS Genetics 15 (2019).","ieee":"V. Pokusaeva et al., “An experimental assay of the interactions of amino acids from orthologous sequences shaping a complex fitness landscape,” PLoS Genetics, vol. 15, no. 4. Public Library of Science, 2019.","ama":"Pokusaeva V, Usmanova DR, Putintseva EV, et al. An experimental assay of the interactions of amino acids from orthologous sequences shaping a complex fitness landscape. PLoS Genetics. 2019;15(4). doi:10.1371/journal.pgen.1008079","apa":"Pokusaeva, V., Usmanova, D. R., Putintseva, E. V., Espinar, L., Sarkisyan, K., Mishin, A. S., … Kondrashov, F. (2019). An experimental assay of the interactions of amino acids from orthologous sequences shaping a complex fitness landscape. PLoS Genetics. Public Library of Science. https://doi.org/10.1371/journal.pgen.1008079","mla":"Pokusaeva, Victoria, et al. “An Experimental Assay of the Interactions of Amino Acids from Orthologous Sequences Shaping a Complex Fitness Landscape.” PLoS Genetics, vol. 15, no. 4, e1008079, Public Library of Science, 2019, doi:10.1371/journal.pgen.1008079."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","month":"04","intvolume":" 15","abstract":[{"lang":"eng","text":"Characterizing the fitness landscape, a representation of fitness for a large set of genotypes, is key to understanding how genetic information is interpreted to create functional organisms. Here we determined the evolutionarily-relevant segment of the fitness landscape of His3, a gene coding for an enzyme in the histidine synthesis pathway, focusing on combinations of amino acid states found at orthologous sites of extant species. Just 15% of amino acids found in yeast His3 orthologues were always neutral while the impact on fitness of the remaining 85% depended on the genetic background. Furthermore, at 67% of sites, amino acid replacements were under sign epistasis, having both strongly positive and negative effect in different genetic backgrounds. 46% of sites were under reciprocal sign epistasis. The fitness impact of amino acid replacements was influenced by only a few genetic backgrounds but involved interaction of multiple sites, shaping a rugged fitness landscape in which many of the shortest paths between highly fit genotypes are inaccessible."}],"oa_version":"Published Version","issue":"4","related_material":{"record":[{"status":"public","id":"9789","relation":"research_data"},{"relation":"research_data","id":"9790","status":"public"},{"status":"public","id":"9797","relation":"research_data"}]},"volume":15,"ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","publication_identifier":{"eissn":["15537404"]},"publication_status":"published","file":[{"creator":"dernst","file_size":3726017,"date_updated":"2020-07-14T12:47:30Z","file_name":"2019_PLOSGenetics_Pokusaeva.pdf","date_created":"2019-05-14T08:26:08Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","checksum":"cf3889c8a8a16053dacf9c3776cbe217","file_id":"6445"}],"language":[{"iso":"eng"}],"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","_id":"6419","department":[{"_id":"FyKo"}],"file_date_updated":"2020-07-14T12:47:30Z","date_updated":"2023-08-25T10:30:37Z","ddc":["570"]},{"type":"research_data_reference","status":"public","_id":"9790","author":[{"orcid":"0000-0001-7660-444X","full_name":"Pokusaeva, Victoria","last_name":"Pokusaeva","id":"3184041C-F248-11E8-B48F-1D18A9856A87","first_name":"Victoria"},{"first_name":"Dinara R.","last_name":"Usmanova","full_name":"Usmanova, Dinara R."},{"full_name":"Putintseva, Ekaterina V.","last_name":"Putintseva","first_name":"Ekaterina V."},{"first_name":"Lorena","full_name":"Espinar, Lorena","last_name":"Espinar"},{"full_name":"Sarkisyan, Karen","orcid":"0000-0002-5375-6341","last_name":"Sarkisyan","first_name":"Karen","id":"39A7BF80-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mishin, Alexander S.","last_name":"Mishin","first_name":"Alexander S."},{"first_name":"Natalya S.","full_name":"Bogatyreva, Natalya S.","last_name":"Bogatyreva"},{"last_name":"Ivankov","full_name":"Ivankov, Dmitry","first_name":"Dmitry","id":"49FF1036-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Avvakumov, Sergey","last_name":"Avvakumov","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Inna S.","last_name":"Povolotskaya","full_name":"Povolotskaya, Inna S."},{"first_name":"Guillaume J.","full_name":"Filion, Guillaume J.","last_name":"Filion"},{"full_name":"Carey, Lucas B.","last_name":"Carey","first_name":"Lucas B."},{"id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","first_name":"Fyodor","last_name":"Kondrashov","orcid":"0000-0001-8243-4694","full_name":"Kondrashov, Fyodor"}],"article_processing_charge":"No","department":[{"_id":"FyKo"}],"title":"A statistical summary of segment libraries and sequencing results","date_updated":"2023-08-25T10:30:36Z","citation":{"mla":"Pokusaeva, Victoria, et al. A Statistical Summary of Segment Libraries and Sequencing Results. Public Library of Science, 2019, doi:10.1371/journal.pgen.1008079.s011.","apa":"Pokusaeva, V., Usmanova, D. R., Putintseva, E. V., Espinar, L., Sarkisyan, K., Mishin, A. S., … Kondrashov, F. (2019). A statistical summary of segment libraries and sequencing results. Public Library of Science. https://doi.org/10.1371/journal.pgen.1008079.s011","ama":"Pokusaeva V, Usmanova DR, Putintseva EV, et al. A statistical summary of segment libraries and sequencing results. 2019. doi:10.1371/journal.pgen.1008079.s011","short":"V. Pokusaeva, D.R. Usmanova, E.V. Putintseva, L. Espinar, K. Sarkisyan, A.S. Mishin, N.S. Bogatyreva, D. Ivankov, A. Akopyan, S. Avvakumov, I.S. Povolotskaya, G.J. Filion, L.B. Carey, F. Kondrashov, (2019).","ieee":"V. Pokusaeva et al., “A statistical summary of segment libraries and sequencing results.” Public Library of Science, 2019.","chicago":"Pokusaeva, Victoria, Dinara R. Usmanova, Ekaterina V. Putintseva, Lorena Espinar, Karen Sarkisyan, Alexander S. Mishin, Natalya S. Bogatyreva, et al. “A Statistical Summary of Segment Libraries and Sequencing Results.” Public Library of Science, 2019. https://doi.org/10.1371/journal.pgen.1008079.s011.","ista":"Pokusaeva V, Usmanova DR, Putintseva EV, Espinar L, Sarkisyan K, Mishin AS, Bogatyreva NS, Ivankov D, Akopyan A, Avvakumov S, Povolotskaya IS, Filion GJ, Carey LB, Kondrashov F. 2019. A statistical summary of segment libraries and sequencing results, Public Library of Science, 10.1371/journal.pgen.1008079.s011."},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","publisher":"Public Library of Science","month":"04","oa_version":"Published Version","related_material":{"record":[{"relation":"used_in_publication","status":"public","id":"6419"}]},"doi":"10.1371/journal.pgen.1008079.s011","date_published":"2019-04-10T00:00:00Z","date_created":"2021-08-06T08:50:15Z","year":"2019","day":"10"},{"type":"research_data_reference","status":"public","_id":"9789","article_processing_charge":"No","author":[{"last_name":"Pokusaeva","orcid":"0000-0001-7660-444X","full_name":"Pokusaeva, Victoria","first_name":"Victoria","id":"3184041C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Usmanova, Dinara R.","last_name":"Usmanova","first_name":"Dinara R."},{"first_name":"Ekaterina V.","last_name":"Putintseva","full_name":"Putintseva, Ekaterina V."},{"first_name":"Lorena","last_name":"Espinar","full_name":"Espinar, Lorena"},{"orcid":"0000-0002-5375-6341","full_name":"Sarkisyan, Karen","last_name":"Sarkisyan","id":"39A7BF80-F248-11E8-B48F-1D18A9856A87","first_name":"Karen"},{"first_name":"Alexander S.","full_name":"Mishin, Alexander S.","last_name":"Mishin"},{"first_name":"Natalya S.","last_name":"Bogatyreva","full_name":"Bogatyreva, Natalya S."},{"full_name":"Ivankov, Dmitry","last_name":"Ivankov","id":"49FF1036-F248-11E8-B48F-1D18A9856A87","first_name":"Dmitry"},{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Povolotskaya","full_name":"Povolotskaya, Inna S.","first_name":"Inna S."},{"first_name":"Guillaume J.","full_name":"Filion, Guillaume J.","last_name":"Filion"},{"first_name":"Lucas B.","full_name":"Carey, Lucas B.","last_name":"Carey"},{"last_name":"Kondrashov","orcid":"0000-0001-8243-4694","full_name":"Kondrashov, Fyodor","first_name":"Fyodor","id":"44FDEF62-F248-11E8-B48F-1D18A9856A87"}],"title":"Multiple alignment of His3 orthologues","department":[{"_id":"FyKo"}],"date_updated":"2023-08-25T10:30:36Z","citation":{"short":"V. Pokusaeva, D.R. Usmanova, E.V. Putintseva, L. Espinar, K. Sarkisyan, A.S. Mishin, N.S. Bogatyreva, D. Ivankov, A. Akopyan, S. Avvakumov, I.S. Povolotskaya, G.J. Filion, L.B. Carey, F. Kondrashov, (2019).","ieee":"V. Pokusaeva et al., “Multiple alignment of His3 orthologues.” Public Library of Science, 2019.","ama":"Pokusaeva V, Usmanova DR, Putintseva EV, et al. Multiple alignment of His3 orthologues. 2019. doi:10.1371/journal.pgen.1008079.s010","apa":"Pokusaeva, V., Usmanova, D. R., Putintseva, E. V., Espinar, L., Sarkisyan, K., Mishin, A. S., … Kondrashov, F. (2019). Multiple alignment of His3 orthologues. Public Library of Science. https://doi.org/10.1371/journal.pgen.1008079.s010","mla":"Pokusaeva, Victoria, et al. Multiple Alignment of His3 Orthologues. Public Library of Science, 2019, doi:10.1371/journal.pgen.1008079.s010.","ista":"Pokusaeva V, Usmanova DR, Putintseva EV, Espinar L, Sarkisyan K, Mishin AS, Bogatyreva NS, Ivankov D, Akopyan A, Avvakumov S, Povolotskaya IS, Filion GJ, Carey LB, Kondrashov F. 2019. Multiple alignment of His3 orthologues, Public Library of Science, 10.1371/journal.pgen.1008079.s010.","chicago":"Pokusaeva, Victoria, Dinara R. Usmanova, Ekaterina V. Putintseva, Lorena Espinar, Karen Sarkisyan, Alexander S. Mishin, Natalya S. Bogatyreva, et al. “Multiple Alignment of His3 Orthologues.” Public Library of Science, 2019. https://doi.org/10.1371/journal.pgen.1008079.s010."},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","publisher":"Public Library of Science","month":"04","oa_version":"Published Version","date_created":"2021-08-06T08:38:50Z","related_material":{"record":[{"id":"6419","status":"public","relation":"used_in_publication"}]},"date_published":"2019-04-10T00:00:00Z","doi":"10.1371/journal.pgen.1008079.s010","year":"2019","day":"10"},{"article_number":"1910.12628","_id":"8182","project":[{"call_identifier":"FWF","_id":"26611F5C-B435-11E9-9278-68D0E5697425","grant_number":"P31312","name":"Algorithms for Embeddings and Homotopy Theory"}],"status":"public","type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.).","ieee":"S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” arXiv. arXiv.","apa":"Avvakumov, S., & Kudrya, S. (n.d.). Vanishing of all equivariant obstructions and the mapping degree. arXiv. arXiv.","ama":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv.","chicago":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” ArXiv. arXiv, n.d.","ista":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv, 1910.12628."},"date_updated":"2023-09-07T13:12:17Z","title":"Vanishing of all equivariant obstructions and the mapping degree","department":[{"_id":"UlWa"}],"author":[{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey"},{"last_name":"Kudrya","full_name":"Kudrya, Sergey","first_name":"Sergey","id":"ecf01965-d252-11ea-95a5-8ada5f6c6a67"}],"external_id":{"arxiv":["1910.12628"]},"article_processing_charge":"No","oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"month":"10","publisher":"arXiv","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.12628"}],"day":"28","publication":"arXiv","language":[{"iso":"eng"}],"year":"2019","publication_status":"submitted","related_material":{"record":[{"relation":"later_version","id":"11446","status":"public"},{"relation":"dissertation_contains","id":"8156","status":"public"}]},"date_published":"2019-10-28T00:00:00Z","date_created":"2020-07-30T10:45:08Z"},{"type":"preprint","status":"public","project":[{"call_identifier":"FWF","_id":"26611F5C-B435-11E9-9278-68D0E5697425","grant_number":"P31312","name":"Algorithms for Embeddings and Homotopy Theory"}],"_id":"8185","article_number":"1907.11183","author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","last_name":"Avvakumov","full_name":"Avvakumov, Sergey"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"external_id":{"arxiv":["1907.11183"]},"article_processing_charge":"No","department":[{"_id":"UlWa"}],"title":"Envy-free division using mapping degree","date_updated":"2023-09-07T13:12:17Z","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","short":"S. Avvakumov, R. Karasev, ArXiv (n.d.).","ieee":"S. Avvakumov and R. Karasev, “Envy-free division using mapping degree,” arXiv. .","mla":"Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, 1907.11183, doi:10.48550/arXiv.1907.11183.","ista":"Avvakumov S, Karasev R. Envy-free division using mapping degree. 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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/1907.11183","open_access":"1"}],"oa":1,"month":"07","abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","related_material":{"link":[{"relation":"later_version","url":"https://doi.org/10.1112/mtk.12059"}],"record":[{"relation":"dissertation_contains","id":"8156","status":"public"}]},"date_published":"2019-07-25T00:00:00Z","doi":"10.48550/arXiv.1907.11183","date_created":"2020-07-30T10:45:51Z","year":"2019","publication_status":"submitted","day":"25","language":[{"iso":"eng"}],"publication":"arXiv"},{"_id":"8184","article_number":"1908.08731","type":"preprint","project":[{"name":"Algorithms for Embeddings and Homotopy Theory","grant_number":"P31312","call_identifier":"FWF","_id":"26611F5C-B435-11E9-9278-68D0E5697425"}],"status":"public","citation":{"ista":"Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. arXiv, 1908.08731.","chicago":"Avvakumov, Sergey, R. Karasev, and A. Skopenkov. “Stronger Counterexamples to the Topological Tverberg Conjecture.” ArXiv. arXiv, n.d.","short":"S. Avvakumov, R. Karasev, A. Skopenkov, ArXiv (n.d.).","ieee":"S. Avvakumov, R. Karasev, and A. Skopenkov, “Stronger counterexamples to the topological Tverberg conjecture,” arXiv. arXiv.","apa":"Avvakumov, S., Karasev, R., & Skopenkov, A. (n.d.). Stronger counterexamples to the topological Tverberg conjecture. arXiv. arXiv.","ama":"Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. arXiv.","mla":"Avvakumov, Sergey, et al. “Stronger Counterexamples to the Topological Tverberg Conjecture.” ArXiv, 1908.08731, arXiv."},"date_updated":"2023-09-08T11:20:02Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"arxiv":["1908.08731"],"isi":["000986519600004"]},"article_processing_charge":"No","author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","last_name":"Avvakumov","full_name":"Avvakumov, Sergey"},{"full_name":"Karasev, R.","last_name":"Karasev","first_name":"R."},{"full_name":"Skopenkov, A.","last_name":"Skopenkov","first_name":"A."}],"title":"Stronger counterexamples to the topological Tverberg conjecture","department":[{"_id":"UlWa"}],"abstract":[{"text":"Denote by ∆N the N-dimensional simplex. A map f : ∆N → Rd is an almost r-embedding if fσ1∩. . .∩fσr = ∅ whenever σ1, . . . , σr are pairwise disjoint faces. A counterexample to the topological Tverberg conjecture asserts that if r is not a prime power and d ≥ 2r + 1, then there is an almost r-embedding ∆(d+1)(r−1) → Rd. This was improved by Blagojevi´c–Frick–Ziegler using a simple construction of higher-dimensional counterexamples by taking k-fold join power of lower-dimensional ones. We improve this further (for d large compared to r): If r is not a prime power and N := (d+ 1)r−r l\r\nd + 2 r + 1 m−2, then there is an almost r-embedding ∆N → Rd. For the r-fold van Kampen–Flores conjecture we also produce counterexamples which are stronger than previously known. Our proof is based on generalizations of the Mabillard–Wagner theorem on construction of almost r-embeddings from equivariant maps, and of the Ozaydin theorem on existence of equivariant maps. ","lang":"eng"}],"acknowledgement":"We would like to thank F. Frick for helpful discussions","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1908.08731","open_access":"1"}],"oa":1,"publisher":"arXiv","month":"08","publication_status":"submitted","year":"2019","isi":1,"language":[{"iso":"eng"}],"publication":"arXiv","day":"23","date_created":"2020-07-30T10:45:34Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"8156"}]},"date_published":"2019-08-23T00:00:00Z"},{"publication":"Forum of Mathematics, Sigma","day":"31","year":"2018","has_accepted_license":"1","isi":1,"date_created":"2019-04-30T06:09:57Z","doi":"10.1017/fms.2018.7","date_published":"2018-05-31T00:00:00Z","oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.","apa":"Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018."},"title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","article_processing_charge":"No","external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey"}],"article_number":"e7","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"language":[{"iso":"eng"}],"file":[{"date_created":"2019-04-30T06:14:58Z","file_name":"2018_ForumMahtematics_Akopyan.pdf","date_updated":"2020-07-14T12:47:28Z","file_size":249246,"creator":"dernst","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","file_id":"6356","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","publication_identifier":{"issn":["2050-5094"]},"ec_funded":1,"related_material":{"record":[{"id":"8156","status":"public","relation":"dissertation_contains"}]},"volume":6,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle."}],"intvolume":" 6","month":"05","ddc":["510"],"date_updated":"2023-09-19T14:50:12Z","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:28Z","_id":"6355","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"},{"oa_version":"Preprint","abstract":[{"text":"We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization.","lang":"eng"}],"month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.03057"}],"oa":1,"publisher":"arXiv","language":[{"iso":"eng"}],"day":"13","publication_status":"published","year":"2018","date_created":"2018-12-11T11:44:30Z","ec_funded":1,"date_published":"2018-09-13T00:00:00Z","related_material":{"record":[{"status":"public","id":"8156","relation":"dissertation_contains"}]},"doi":"10.48550/arXiv.1804.03057","article_number":"1804.03057","_id":"75","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"status":"public","type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","apa":"Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:10.48550/arXiv.1804.03057","mla":"Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057.","chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057."},"date_updated":"2023-12-18T10:51:02Z","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"title":"Convex fair partitions into arbitrary number of pieces","external_id":{"arxiv":["1804.03057"]},"article_processing_charge":"No","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Avvakumov, Sergey","last_name":"Avvakumov","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}]},{"citation":{"ista":"Avvakumov S. 2016. The classification of certain linked 3-manifolds in 6-space. Moscow Mathematical Journal. 16(1), 1–25.","chicago":"Avvakumov, Sergey. “The Classification of Certain Linked 3-Manifolds in 6-Space.” Moscow Mathematical Journal. Independent University of Moscow, 2016. https://doi.org/10.17323/1609-4514-2016-16-1-1-25.","short":"S. Avvakumov, Moscow Mathematical Journal 16 (2016) 1–25.","ieee":"S. Avvakumov, “The classification of certain linked 3-manifolds in 6-space,” Moscow Mathematical Journal, vol. 16, no. 1. Independent University of Moscow, pp. 1–25, 2016.","apa":"Avvakumov, S. (2016). The classification of certain linked 3-manifolds in 6-space. Moscow Mathematical Journal. Independent University of Moscow. https://doi.org/10.17323/1609-4514-2016-16-1-1-25","ama":"Avvakumov S. The classification of certain linked 3-manifolds in 6-space. Moscow Mathematical Journal. 2016;16(1):1-25. doi:10.17323/1609-4514-2016-16-1-1-25","mla":"Avvakumov, Sergey. “The Classification of Certain Linked 3-Manifolds in 6-Space.” Moscow Mathematical Journal, vol. 16, no. 1, Independent University of Moscow, 2016, pp. 1–25, doi:10.17323/1609-4514-2016-16-1-1-25."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["1408.3918"]},"author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Serhii","last_name":"Avvakumov","full_name":"Avvakumov, Serhii"}],"publist_id":"5652","title":"The classification of certain linked 3-manifolds in 6-space","year":"2016","publication":"Moscow Mathematical Journal","day":"01","page":"1 - 25","date_created":"2018-12-11T11:52:30Z","doi":"10.17323/1609-4514-2016-16-1-1-25","date_published":"2016-01-01T00:00:00Z","acknowledgement":"I thank A. Skopenkov for telling me about the problem and for his useful remarks. I also thank A. Sossinsky,\r\nA. Zhubr, M. Skopenkov, P. Akhmetiev, and an anonymous referee for their feedback. Author was partially\r\nsupported by Dobrushin fellowship, 2013, and by RFBR grant 15-01-06302.","oa":1,"publisher":"Independent University of Moscow","quality_controlled":"1","date_updated":"2022-02-25T10:15:57Z","department":[{"_id":"UlWa"}],"_id":"1522","article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"eissn":["1609-4514"]},"language":[{"iso":"eng"}],"issue":"1","volume":16,"abstract":[{"lang":"eng","text":"We classify smooth Brunnian (i.e., unknotted on both components) embeddings (S2 × S1) ⊔ S3 → ℝ6. Any Brunnian embedding (S2 × S1) ⊔ S3 → ℝ6 is isotopic to an explicitly constructed embedding fk,m,n for some integers k, m, n such that m ≡ n (mod 2). Two embeddings fk,m,n and fk′ ,m′,n′ are isotopic if and only if k = k′, m ≡ m′ (mod 2k) and n ≡ n′ (mod 2k). We use Haefliger’s classification of embeddings S3 ⊔ S3 → ℝ6 in our proof. The relation between the embeddings (S2 × S1) ⊔ S3 → ℝ6 and S3 ⊔ S3 → ℝ6 is not trivial, however. For example, we show that there exist embeddings f: (S2 ×S1) ⊔ S3 → ℝ6 and g, g′ : S3 ⊔ S3 → ℝ6 such that the componentwise embedded connected sum f # g is isotopic to f # g′ but g is not isotopic to g′."}],"oa_version":"Preprint","main_file_link":[{"url":"http://arxiv.org/abs/1408.3918","open_access":"1"}],"scopus_import":"1","intvolume":" 16","month":"01"},{"date_published":"2015-11-15T00:00:00Z","related_material":{"record":[{"relation":"later_version","id":"9308","status":"public"},{"id":"10220","status":"public","relation":"later_version"},{"relation":"dissertation_contains","status":"public","id":"8156"}]},"date_created":"2020-07-30T10:45:19Z","day":"15","language":[{"iso":"eng"}],"publication":"arXiv","year":"2015","publication_status":"submitted","month":"11","main_file_link":[{"url":"https://arxiv.org/abs/1511.03501","open_access":"1"}],"oa":1,"oa_version":"Preprint","acknowledgement":"We would like to thank A. Klyachko, V. Krushkal, S. Melikhov, M. Tancer, P. Teichner and anonymous referees for helpful discussions.","abstract":[{"lang":"eng","text":"We study conditions under which a finite simplicial complex $K$ can be mapped to $\\mathbb R^d$ without higher-multiplicity intersections. An almost $r$-embedding is a map $f: K\\to \\mathbb R^d$ such that the images of any $r$\r\npairwise disjoint simplices of $K$ do not have a common point. We show that if $r$ is not a prime power and $d\\geq 2r+1$, then there is a counterexample to the topological Tverberg conjecture, i.e., there is an almost $r$-embedding of\r\nthe $(d+1)(r-1)$-simplex in $\\mathbb R^d$. This improves on previous constructions of counterexamples (for $d\\geq 3r$) based on a series of papers by M. \\\"Ozaydin, M. Gromov, P. Blagojevi\\'c, F. Frick, G. Ziegler, and the second and fourth present authors. The counterexamples are obtained by proving the following algebraic criterion in codimension 2: If $r\\ge3$ and if $K$ is a finite $2(r-1)$-complex then there exists an almost $r$-embedding $K\\to \\mathbb R^{2r}$ if and only if there exists a general position PL map $f:K\\to \\mathbb R^{2r}$ such that the algebraic intersection number of the $f$-images of any $r$ pairwise disjoint simplices of $K$ is zero. This result can be restated in terms of cohomological obstructions or equivariant maps, and extends an analogous codimension 3 criterion by the second and fourth authors. As another application we classify ornaments $f:S^3 \\sqcup S^3\\sqcup S^3\\to \\mathbb R^5$ up to ornament\r\nconcordance. It follows from work of M. Freedman, V. Krushkal and P. Teichner that the analogous criterion for $r=2$ is false. We prove a lemma on singular higher-dimensional Borromean rings, yielding an elementary proof of the counterexample."}],"department":[{"_id":"UlWa"}],"title":"Eliminating higher-multiplicity intersections, III. Codimension 2","author":[{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey"},{"full_name":"Mabillard, Isaac","last_name":"Mabillard","first_name":"Isaac","id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Skopenkov, A.","last_name":"Skopenkov","first_name":"A."},{"last_name":"Wagner","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1511.03501"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Avvakumov, Sergey, et al. “Eliminating Higher-Multiplicity Intersections, III. Codimension 2.” ArXiv, 1511.03501.","ieee":"S. Avvakumov, I. Mabillard, A. Skopenkov, and U. Wagner, “Eliminating higher-multiplicity intersections, III. Codimension 2,” arXiv. .","short":"S. Avvakumov, I. Mabillard, A. Skopenkov, U. Wagner, ArXiv (n.d.).","ama":"Avvakumov S, Mabillard I, Skopenkov A, Wagner U. Eliminating higher-multiplicity intersections, III. Codimension 2. arXiv.","apa":"Avvakumov, S., Mabillard, I., Skopenkov, A., & Wagner, U. (n.d.). Eliminating higher-multiplicity intersections, III. Codimension 2. arXiv.","chicago":"Avvakumov, Sergey, Isaac Mabillard, A. Skopenkov, and Uli Wagner. “Eliminating Higher-Multiplicity Intersections, III. Codimension 2.” ArXiv, n.d.","ista":"Avvakumov S, Mabillard I, Skopenkov A, Wagner U. Eliminating higher-multiplicity intersections, III. Codimension 2. arXiv, 1511.03501."},"date_updated":"2023-09-07T13:12:17Z","status":"public","type":"preprint","article_number":"1511.03501","_id":"8183"}]