Steklov Mathematical Institute of RAS Skolkovo Institute of Science and Technology ALGEBRAIC TOPOLOGY, COMBINATORICS AND MATHEMATICAL PHYSICS Abstracts of Talks of the International Conference on Occasion of Victor Buchstaber’s 75th Birthday Moscow, May 24 – June 1, 2018 Moscow, 2018 UDC 514+515.1 BBC 22.16 A45 A45 Algebraic topology, combinatorics and mathematical physics: Abstracts of talks of the international conference on occasion of Victor Buchstaber’s 75th birthday, Moscow, May 24 – June 1, 2018; – M., Steklov Mathematical Institute of Russian Academy of Sciences, 2018. 150 p. ISBN 978-5-98419-080-0 Program Committee: S. P. Novikov, I. M. Krichever, A. A. Gaifullin, T. E. Panov Organising Comittee: A. A. Ayzenberg, A. A. Gaifullin, N. Yu. Erokhovets, T. E. Panov Executive editor N. Yu. Erokhovets Cover design S. V. Mishina ISBN 978-5-98419-080-0 c Steklov Mathematical Institute of Russian Academy of Sciences, 2018 Математический институт им. В.А.Стеклова Российской академии наук Сколковский институт науки и технологии АЛГЕБРАИЧЕСКАЯ ТОПОЛОГИЯ, КОМБИНАТОРИКА И МАТЕМАТИЧЕСКАЯ ФИЗИКА Тезисы докладов Международной конференции, посвящённой 75-летию со дня рождения члена-корреспондента РАН В.М. Бухштабера Москва, 24 мая – 1 июня, 2018 Москва, 2018 УДК 514+515.1 ББК 22.16 A45 A45 Алгебраическая топология, комбинаторика и мате- матическая физика: Тезисы докладов международ- ной конференции, посвящённой 75-летию со дня рож- дения члена-корреспондента РАН В.М. Бухштабера, Москва, 24 мая – 1 июня, 2018; – М., Математический институт им. В.А. Стеклова РАН, 2018. 150 c. ISBN 978-5-98419-080-0 Программный комитет: С. П. Новиков, И. М. Кричевер А. А. Гайфуллин, Т. Е. Панов Организационный комитет: А. А. Айзенберг, А. А. Гайфуллин, Н. Ю. Ероховец, Т. Е. Панов Ответственный редактор Н. Ю. Ероховец Дизайн обложки С. В. Мишина ISBN 978-5-98419-080-0 c Математический институт им. В.А. Стеклова РАН, 2018 Organisers: • Steklov Mathematical Intitute of Russian Academy of Sciences (MI RAS) • Skolkovo Institute of Science and Technology (Skoltech) Program Committee: Sergey Novikov (MI RAS and MSU) Igor Krichever (Skoltech, HSE and IITP RAS) Alexander Gaifullin (MI RAS, Skoltech, MSU, and IITP RAS) Taras Panov (MSU, ITEP and IITP RAS) Organising Comittee: Anton Ayzenberg (HSE) Alexander Gaifullin (MI RAS, Skoltech, MSU, and IITP RAS) Nikolai Erokhovets (MSU) Taras Panov (MSU, ITEP and IITP RAS) Contents Plenary lectures 13 A. Bahri (joint with D. Notbohm, S. Sarkar and J. Song), On the integral cohomology of orbifolds 13 N. P. Dolbilin, Locally Isometric Delone Sets . 16 F. Fang, Locally Isometric Delone Sets . 18 A. G. Khovanskii, Newton polygon method and solvability of equations by quadratures . 19 I. M. Krichever, Linear operators with self- consistent potential . 22 S. K. Lando (joint with S. V. Chmutov and M. E. Kazarian), Integrability property of polynomial graph invariants . 23 M. Masuda (joint with E. Lee), Generic torus orbit closures in Schubert varieties . 25 S. V. Matveev, New aspects of complexity theory for 3-manifolds . 26 A. V. Mikhailov (joint with V. M. Buchstaber), Integrable Hamiltonian systems, naturally defined by symmetric powers of algebraic curves 27 D. Y. Suh (joint with N. Fujita and E. Lee), Algebraic and geometric properties of flag Bott-Samelson varieties and applications to representations . 29 I. A. Taimanov, On the cohomology rings of Riemannian manifolds with special holonomy . 31 M. A. Tsfasman, Dense sphere packings: state of the art and algebraic geometry constructions . 32 6 A. M. Vershik, Asymptotic of RSK- Correspondence and new kind of Laws of Large Numbers for Bernoulli Scheme . 34 A. P. Veselov, From combinatorics to geometry of polyhedra via spectral graph theory . 35 E. B. Vinberg, On free algebras of automorphic forms 36 Jie Wu (joint with F. Pavutnitskiy), Simplicial James-Hopf map and decompositions of the unstable Adams spectral sequence for suspensions 39 R. T. Zivaljevi´cˇ , Cyclohedron and Kantorovich- Rubinstein polytopes . 40 Invited lectures 42 I. V. Arzhantsev (joint with L. Braun, J. Hausen, and M. Wrobel), Log terminal singularities, platonic tuples and iteration of Cox rings . 42 M. Bakuradze, All extensions of C2 by C2n × C2n are good for the Morava K-theory . 43 E. Yu. Bunkova, Hirzebruch Functional Equations . 44 S. Choi (joint with H. Park and Li Cai), Cohomology formulae of real toric spaces . 46 V. Dragovi´c (joint with M. Radnovi´c), Billiards within quadrics and Chebyshev type polynomials 48 A. N. Dranishnikov (joint with S. Ferry and S. Weinberger), Surgery and cell-like maps . 49 I. A. Dynnikov (joint with M. V. Prasolov), Exchange classes of rectangular diagrams, Legendrian knots, and the knot symmetry group 51 E. A. Fominykh, On the Matveev’s complexity of knot complements in thickened surfaces . 53 7 A. A. Glutsyuk, On model of Josephson effect, constrictions and transition matrix of double confluent Heun equation . 54 V. G. Gorbounov, Schubert calculus and quantum integrable systems . 56 M. A. Gorsky, Polytopal realizations of cluster, subword and accordion complexes and representation theory . 57 J. Grbi´c, LS-category of moment-angle manifolds and Massey products . 63 P. G. Grinevich (joint with S. Abenda), From real regular multisoliton solutions of KP-II to finite- gap solutions . 64 V. Gruji´c, Combinatorial Hopf algebras and generalized permutohedra . 65 D. V. Gugnin, Lower Bounds for the Degree of a Branched Covering of a Manifold . 67 S. M. Gusein-Zade (joint with A. Campillo and F. Delgado), Algebraic links in the Poincar´e sphere and the Alexander polynomials . 71 Y. Karshon (joint with A. Tolman), Topology of complexity one quotients . 73 H. M. Khudaverdian (joint with Th. Th. Voronov), Homotopy poisson brackets and thick morphisms . 74 D. Kishimoto (joint with K. Iriye and T. Matsushita), Relative phantom maps . 75 A. A. Kustarev, Moment-angle manifolds and linear programming . 77 Zhi L¨u (joint with A. Darby and F. Li), Algebras from oriented triangulated manifolds . 79 8 A. V. Malyutin, Poincar´e’s rotation number in dynamics and knot theory . 80 S. A. Melikhov, Lim colim versus colim lim . 82 D. V. Millionshchikov, Polynomial Lie algebras and growth rates of their subalgebras . 84 A. E. Mironov (joint with G. S. Mauleshova), On one–point commuting difference operators of rank one . 86 O. R. Musin, Circle actions on 4-manifolds . 87 G. Yu. Panina (joint with J. Gordon), Diagonal complexes . 89 K. M. Pawa lowski, Smooth actions of compact Lie groups on complex projective spaces . 91 A. V. Penskoi (joint with M. Karpukhin, N. Nadirashvili and I. Polterovich), Isoperimetric inequalities for Laplace eigenvalues on the sphere and the real projective plane . 93 Z. Raki´c (joint with B. Dragovi´c),Path integrals on real, p-adic, and adelic spaces . 95 D. V. Talalaev, Towards integrability structure in 3D Ising model . 96 S. Terzi´c (joint with V. M. Buchstaber), Toric topology of the complex Grassmann manifolds and (2n; k)-manifolds . 97 S. Theriault (joint with T. E. Panov), The homotopy theory of polyhedral products associated with flag complexes . 100 D. A. Timashev (joint with S. Cupit-Foutou) , Orbits in real loci of spherical homogeneous spaces . 102 9 A. V. Ustinov, An elementary approach to Somos-4 sequences . 104 Yu. M. Ustinovskiy, On face numbers of flag simplicial complexes . 105 V. V. Vershinin (joint with J. Li and J. Wu) , Twisted Homology and Twisted Simplicial Groups . 107 A. Yu. Vesnin, On Zeros of Yamada Polynomial for Spatial Graphs . 108 Th. Th. Voronov, Microformal geometry and homotopy algebras . 110 Min Yan (joint with S. Cappell and S. Weinbeger), Converse of Smith Theory . 112 International Seminar on Toric Topology and Homotopy Theory 114 S. A. Abramyan, Iterated higher Whitehead products in topology of moment-angle complexes114 D. Barali´c, Toric topology of balanced simplicial complex . 117 J. D. Carlson (joint with O. Goertsches, C. He, and L. Mare), The equivariant cohomology and K- theory of a cohomogeneity-one action . 119 X. Fu (joint with J. Grbi´c),Simplicial G-Complexes and Representation Stability of Polyhedral Products . 120 S. Hasui, On the quasitoric bundles . 121 T. Horiguchi, The cohomology rings of Hessenberg varieties and Schubert polynomials . 122 R. Huang, Homotopy types of gauge groups over high dimensional manifolds . 124 10 T. Hwang (joint with E. Lee and D. Y. Suh), The Gromov width of generalized Bott manifolds . 125 A. V. Kotelskiy, Khovanov homology via immersed curves in the 4-punctured sphere . 126 H. Kuwata (joint with S. Hasui, M. Masuda and S. Park), Toric manifolds over an n-cube with one vertex cut . 127 I. Yu. Limonchenko (joint with V. M. Buchstaber), On the new families of flag nestohedra arising in toric topology . 128 A. Linton, Massey products in toric topology . 130 I. Membrillo-Solis, Homotopy decompositions of gauge groups . 131 J. Moon (joint with S. Choi and H. Park), Projective toric manifolds and wedge operation 132 S. Park (joint with B. Park and H. Park.), Betti numbers of real toric manifolds arising from a graph . 133 F. Yu. Pavutnitskiy, Homotopical approach to group extensions and homology of morphisms . 134 A. D. Rukhovich, On the numbers of fullerenes . 135 S. Sarkar (joint with V. Uma), Equivariant K- theory of toric orbifolds . 137 T. Sato, On the coinvariant rings of pseudo- reflection groups . 138 K. Schaller (joint with V. Batyrev), Stringy invariants, lattice polytopes, and combinatorial identities . 140 E. S. Shemyakova, Obstructions to factorization of differential operators on the algebra of densities on the line . 141 11 T. So, Classification of gauge groups over 4-manifolds142 G. D. Solomadin, Totally normally split quasitoric manifolds . 143 J. Song (joint with A. Darby and S. Kuroki), GKM- orbifolds and their equivariant cohomology rings 145 Y. A. Veryovkin (joint with T. E. Panov), Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groups . 146 H. Zeng (joint with H.