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BEGIN:VEVENT
SUMMARY:On the A1-fundamental groups of Chevalley groups
DTSTART;VALUE=DATE-TIME:20211112T123000Z
DTEND;VALUE=DATE-TIME:20211112T125500Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-312@indico.eimi.ru
DESCRIPTION:Speakers: Sergey Sinchuk (SPbU)\nLet $k$ be an arbitrary field
 . The aim of the talk is to give on overview of a recent preprint\, in whi
 ch it is shown that in the linear case ($\\Phi=\\mathrm{A}_\\ell$\, $\\ell
  \\geq 4$) and even orthogonal case ($\\Phi = \\mathrm{D}_\\ell$\, $\\ell\
 \geq 7$\, $\\mathrm{char}(k)\\neq 2$) the unstable functor $\\mathrm{K}_2(
 \\Phi\, R)$ possesses the $\\mathbb{A}^1$-invariance property and therefor
 e can be represented in the unstable $\\mathbb{A}^1$-homotopy category $\\
 mathcal{H}^{\\mathbb{A}^1}_{k}$ as the fundamental group of the simply-con
 nected Chevalley--Demazure group scheme $\\mathrm{G}_\\mathrm{sc}(\\Phi\,-
 )$. This invariance result can be considered as the $\\mathrm{K}_2$-analog
 ue of the geometric case of Bass--Quillen conjecture. With our technique w
 e are also able to show for a semilocal regular $k$-algebra $A$ that $\\ma
 thrm{K}_2(\\Phi\, A)$ embeds as a subgroup into the Milnor group $\\mathrm
 {K}^\\mathrm{M}_2(\\mathrm{Frac}(A))$.\n\nhttps://indico.eimi.ru/event/437
 /contributions/312/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/312/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stability\, non-approximated groups\, and high-dimensional expande
 rs
DTSTART;VALUE=DATE-TIME:20211111T140000Z
DTEND;VALUE=DATE-TIME:20211111T145000Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-305@indico.eimi.ru
DESCRIPTION:Speakers: Alex Lubotzky (Weizmann Inst.)\nSeveral well-known o
 pen questions\, such as: "are all groups sofic or hyperlinear?"\, have a c
 ommon form: can all groups be approximated by asymptotic homomorphisms int
 o the symmetric groups Sym(n) (in the sofic case) or the unitary groups U
 (n) (in the hyperlinear case)? In the case of U(n)\, the question can be a
 sked with respect to different metrics and norms. We answer\, for the fir
 st time\, some of these versions\, showing that there exist finitely prese
 nted groups that are  not approximated by U(n) with respect to the Frobe
 nius (=L_2) norm and many other norms. The strategy is via the notion of "
 stability": Some higher dimensional cohomology vanishing phenomenon is pr
 oven to imply stability. Using the Garland method  (a.k.a. high dimension
 al expanders as quotients of Bruhat-Tits buildings)\, it is shown that som
 e non-residually-finite groups are stable and hence cannot be approximated
 . These groups are central extensions of some lattices in p-adic Lie group
 s (constructed via a p-adic version of a result of Deligne).\n\nAll notion
 s will be explained. Based on joint works with M. De Chiffre\, L. Glebsky
  and A. Thom and with I. Oppenheim .\n\nhttps://indico.eimi.ru/event/437
 /contributions/305/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/305/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paving Springer fibers. The Case of E7
DTSTART;VALUE=DATE-TIME:20211111T100000Z
DTEND;VALUE=DATE-TIME:20211111T105000Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-303@indico.eimi.ru
DESCRIPTION:Speakers: Corrado De Concini (Univ. Roma I)\nIn the paper De C
 oncini\, C.\; Lusztig\, G.\; Procesi\, C. Homology of the zero-set of a ni
 lpotent vector field on a flag manifold. J. Amer. Math. Soc. 1 (1988)\, no
 . 1\, 15-34\, it was proven the so-called Springer fiber $B_n$ for any nil
 potent n element in a complex simple Lie algebra $g$ has homological prope
 rties that suggest that $B_n$ should have a paving by affine spaces. This 
 last statement was proved to hold in the case in which $g$ is classical bu
 t remained open for exceptional groups in types $E_7$ and $E_8$. In a join
 t project with Maffei we are trying to fill this gap. At this point our ef
 forts has been successful in type $E_7$ and "almost" in type $E_8$ where o
 ne is reduced to show it only in one case. \nThe goal of the talk is to su
 rvey the problem and give an idea on how to show our new results.\n\nhttps
 ://indico.eimi.ru/event/437/contributions/303/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/303/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Explicit presentation of relative Steinberg groups
DTSTART;VALUE=DATE-TIME:20211112T140000Z
DTEND;VALUE=DATE-TIME:20211112T142500Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-315@indico.eimi.ru
DESCRIPTION:Speakers: Egor Voronetsky (SPbU)\nRelative Steinberg groups ar
 e defined as crossed modules over the absolute Steinberg group with some g
 enerators and relations. We find their presentations as abstract groups.\n
 \nhttps://indico.eimi.ru/event/437/contributions/315/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/315/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bounded reduction of orthogonal matrices over polynomial rings
DTSTART;VALUE=DATE-TIME:20211112T133000Z
DTEND;VALUE=DATE-TIME:20211112T135500Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-314@indico.eimi.ru
DESCRIPTION:Speakers: Pavel Gvozdevsky (SPbU)\nThe talk is based on the au
 thor’s paper [1].In the paper [2]\, Vaserstein showed that for any coeff
 icient ring $C$ of finite Krull dimension and any $r \\ge \\max(3\, \\dim 
 C +2)$\, an arbitrary matrix from the special linear group over a polynomi
 al ring $g \\in SL_r(C[x_1\, . . . \, x_n])$ can be reduced to the diagona
 l  shape $diag(g’\,1)$ where $g’ \\in SL_{r−1}(C[x_1\, . . . \, x_n]
 )$\, by a bounded number (namely $n(21n − 79)/2 + 33nr + 4r − 4)$ of e
 lementary operations. He also deduced from this the similar result for the
  symplectic group.\nIn the talk we state the similar result recently obtai
 ned by the author for the split orthogonal group. That is the last remaini
 ng case among the split classical groups. This result can be viewed as the
  effective version of the early surjective $K_1$-functor stability\, prove
 d by Suslin and Kopeiko in [3].\nWe also discuss the connection of such th
 eorems with the proof of the Kazhdan property (T) for split groups over fi
 nitely generated rings.\n\nhttps://indico.eimi.ru/event/437/contributions/
 314/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/314/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Morava K-theory of orthogonal groups
DTSTART;VALUE=DATE-TIME:20211112T130000Z
DTEND;VALUE=DATE-TIME:20211112T132500Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-313@indico.eimi.ru
DESCRIPTION:Speakers: Andrei Lavrenov (SPbU)\nLet $G$ be a Chevalley group
 \, and $A^*$ denote an oriented cohomology theory in the sense of Levine-M
 orel (e.g.\, Grothendieck's $K$-theory\, Chow group\, etc.) Then the ring 
 $A^*(G)$ is an interesting invariant of the group. In the talk I will expl
 ain how to compute this ring for the special orthogonal group $G = SO_m$ a
 nd the Morava $K$-theory $A^* = K(n)^*$. The talk is based on a joint work
  with V. Petrov\, P. Sechin\, and N. Semenov.\n\nhttps://indico.eimi.ru/ev
 ent/437/contributions/313/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/313/
END:VEVENT
BEGIN:VEVENT
SUMMARY:R-equivalence on reductive algebraic groups
DTSTART;VALUE=DATE-TIME:20211112T100000Z
DTEND;VALUE=DATE-TIME:20211112T102500Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-311@indico.eimi.ru
DESCRIPTION:Speakers: Anastasia Stavrova (SPbU)\nWe generalize Manin’s n
 otion of R-equivalence for algebraic varieties to schemes and use this gen
 eralization to solve the specialization problem for R-equivalence class g
 roups of reductive groups in the equicharacteristic case. The talk is base
 d on the joint work with Philippe Gille https://arxiv.org/abs/2107.01950
 .\n\nhttps://indico.eimi.ru/event/437/contributions/311/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/311/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isotropy of Tits construction
DTSTART;VALUE=DATE-TIME:20211112T093000Z
DTEND;VALUE=DATE-TIME:20211112T095500Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-310@indico.eimi.ru
DESCRIPTION:Speakers: Victor Petrov (SPbU)\nTits construction produces a 
 Lie algebra out of a composition algebra and an exceptional Jordan algeb
 ra. The type of the result is $F_4$\, ${}^2E_6$\, $E_7$ or $E_8$ when th
 e composition algebra has dimension 1\,2\,4 or 8 respectively. Garibaldi a
 nd Petersson noted that the Tits index ${}^2E_6^{35}$ cannot occur as a 
 result of Tits construction. Recently Alex Henke proved that the Tits
  index $E_7^{66}$ is also not possible. We push the analogy further and s
 how that Lie algebras of Tits index $E_8^{133}$ don't lie in the image
  of the Tits construction. The proof relies on basic facts about symme
 tric spaces and our joint result with Garibaldi and Semenov about isotrop
 y of groups of type $E_7$ in terms of the Rost invariant. This is a 
 part of a work joint with Simon Rigby.\n\nhttps://indico.eimi.ru/event/
 437/contributions/310/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/310/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Grothendieck---Serre conjecture in mixed characteristic.
DTSTART;VALUE=DATE-TIME:20211112T083000Z
DTEND;VALUE=DATE-TIME:20211112T092000Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-309@indico.eimi.ru
DESCRIPTION:Speakers: Ivan Panin (PDMI RAS)\nWe prove the conjecture for t
 he group $SL_{1\,D}$ in the mixed characteristic smooth case.\n\nhttps://i
 ndico.eimi.ru/event/437/contributions/309/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/309/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dense images of word maps
DTSTART;VALUE=DATE-TIME:20211112T073000Z
DTEND;VALUE=DATE-TIME:20211112T082000Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-308@indico.eimi.ru
DESCRIPTION:Speakers: Andreas Thom (TU Dresden)\nLet $w$ be a non-trivial 
 element of the free group. For $\\varepsilon >0$\, we prove that there exi
 sts an integer $N(\\varepsilon\,w)$ such that $w(G)$ is $\\varepsilon$-den
 se in $G$\, where $G$ is a finite simple group or compact Lie group of ran
 k $N(\\varepsilon\,w)$ endowed with its natural bi-invariant metric. This 
 confirms metric versions of a conjectures by Shalev and Larsen.\n\nhttps:/
 /indico.eimi.ru/event/437/contributions/308/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/308/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Degree two negligible cohomology of finite groups
DTSTART;VALUE=DATE-TIME:20211112T060000Z
DTEND;VALUE=DATE-TIME:20211112T065000Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-307@indico.eimi.ru
DESCRIPTION:Speakers: Alexander Merkurjev (UCLA)\nLet $G$ be a finite grou
 p and let M be an abelian group viewed as a $G$-module with trivial $G$-ac
 tion. Fix a field $F$. A cohomology class $c$ in $H^n(G\,M)$ is called neg
 ligible over $F$ if for every field extension $L/F$ and every continuous g
 roup homomorphism of the absolute Galois group of $L$ to $G$ the class $c$
  belongs to the kernel of the induced homomorphism $H^n(G\,M) \\to H^n(L\,
 M)$. We determine all negligible cohomology classes $c$ in $H^2(G\,M)$.\nT
 his is a joint work with M.Gherman.\n\nhttps://indico.eimi.ru/event/437/co
 ntributions/307/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/307/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On conjugacy of Cartan subalgebras in extended affine Lie algebras
  and classification of torsors over  Laurent polynomial rings
DTSTART;VALUE=DATE-TIME:20211111T150000Z
DTEND;VALUE=DATE-TIME:20211111T155000Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-306@indico.eimi.ru
DESCRIPTION:Speakers: Vladimir Chernousov (Univ. Alberta)\nIn the talk we 
 will present results on a problem of conjugacy of Cartan subalgebras for a
  class of infinite dimensional Lie algebras called extended affine Lie alg
 ebras and how this problem intertwinds with the classification of torsors 
 over Laurent polynomial rings. Joint work with P. Gille\, E. Neher\, A. Pi
 anzola\, U. Yahorau.\n\nhttps://indico.eimi.ru/event/437/contributions/306
 /
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/306/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Automorphisms of K3 surfaces and isometries of lattices
DTSTART;VALUE=DATE-TIME:20211111T130000Z
DTEND;VALUE=DATE-TIME:20211111T135000Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-304@indico.eimi.ru
DESCRIPTION:Speakers: Eva Bayer-Fluckiger (EPF Lausanne)\nWe show that eve
 ry Salem number of degree $4\, 6\, 8\, 12\, 14\, 16$ and $18$ is the dynam
 ical degree of an automorphism of a complex K3 surface\, and give necessar
 y and sufficient conditions for this in degrees $10$ and $18$.\n\nhttps://
 indico.eimi.ru/event/437/contributions/304/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/304/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Group varieties and group structures of algebraic groups
DTSTART;VALUE=DATE-TIME:20211111T090000Z
DTEND;VALUE=DATE-TIME:20211111T095000Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-302@indico.eimi.ru
DESCRIPTION:Speakers: Vladimir Popov (MI RAS)\nThe talk is aimed to discus
 s to what extent the group variety of a connected algebraic group or the g
 roup manifold of a connected real Lie group determines its group structure
 .\n\nhttps://indico.eimi.ru/event/437/contributions/302/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/302/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A new look at groups generated by involutions
DTSTART;VALUE=DATE-TIME:20211111T080000Z
DTEND;VALUE=DATE-TIME:20211111T085000Z
DTSTAMP;VALUE=DATE-TIME:20260714T061954Z
UID:indico-contribution-437-301@indico.eimi.ru
DESCRIPTION:Speakers: Anatoly Vershik (PDMI RAS)\nWe construct a general t
 heory of finite groups generated by reflections based on the notion of nu
 mberings of partially ordered sets. The classical theory of Coxeter group
 s (for the case of the symmetric group) corresponds to a special choice of
  an ordered set --- the simplest Young diagram $(n\,1)$. From a formal vie
 wpoint\, we replace the defining relation $(\\sigma_i \\cdot \\sigma_{i + 
 1})^3 = Id$\, where $\\sigma_i\, i = 1\,2 ... k$\, are involutions\, by th
 e relation $(\\sigma_i \\cdot \\sigma_{i + 1})^6 = Id$ leaving the commuta
 tion condition unchanged: $(\\sigma_i \\cdot \\sigma_j)^2 = Id$ for $|i-j|
 >1$\, with the following extra condition: the group generated by the adjac
 ent involutions $\\sigma_i$ and $\\sigma_{i+1}$ is a finite product of the
  groups of orders $2$ and $3$. Such symmetry groups (finite and countable)
  naturally arise in combinatorics and their classification does not seem h
 opeless. For example\, if the ordered set is a finite Young diagram\, then
  hypothetically we do not go beyond the Coxeter groups. The characteristic
  of our approach is that groups are considered as special subgroups of sym
 metric groups. Particularly interesting are infinite such groups and their
  representations.\n\nhttps://indico.eimi.ru/event/437/contributions/301/
LOCATION:Online
URL:https://indico.eimi.ru/event/437/contributions/301/
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