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BEGIN:VEVENT
SUMMARY:Alex Lubotzky (The Hebrew University of Jerusalem)
DTSTART:20211005T150000Z
DTEND:20211005T163000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/1
DESCRIPTION:Title: Stability and testability of permutations' equations\nby Alex L
ubotzky (The Hebrew University of Jerusalem) as part of The Vinberg Lectur
e Series\n\n\nAbstract\nLet $A$ and $B$ be two permutations in $\\text{Sym
}(n)$ that ``almost commute'' -- are they a small deformation of permutati
ons that truly commute? More generally\, if $R$ is a system of words-equat
ions in variables $X = \\{x_1\, \\ldots \,x_d\\}$ and $A_1\, \\ldots \,A_d
$ are permutations that are nearly solutions\; are they near true solution
s? \n\nIt turns out that the answer to this question depends only on the g
roup presented by the generators $X$ and relations $R$. This leads to the
notions of ``stable groups'' and ``testable groups''. \n\nWe will present
a few results and methods which were developed in recent years to check wh
ether a group is stable or testable. We will also describe the connection
of this subject with property testing in computer science\, with the long-
standing problem of whether every group is sofic\, and with invariant rand
om subgroups.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Reid (Rice University\, USA)
DTSTART:20211019T150000Z
DTEND:20211019T163000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/2
DESCRIPTION:Title: The geometry and topology of arithmetic hyperbolic manifolds of sim
plest type\nby Alan Reid (Rice University\, USA) as part of The Vinber
g Lecture Series\n\n\nAbstract\nThis talk will survey as well as discuss g
eometric and topological properties of arithmetic hyperbolic manifolds of
simplest type. These are precisely the class of arithmetic hyperbolic mani
folds that contain an immersed co-dimension one totally geodesic submanifo
lds.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Alekseevsky (IITP RAS\, Moscow\, Russia)
DTSTART:20211123T150000Z
DTEND:20211123T163000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/4
DESCRIPTION:Title: Special Vinberg cones and their application to Supergravity\nby
Dmitry Alekseevsky (IITP RAS\, Moscow\, Russia) as part of The Vinberg Le
cture Series\n\n\nAbstract\nIn the early 1960s\, Vinberg gave a descriptio
n of homogeneous convex cones as cones of Hermitian positive definite matr
ices in a matrix $T$-algebra $M_n$ of $(n\\times n)$-matrices whose diagon
al entries are just real numbers\, but off-diagonal elements belong to dif
ferent vector spaces. It turns out that rank 3 special Vinberg cones (corr
esponding to Clifford algebras) have important applications to Supergravit
y. No special background is required. The talk is based on joint works wit
h V. Cortes\; and with A. Marrani and A. Spiro.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Sarnak (IAS Princeton\, USA)
DTSTART:20211130T150000Z
DTEND:20211130T163000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/5
DESCRIPTION:Title: Reflection groups and monodromy\nby Peter Sarnak (IAS Princeton
\, USA) as part of The Vinberg Lecture Series\n\n\nAbstract\nVinberg's the
ory of reflection groups has wide applications. We discuss some of these\,
to monodromy groups of hypergeometric and Painlevé equations. The nonlin
ear case is intimately connected to affine Markoff surfaces and it is a ce
ntral ingredient in the Diophantine analysis of these surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryna Viazovska (EPF Lausanne\, Switzerland)
DTSTART:20211207T150000Z
DTEND:20211207T163000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/6
DESCRIPTION:Title: The sphere packing problem\nby Maryna Viazovska (EPF Lausanne\,
Switzerland) as part of The Vinberg Lecture Series\n\n\nAbstract\nThe sph
ere packing problem asks for the densest configuration of non-overlapping
unit balls in space. In this talk I shall speak about the sphere packing p
roblem in various spaces and its generalisations. The talk will focus on l
inear programming and semidefinite programming methods as powerful tools f
or analysing and\, in some cases\, completely solving geometric optimisati
on questions.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjorn Poonen (MIT)
DTSTART:20220126T153000Z
DTEND:20220126T170000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/8
DESCRIPTION:Title: Undecidability in number theory\nby Bjorn Poonen (MIT) as part
of The Vinberg Lecture Series\n\n\nAbstract\nHilbert's tenth problem asked
for an algorithm that\, given a\nmultivariable polynomial equation with i
nteger coefficients\, would\ndecide whether there exists a solution in int
egers. Around 1970\,\nMatiyasevich\, building on earlier work of Davis\,
Putnam\, and Robinson\,\nshowed that no such algorithm exists. But the an
swer to the analogous\nquestion with integers replaced by rational numbers
is still unknown\,\nand there is not even agreement among experts as to w
hat the answer\nshould be. The second half of the lecture will explore so
me of the\ntechniques from arithmetic geometry that have been used towards
\nanswering this question and the related question for the ring\nof intege
rs of a number field.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHES)
DTSTART:20220223T153000Z
DTEND:20220223T170000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/10
DESCRIPTION:Title: Introduction to wall-crossing\nby Maxim Kontsevich (IHES) as p
art of The Vinberg Lecture Series\n\n\nAbstract\nWall-crossing structures
appeared several years ago in several mathematical contexts\, including cl
uster algebras and theory of generalized Donaldson-Thomas invariants. In m
y lecture I will describe the general formalism based on a graded Lie alge
bra and an additive map from the grading lattice to an oriented plane ("ce
ntral charge").\n\nA geometric example of a wall-crossing structure comes
from theory of translation surfaces. The number of saddle connections in a
given homology class is an integer-valued function on the parameter space
(moduli space of abelian or quadratic differentials)\, which jumps along
certain walls. The whole theory can be made totally explicit in this case.
Also\, I'll talk about another closely related example\, which can be dub
bed a "holomorphic Morse-Novikov theory".\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Fisher (Indiana University)
DTSTART:20220323T143000Z
DTEND:20220323T160000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/11
DESCRIPTION:Title: Arithmeticity\, superrigidity\, and totally geodesic submanifolds<
/a>\nby David Fisher (Indiana University) as part of The Vinberg Lecture S
eries\n\n\nAbstract\nArithmeticity of locally symmetric spaces is an old a
nd important\narea of study in which Vinberg proved some central results.
I will\ndiscuss the history of the area\, some open questions and then\nf
ocus on recent joint work with Bader\, Miller and Stover. We prove\nthat
non-arithmetic real and complex hyperbolic manifolds cannot\nhave infinit
ely many maximal totally geodesic submanifolds.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Kazhdan (Hebrew University\, Israel)
DTSTART:20220413T143000Z
DTEND:20220413T160000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/14
DESCRIPTION:Title: On the Langlands correspondence for curves over local fields\n
by David Kazhdan (Hebrew University\, Israel) as part of The Vinberg Lectu
re Series\n\n\nAbstract\nOn results and (mostly) conjectures on automorphi
c functions on moduli spaces of 2-dimensional vector bundles on curves ove
r local fields.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Pak (UCLA)
DTSTART:20220504T163000Z
DTEND:20220504T183000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/16
DESCRIPTION:Title: Combinatorial inequalities\nby Igor Pak (UCLA) as part of The
Vinberg Lecture Series\n\n\nAbstract\nIn the ocean of combinatorial inequa
lities\, two islands are especially difficult. First\, Mason's conjecture
s say that the number of forests in a graph with k edges is log-concave.
More generally\, the number of independent sets of size k in a matroid is
log-concave. Versions of these results were established just recently\, i
n a remarkable series of papers by Huh and others\, inspired by algebro-ge
ometric considerations. \n\nSecond\, Stanley's inequality for the numbers
of linear extensions of a poset with value k at a given poset element\, i
s log-concave. This was originally conjectured by Chung\, Fishburn and Gr
aham\, and famously proved by Stanley in 1981 using the Alexandrov–Fench
el inequalities in convex geometry. No direct combinatorial proof for eit
her result is known. Why not? \n\nIn the first part of the talk we will
survey a number of combinatorial inequalities. We then present a new fram
ework of combinatorial atlas which allows one to give elementary proofs of
the two results above\, and extend them in several directions. This talk
is aimed at the general audience.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Kac (MIT)
DTSTART:20230424T150000Z
DTEND:20230424T170000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/17
DESCRIPTION:Title: Exceptional de Rham complexes\nby Victor Kac (MIT) as part of
The Vinberg Lecture Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Borcherds (UC Berkeley)
DTSTART:20240226T160000Z
DTEND:20240226T180000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/18
DESCRIPTION:Title: Vinberg’s Algorithm and Kac-Moody algebras\nby Richard Borch
erds (UC Berkeley) as part of The Vinberg Lecture Series\n\n\nAbstract\nVi
nberg’s algorithm was introduced by Vinberg in order to calculate the fu
ndamental domains of hyperbolic reflection groups\, especially those comin
g from Lorentzian lattices. We will show how to use it to calculate the au
tomorphism groups of some lattices\, culminating in Conway’s spectacular
discovery that the Dynkin diagram of the 26-dimensional even unimodular L
orentzian lattice is the Leech lattice. We will then discuss some of the K
ac-Moody algebras associated with Vinberg’s Dynkin diagrams.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Loseu (Yale University)
DTSTART:20241213T170000Z
DTEND:20241213T190000Z
DTSTAMP:20260404T094833Z
UID:Vinberg/19
DESCRIPTION:Title: Quantizations and unitary representations\nby Ivan Loseu (Yale
University) as part of The Vinberg Lecture Series\n\n\nAbstract\nThe stud
y of unitary representations of Lie groups is a classical subject in Repre
sentation theory going back to Gelfand and Harish-Chandra. The main\, curr
ently open\, problem is to classify the irreducible unitary representation
s of semisimple Lie groups. Thanks to the work of Kirillov and Kostant the
question of classifying the irreducibles fits into Geometric quantization
that seeks to produce quantum mechanical systems from classical ones. In
my talk I will explain some recent advances in Algebraic (a.k.a. Deformati
on) quantization of singular symplectic varieties and how they help to und
erstand unipotent representations\, an important class of unitary represen
tations that are expected to serve as building blocks. This is based on my
solo works as well as joint papers with Dmytro Matvieievskyi\, Lucas Maso
n-Brown and Shilin Yu.\n
LOCATION:https://stable.researchseminars.org/talk/Vinberg/19/
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