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 Events
MIT
Mon 8 Mar 2021, 3:00pm
Algebraic Geometry Seminar
https://ubc.zoom.us/j/67916711780 (password:the number of lines on a generic quintic threefold)
Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture
https://ubc.zoom.us/j/67916711780 (password:the number of lines on a generic quintic threefold)
Mon 8 Mar 2021, 3:00pm-4:00pm

Abstract

In this talk, I will discuss some results on the structure of the cohomology of the moduli space of stable SL_n Higgs bundles on a curve. One consequence is a new proof of the Hausel-Thaddeus conjecture proven previously by Groechenig-Wyss-Ziegler via p-adic integration. We will also discuss connections to the P=W conjecture if time permits. Based on joint work with Junliang Shen.
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Princeton University
Tue 9 Mar 2021, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
Online, link available from Sven Bachmann
Electromagnetic-gravitational perturbations of Kerr-Newman spacetime
Online, link available from Sven Bachmann
Tue 9 Mar 2021, 3:30pm-4:30pm

Abstract

The Kerr-Newman spacetime is the most general explicit black hole solution, and represents a stationary rotating charged black hole. Its stability to gravitational and electromagnetic perturbations has eluded a proof since the 80s in the black hole perturbation community, because of the "apparent indissolubility of the coupling between the spin-1 and spin-2 fields in the perturbed spacetime", as put by Chandrasekhar. We will present a derivation of the relevant equations which can be analyzed in physical-space to obtain a quantitative proof of stability.
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UIUC
Tue 9 Mar 2021, 4:00pm
Discrete Math Seminar
https://ubc.zoom.us/j/62676242229?pwd=RURtUC9UYXEweVZTMTNGT1EvY1FLZz09
An efficient algorithm for deciding the vanishing of Schubert polynomial coefficients
https://ubc.zoom.us/j/62676242229?pwd=RURtUC9UYXEweVZTMTNGT1EvY1FLZz09
Tue 9 Mar 2021, 4:00pm-5:00pm

Abstract

Schubert polynomials form a basis of all polynomials and appear in the study of cohomology rings of flag manifolds. The vanishing problem for Schubert polynomials asks if a coefficient of a Schubert polynomial is zero. We give a tableau criterion to solve this problem, from which we deduce the first polynomial time algorithm. These results are obtained from new characterizations of the Schubitope, a generalization of the permutahedron defined for any subset of the n x n grid. In contrast, we show that computing these coefficients explicitly is #P-complete. This is joint work with Anshul Adve and Alexander Yong.
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Steklov Institute of Mathematics, Moscow
Wed 10 Mar 2021, 8:30am
Algebraic Groups and Related Structures
Online: link available at https://researchseminars.org/ or from Zinovy Reichstein
Root systems and root lattices in number fields
Online: link available at https://researchseminars.org/ or from Zinovy Reichstein
Wed 10 Mar 2021, 8:30am-9:30am

Abstract

The following construction of a root system of type G_2 is given in J.-P. Serre’s book “Complex Semisimple Lie algebras” (Chapter V, Section 16): “It can be described as the set of algebraic integers of a cyclotomic field generated by a cubic root of unity, with norm 1 and 3”. This talk, based on joint work with Yu. G. Zarhin, concerns the problem of realization of root systems, their Weyl groups and their root lattices in the form of groups and lattices naturally associated with number fields.
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Jan Grebík and Václav Rozhon
University of Warwick and ETH Zurich
Wed 10 Mar 2021, 12:00pm SPECIAL
Probability Seminar
https://ubc.zoom.us/j/67941158154?pwd=TDRjdm1ta2Fxbi9tVjJyaWdKb3A5QT09
Distributed computing and finitary factors of iid labelings
https://ubc.zoom.us/j/67941158154?pwd=TDRjdm1ta2Fxbi9tVjJyaWdKb3A5QT09
Wed 10 Mar 2021, 12:00pm-2:00pm

Abstract

Locally checkable labeling (LCL) problems are graph problems where the validity of a solution can be checked locally. Examples include proper vertex or edge colorings, perfect matching etc.
 
Such problems have been studied from different points of view. Most important for our investigation is the perspective of distributed computing and random processes. The connection between the two fields has been suspected for some time [Holroyd, Schramm, Wilson. Annals of Prob. 2017, Brandt et al. 2017 ] but in our work we give probably the first precise translation between the two worlds. Among others, this almost automatically answers 3 out of 4 open questions from [Holroyd, Schramm, Wilson. Annals of Prob. 2017].
 
In the first part of the talk we introduce the basic notions from distributed computing. In the second part we use this theory to answer aforementioned questions from [Holroyd, Schramm, Wilson. Annals of Prob. 2017].
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UCLA
Wed 10 Mar 2021, 3:00pm
Topology and related seminars
Zoom (see Notes for Attendees)
An equivariant Thom isomorphism theorem and equivariant fundamental classes
Zoom (see Notes for Attendees)
Wed 10 Mar 2021, 3:00pm-4:00pm

Abstract

Let C_2 denote the cyclic group of order two. Given a manifold with a C_2-action, we can consider its equivariant Bredon RO(C_2)-graded cohomology. In this talk, we give an overview of RO(C_2)-graded cohomology in constant Z/2 coefficients, and then explain how a version Thom isomorphism theorem in this setting can be used to develop a theory of fundamental classes for equivariant submanifolds.
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University of Toronto
Fri 12 Mar 2021, 3:00pm
Department Colloquium
https://ubc.zoom.us/j/64534351248?pwd=d21zRk9EekhEM01oSDlHM2o0Rk0rZz09
UBC Science Early Career Invited Lecture: On restrictions of representations
https://ubc.zoom.us/j/64534351248?pwd=d21zRk9EekhEM01oSDlHM2o0Rk0rZz09
Fri 12 Mar 2021, 3:00pm-4:00pm

Abstract

A classical problem in representation theory is how a representation of a group decomposes when restricted to a subgroup. In the 1990s, Gross-Prasad formulated a conjecture regarding the restriction of representations, also known as branching laws, of special orthogonal groups.  Gan, Gross and Prasad extended this conjecture, now known as the Gan-Gross-Prasad (GGP) conjecture, to the remaining classical groups.
In this talk, we will discuss the GGP conjecture and the connection with period integrals.  In addition, we will discuss the first step in provingthe GGP conjecture: a multiplicity at most one theorem. Aizenbud, Gourevitch, Rallis and Schiffmann proved a multiplicity at most one theorem for restrictions of irreducible representations of certain classical groups and Waldspurger proved the same theorem for the special orthogonal groups. We will discuss work that establishes a multiplicity at most one theorem for restrictions of irreducible representations for a non-classical group, the general spin group. This is joint work with Shuichiro Takeda.

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