Transformation Groups Seminar

Speaker: Rafael Gomes (Western)

"Localization Theorem for Equivariant Cohomology"

Time: 09:30

Room: WSC 184 & online

The Localization Theorem is a very convenient tool to compute the equivariant cohomology of $G$-spaces. It provides an isomorphism between the localized equivariant cohomology of a $G$-space (with respect to $S$) and the localized equivariant cohomology of its $G$-fixed points. We then have a complete description of the equivariant cohomology of $X$ up to $S$-torsion. In this talk, we review some properties regarding Localization (in algebra), then explain the statement of the Localization Theorem and finally give some examples of its applications.

Meeting ID: 997 4840 9440 Passcode: 911104

Random Matrix Theory Seminar

Speaker: Masoud Khalkhali (Western)

"Planck length, noncommutative spaces, and random matrix theory"

Time: 14:30

Room: MC 106

GAP Seminar

Speaker: Luuk Verhoeven (Western)

"Factorization of Dirac operators along a submersion"

Time: 10:30

Room: MC 108

Spectral triples (A,H,D) can be interpreted as unbounded representatives for classes in KK-theory, specifically in KK(A,C). It therefore seems natural to investigate if, and how, constructions from KK-theory are reflected back in noncommutative geometry. In this talk we will look at a specific case of this; given a submersion pi:M->B there is a class, pi!, in KK(C(M), C(B)) such that there is a Kasparov product [M] = pi! x [B]. In this talk we will cover an article by W. van Suijlekom and J. Kaad on how this Kasparov product works at the level of spectral triples and correspondences. It turns out that the factorization is exact, up to a curvature term.

Algebra Seminar

Speaker: Senate meeting - no Algebra Seminar (Western)

"No talk"

Time: 14:30

Room:

Transformation Groups Seminar

Speaker: Kumar Sannidhya Shukla

"Euler Class"

Time: 09:30

Room: online

Given a vector bundle, its characteristic classes are cohomology classes of the base space which measure how 'twisted' the vector bundle is. In other words, they are obstructions to the vector bundle being trivial. One such class is the Euler class, which is Poincare dual to the zero set of a section which is transverse to the zero section of the bundle. We will discuss Thom isomorphism and discuss the relation between Euler class and Thom class. Lastly, we will discuss equivariant Euler class (which will be used in localization formula).

Meeting ID: 997 4840 9440 Passcode: 911104

Random Matrix Theory Seminar

Speaker: Masoud Khalkhali (Western)

"Planck length, noncommutative spaces, and random matrix theory II"

Time: 14:30

Room: MC 106

Algebra Seminar

Speaker: Kimberly Klinger-Logan (Rutgers University and Kansas State University)

"Linear Operators and the Hurwitz Zeta Function"

Time: 14:30

Room: ZOOM

At the 1900 International Congress of Mathematicians, Hilbert claimed that the Riemann zeta function is not the solution of any algebraic ordinary differential equation its region of analyticity. In 2015, Van Gorder addresses the question of whether the Riemann zeta function satisfies a non-algebraic differential equation and constructs a differential equation of infinite order which zeta satisfies. However, as he notes in the paper, this representation is formal and Van Gorder does not attempt to claim a region or type of convergence. In this talk, we show that Van Gorder's operator applied to the zeta function does not converge pointwise at any point in the complex plane. We also investigate the accuracy of truncations of Van Gorder's operator applied to the zeta function and show that a similar operator applied to zeta and other $L$-functions does converge.

Random Matrix Theory Seminar

Speaker: Nathan Pagliaroli (Western)

"The Double Scaling Limit in RMT"

Time: 14:30

Room: MC 106

In this talk I will introduce the audience to what physicists call the "double scaling limit" of RMT invariant ensembles. In this double scaling limit the coupling constants of the model are taken to their "critical value" while simultaneously the matrix size N goes to infinity (the intuition behind this will be explored). The result is that the partition function forms a tau-function of a minimal model reduction of the Kkadamtsev-Petviashvili (KP) integrable hierarchy.

Transformation Groups Seminar

Speaker: Rafael Gomes (Western)

"Localization Theorem for Equivariant Cohomology"

Time: 09:00

Room: WSC 184 & online

Part 2: proof and examples

Meeting ID: 997 4840 9440 Passcode: 911104