Geometry and Combinatorics

Speaker: Johannes Hofscheier (University of Nottingham)

"Experimenting with polytopes: exploring the landscape of lattice polytopes"

Time: 13:30

Room: Zoom

Algebraic geometry and combinatorics have a long-established culture of producing and interrogating classification datasets. These datasets can be at the limit of current computing resources, e.g., the Kreuzer-Skarke classification has almost half-a-billion entries. The time is ripe to explore the landscape of algebra-geometric datasets by means of data science techniques. In this talk, I will report on initial joint work with Bao, He, Hirst, Kasprzyk, and Majumder investigating the effectiveness of machine learning (ML) methods for predicting properties of Hilbert series and lattice polytopes. Our results support the idea that in many cases a mathematical theorem underlies ML predictions of high accuracy. Furthermore, our observations show that ML can also provide hints to new exciting and unexpected relations.

Random Matrix Theory Seminar

Speaker: Masoud Khalkhali (Western)

"Topological expansion for matrix integrals IV"

Time: 14:30

Room: MC 106

Feynman rules, 1-particle irreducible graphs, effective action and Legendre transform.

Algebra Seminar

Speaker: Khanh Nguyen Duc (Otto-von-Guericke-University Magdeburg)

"The relations between Littlewood-Richardson coefficients and its shifted version"

Time: 14:30

Room: ZOOM (968 6609 0477)

We give a new interpretation of the shifted Littlewood-Richardson coefficients $f_{\lambda\mu}^\nu$ ($\lambda,\mu,\nu$ are strict partitions). The coefficients $g_{\lambda\mu}$ which appear in the decomposition of Schur $Q$-function $Q_\lambda$ into the sum of Schur functions $Q_\lambda = 2^{l(\lambda)}\sum\limits_{\mu}g_{\lambda\mu}s_\mu$ can be considered as a special case of $f_{\lambda\mu}^\nu$ (here $\lambda$ is a strict partition of length $l(\lambda)$). We also give another description for $g_{\lambda\mu}$ as the cardinal of a subset of a set that counts Littlewood-Richardson coefficients $c_{\mu^t\mu}^{\tilde{\lambda}}$. This new point of view allows us to establish connections between $g_{\lambda\mu}$ and $c_{\mu^t \mu}^{\tilde{\lambda}}$. More precisely, we prove that $g_{\lambda\mu}=g_{\lambda\mu^t}$, and $g_{\lambda\mu} \leq c_{\mu^t\mu}^{\tilde{\lambda}}$. We conjecture that $g_{\lambda\mu}^2 \leq c^{\tilde{\lambda}}_{\mu^t\mu}$ and formulate some conjectures on our combinatorial models which would imply this inequality if it is valid. We present an approach using Fomin diagrams and Viennot's geometric construction for RSK correspondence to attack the conjecture.

Transformation Groups Seminar

Speaker: Kumar Sannidhya Shukla

"The Weil model for the equivariant de Rham cohomology of $G$-manifolds, III"

Time: 09:30

Room: online

Last time we described the Weil model for circle actions and showed that it is isomorphic to polynomial ring with coefficients in invariant forms. This week, we will prove the Cartan-Weil Isomorphism for general connected Lie groups and determine the Cartan differential. Then we will determine the Cartan model for torus actions. Lastly, we will compute the equivariant cohomology for torus action on a point.

Meeting ID: 997 4840 9440 Passcode: 911104

Random Matrix Theory Seminar

Speaker: Nathan Pagliaroli (Western)

"Matrix integrals and Maps"

Time: 14:30

Room: MC 106

In this talk we will return our attention to matrix integrals and maps. I will review the definition and compare to the Feynman integrals previously discussed.

GAP Seminar

Speaker: Rasul Shafikov (Western)

"Survey of local theory of singular Levi-flat hypersurfaces"

Time: 10:30

Room: MC 108

Levi-flat hypersurfaces are important in the context of minimal sets of holomorphic foliations in complex projective spaces. It is well-known that closed smooth real analytic Levi-flats do not exist in $\mathbb C \mathbb P^n$ for $n>2$, and it is an open problem if such hypersurfaces exist in $\mathbb C \mathbb P^2$. On the other hand, singular real-analytic Levi-flats exist in any dimension, and we discuss some recent developments in this subject.

Algebra Seminar

Speaker: Senate meeting - no Algebra Seminar

"No Talk"

Time: 14:30

Room:

Random Matrix Theory Seminar

Speaker: Hamed Hessam (Western)

"Schwinger-Dyson Equations"

Time: 14:30

Room: MC 106

In this talk we shall derive Tutte's Recursion from 1 marked boundary planar maps. We shall then obtain the Schwinger-Dyson Equations (SDEs) and give a matrix model proof of Tutte's Recursion, and time permitting, we will study higher genus Tutt's Recursions.

GAP Seminar

Speaker: Hamed Hessam (Western)

"Bootstrapping Dirac Ensembles"

Time: 10:30

Room: MC 108

In this talk we will see a technique called bootstraps can be applied to find the moments of a single matrix and two-matrix models taken from finite noncommutative geometries. We will discuss the relationships between the order parameter of the model and the second moment. From there all other moments are able to be expressed as in terms of the order parameter and the second moment, allowing them to be computed. This work is based on the joint paper of mine with Masoud Khalkhali and Nathan Pagliaroli.

Algebra Seminar

Speaker: Rachel Davis (The University of Wisconsin-Madison)

"The Galois action on the exceptional curves of del Pezzo surfaces"

Time: 14:30

Room: ZOOM

This talk will be a survey of literature about the Galois action on exceptional curves on del Pezzo surfaces. We will begin by discussing the permutation of the 27 lines on a cubic surface and giving examples. Other examples are the 28 bitangents on a quartic plane curve and the 240 (-1)-curves on a degree 1 del Pezzo surface. The story will reference work by Carter, Corn, Elsenhans-Jahnel, Kulkarni, Shioda, and Varilly-Alvarado.

Random Matrix Theory Seminar

Speaker: Hamed Hessam (Western)

"Schwinger-Dyson Equations Part 2"

Time: 14:30

Room: MC 106

In this talk we shall derive Tutte's Recursion from 1 marked boundary planar maps. We shall then obtain the Schwinger-Dyson Equations (SDEs) and give a matrix model proof of Tutte's Recursion, and time permitting, we will study higher genus Tutt's Recursions.

GAP Seminar

Speaker: Nathan Pagliaroli (Western)

"Dirac Ensembles"

Time: 10:30

Room: MC 108

In this talk I will give a brief introduction to random matrix theory and Dirac ensembles. We will discuss their spectral statistics, relationship to random matrix ensembles, and the use of a procedure known as "Topological Recursion".

Algebra Seminar

Speaker: Xuan Kien Phung (UQAM | Universite du Quebec a Montreal)

"On Noetherian group rings and linear symbolic dynamics"

Time: 14:30

Room: ZOOM

Abstract: In this talk, we will explain recent finiteness results in the theory of linear symbolic dynamics. These results allow us to reformulate in the language of symbolic dynamics the very old classification problem of all groups whose group rings are Noetherian. If time permits, we will also mention another application on the shadowing property of linear cellular automata.

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: