Events for 09/16/2022 from all calendars

Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: ZOOM

Speaker: Omar Mohsen , Paris-Saclay University

Title: Characterization of Maximally Hypoelliptic Differential Operators Using Symbols, and Index Theory

Abstract: In this talk we will give an introduction to maximally hypoelliptic differential operators. This is a class of differential operators generalizing elliptic operators and includes operators like Hormander’s sum of squares. We will present our work where we define a principal symbol and show that maximally hypoellipticity is equivalent to invertibility of our principal symbol generalizing the classical regularity theorem for elliptic operators. We will also give a topological index formula for maximally hypoelliptic differential operators using our symbol. Explicit examples of index computations will be included at the end. This talk is based on joint work with Androulidakis and Yuncken.

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Student/Postdoc Working Geometry Seminar

Time: 1:30PM - 2:30PM

Location: BLOC 628

Speaker: Vincent Steffan, TAMU and Copenhagen

Title: Quantum information theory news from Copenhagen

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Youngho Yoo, TAMU

Title: A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups

Abstract: Erdős and Pósa showed in 1965 that cycles obey an approximate packing-covering duality. While odd cycles do not satisfy such a duality, Reed proved that the only obstruction is the presence of a certain projective planar grid. In this talk we discuss generalizations of these results. Namely, in undirected group-labelled graphs, we characterize the topological obstructions to the Erdős-Pósa property of cycles with "allowable" group values, under some additional assumptions on the structure of the set of allowable values. This recovers many known results in the area and resolves a question of Dejter and Neumann-Lara from 1987 on characterizing when cycles of length L mod M satisfy the Erdős-Pósa property. Joint work with Pascal Gollin, Kevin Hendrey, O-joung Kwon, and Sang-il Oum.

Geometry Seminar

Time: 4:00PM - 4:50PM

Location: BLOC 302

Speaker: Thomas Yahl, Texas A&M University

Title: Computing Galois groups of Fano problems

Abstract: A Fano problem consists of enumerating linear spaces of a fixed dimension on a variety, generalizing the classical problem of the 27 lines on a smooth cubic surface. Those Fano problems with finitely many linear spaces have an associated Galois group that acts on these linear spaces and controls the complexity of computing them in coordinates via radicals. Galois groups of Fano problems have been studied both classically and modernly and have been determined in some special cases. We use computational tools to prove that several Fano problems of moderate size have Galois group equal to the full symmetric group, all of which were previously unknown.