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Texas A&M University

Events for 04/11/2022 from all calendars

Geometry Seminar

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Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Markus Hunziker, Baylor University

Title: Classical invariant theory, Hermitian symmetric spaces, and covariant differential operators

Abstract: Classical invariant theory is concerned with the explicit calculation of syzygies of rings of invariants and modules of covariants for the classical groups. In this talk, I will explain how some of these computations can be organized by using a diagrammatic description of certain highest weight categories related to Hermitian symmetric spaces. I will then show how this approach leads to the solution of several previously open problems in invariant theory. If time permits, I will also explain how the boundary maps of the minimal free resolutions of modules of covariants correspond to so-called covariant differential operators (which are matrix-valued differential operators between holomorphically induced representations.)

Colloquium: The Dynamics of Boolean Networks

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Time: 4:00PM - 5:00PM

Location: Bloc 117

Speaker: Reinhard Laubenbacher, University of Florida

Description: A Boolean network in n variables is a function from the set of binary strings of length n to itself, defined through n Boolean rules. Boolean networks are used in several applications, from electrical engineering to systems biology. Aside from their usefulness, there are many interesting mathematical questions about their properties. Perhaps the most fundamental one is about the relationship between the structure of the Boolean rules in the network, its “genotype,” and the resulting dynamics, its “phenotype,” in the language of biology. Boolean rules can be viewed as polynomials over the field with two elements, making them amenable to analysis using computational algebra. As a result, research motivated by these questions leads to a rich interplay between combinatorics, computer algebra, and dynamical systems theory, motivated by concepts from biology. This talk will present some results in this field and discuss some open problems. In particular, it will explore a mathematical instantiation of the well-known property of biological systems that they display a modular structure.

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Spectral Theory Reading Seminar

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Time: 4:00PM - 5:00PM

Location: Zoom