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Texas A&M University
Mathematics

Events for 03/01/2019 from all calendars

Working Seminar on Quantum Groups

iCal  iCal

Time: 10:30AM - 12:00PM

Location: BLOC 624

Speaker: Kari Eifler, TAMU

Title: Infinite dimensional representations


Combinatorial Algebraic Geometry

iCal  iCal

Time: 11:00AM - 11:50AM

Location: Bloc 605AX

Speaker: Taylor Brysiewicz, Texas A&M University

Title: Solving equations using monodromy

Abstract: Given a zero-dimensional parametrized polynomial system in variables x and parameters c the projection f : X -> C_c forms a branched cover where the fibre over any parameter c′ is the finite set of solutions to the system restricted to c′. If D is the branch locus of this map, the fundamental group pi_1(C_c-D,c′) based at c′ acts on the fibre over c′ via analytic continuation which induces a set of permutations called the monodromy group of f.

While the computations of monodromy groups are interesting in their own right, leveraging the monodromy group to compute the fibres of f has proven to be quite effective. Recently, there has been serious improvements to monodromy solving algorithms and software. I will discuss these monodromy algorithms as well as their applications.


Working Seminar in Groups, Dynamics, and Operator Algebras

iCal  iCal

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Xin Ma, Texas A&M University

Title: Topological full groups of one-sided shifts of finite type XI


Algebra and Combinatorics Seminar

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Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Benjamin Briggs, University of Utah

Title: Reflection Groups and Derivations

Abstract: If you start with a polynomial ring (say over the complex numbers) and you factor out by the ideal generated by symmetric polynomials (of positive degree), then you get a very interesting ring. For example, it is isomorphic to the cohomology ring of a flag manifold.

How many derivations does this ring have (i.e. what is the dimension of the space of C-linear derivations)? The ring is also graded: how many derivations does it have in each degree? These are tricky to count, but it turns out there is a surprisingly nice formula. You get this formula by writing down a free resolution of the module of derivations, which for some reason turns out to be periodic.

You can do all this by messing around with symmetric polynomials (but the combinatorics get quite complicated). It turns out though that this all works for certain reflection groups (all the real reflection groups included, and some complex reflection groups). I'll talk about this too, mainly focusing on the symmetric group example.


Student Working Seminar in Groups and Dynamics

iCal  iCal

Time: 3:00PM - 4:00PM

Location: BLOC 246

Speaker: James O'Quinn

Title: The Ornstein-Weiss Quasitiling Theorem

Abstract: The Ornstein-Weiss Quasitiling Theorem roughly states that approximately invariant finite subsets of a group can almost be tiled by translates of finitely many subsets of the group with nice invariance properties. I will discuss the ideas behind this theorem and give a proof for it.


Linear Analysis Seminar

iCal  iCal

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Roy Araiza, Purdue University

Title: On operator systems and matrix convexity

Abstract: Operator systems (self-adjoint unital subspaces of C*-algebras) had been looked as early as the 1970's. As early as the 1980's, operator algebraists realized that there was a rich theory in noncommutative convexity (matrix convexity). Though it was not until 1999 that it was noticed by Webster and Winkler that operator systems and compact matrix convex sets were intimately connected. Using Webster-Winkler duality and noncommutative Choquet theory, we have been able to present a new way in looking at Choquet points of finite-dimensional compact matrix convex sets. We will begin by reviewing noncommutative convex theory and Webster-Winkler duality. Operator system tensor products will be reviewed (if needed). As time permits we will then discuss Choquet points of finite-dimensional compact matrix convex sets. This is joint work with Adam Dor-On and Thomas Sinclair.


Geometry Seminar

iCal  iCal

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Visu Makam, IAS

Title: Exponential degree lower bounds for invariant rings

Abstract: The ring of invariants for a rational representation of a reductive group is finitely generated and graded. We give a general technique that can be used to show that an invariant ring is not generated by invariants of small degree. The main ingredients are Grosshans principle and the moment map, which I will explain. As an example, we apply this technique to show "exponential" lower bounds for the action of SL(n) on 4-tuples of cubic forms.