Events for 03/01/2019 from all calendars
Working Seminar on Quantum Groups
Time: 10:30AM - 12:00PM
Location: BLOC 624
Speaker: Kari Eifler, TAMU
Title: Infinite dimensional representations
Combinatorial Algebraic Geometry
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
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
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
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
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
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.