Skip to content
# Events for 01/31/2020 from all calendars

## Several Complex Variables Seminar

## Probability Seminar

## Working Seminar on Quantum Computation and Quantum Information

## Algebra and Combinatorics Seminar

**Time: ** 10:20AM - 11:10AM

**Location: ** BLOC 605AX

**Speaker: **Shreedhar Bhat, Texas A&M University

**Title: ***Student reading seminar on reproducing kernels*

**Time: ** 11:30AM - 12:30PM

**Location: ** BLOC 628

**Speaker: **Sarai Hernandez-Torres, UBC

**Title: ***Scaling Limits of Uniform Spanning Trees in Three Dimensions*

**Abstract: **Wilson's algorithm allows efficient sampling of the uniform spanning tree (UST) by using loop-erased random walks. This connection gives a tractable method to study the UST. The strategy has been fruitful for scaling limits of the UST in the planar case and in high dimensions. However, three-dimensional scaling limits are far from understood. This talk is about recent advances on this problem. First, we will show that rescaled subtrees of the UST in three dimensions converge to a limiting object. Then we will describe the UST as a metric measure space. We will show that the scaling limit of the UST exists with respect to a Gromov-Hausdorff-type topology. This talk is based on joint work with Omer Angel, David Croydon, and Daisuke Shiraishi.

**Time: ** 1:30PM - 3:00PM

**Location: ** BLOC 624

**Speaker: **Priyanga Ganesan, TAMU MATH

**Title: ***Mixed states, Quantum Circuit Model*

**Time: ** 3:00PM - 3:50PM

**Location: ** BLOC 628

**Speaker: **Chelsea Drescher , University of North Texas

**Title: ***Invariants of polynomials modulo Frobenius powers and Hilbert series*

**Abstract: ** In 2017, Lewis, Reiner, and Stanton conjectured a connection between the modular general linear group and (q,t)-binomial coefficients. This conjecture was an analog to a theorem connecting the representation theory of rational Cherednik algebras for Coxeter groups and Catalan numbers. We will describe a local case - the invariant ring for groups reflecting about a fixed hyperplane acting on a polynomial ring modulo Frobenius powers. When the characteristic of the underlying field divides the order of the group, the subgroup fixing a reflecting hyperplane is a semi-direct product of diagonalizable reflections and transvections. The resulting Hilbert series counts the number of orbits of the group acting on a vector space, solving a special case of the Lewis, Reiner, Stanton conjecture.