## Seminars and Colloquia Schedule

### Graded rings with rational twist in prime characteristic

Series
Algebra Seminar
Time
Tuesday, October 26, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Florian EnescuGeorgia State

Prompted by the definition for the Frobenius complexity of a local ring of positive characteristic, we examine generating functions that can be associated to the twisted construction of a graded ring of positive characteristic. There is a large class of graded rings for which this generating function is rational. We will discuss this class of rings.  This work is joint with Yongwei Yao.

### Geometric bijections between subgraphs and orientations of a graph

Series
Graph Theory Seminar
Time
Tuesday, October 26, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
Zoom
Speaker
Changxin DingBrandeis University

Let $G$ be a connected finite graph. Backman, Baker, and Yuen have constructed a family of explicit and easy-to-describe bijections $g_{\sigma,\sigma^*}$ between spanning trees of $G$ and $(\sigma,\sigma^*)$-compatible orientations, where the $(\sigma,\sigma^*)$-compatible orientations are the representatives of equivalence classes of orientations up to cycle-cocycle reversal which are determined by a cycle signature $\sigma$ and a cocycle signature $\sigma^*$. Their proof makes use of zonotopal subdivisions and the bijections $g_{\sigma,\sigma^*}$ are called geometric bijections. Recently we have extended the geometric bijections to  subgraph-orientation correspondences. In this talk, I will introduce the bijections and the geometry behind them.

### Unknotting operations

Series
Research Horizons Seminar
Time
Wednesday, October 27, 2021 - 12:30 for 1 hour (actually 50 minutes)
Location
Skiles 006 / https://bluejeans.com/396232086/4264
Speaker
Hannah TurnerGeorgia Tech

Talk will be presented live as well as streamed. Questions will be fielded by the organizer.

We'll discuss various operations which can be applied to a knot to "simplify" or "unknot" it. Study of these "unknotting operations" began in the 1800s and continues to be an active area of research in low-dimensional topology. Many of these operations have applications more broadly in topology including to 3- and 4-manifolds and even to DNA topology. I will define some of these operations and highlight a few open problems.

### Automorphisms of B_n via Total Symmetry

Series
Geometry Topology Student Seminar
Time
Wednesday, October 27, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 (also in BlueJeans)
Speaker
Noah CaplingerGeorgia Tech

In this talk, I will present a proof of Dyer-Grossman's description of Aut(B_n) inspired by Kordek-Margalit's work classifying homomorphisms B_n' to B_n. Time permitting, I will also discuss how these techniques can be used to classify homomorphisms B_n to B_m.

### Many nodal domains in random regular graphs

Series
Stochastics Seminar
Time
Thursday, October 28, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Theo McKenzieBerkeley

If we partition a graph according to the positive and negative components of an eigenvector of the adjacency matrix, the resulting connected subcomponents are called nodal domains. Examining the structure of nodal domains has been used for more than 150 years to deduce properties of eigenfunctions. Dekel, Lee, and Linial observed that according to simulations, most eigenvectors of the adjacency matrix of random regular graphs have many nodal domains, unlike dense Erdős-Rényi graphs. In this talk, we show that for the most negative eigenvalues of the adjacency matrix of a random regular graph, there is an almost linear number of nodal domains. Joint work with Shirshendu Ganguly, Sidhanth Mohanty, and Nikhil Srivastava.

### Representation of Delta-matroids and the spinor varieties

Series
Algebra Student Seminar
Time
Friday, October 29, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tong JinGeorgia Tech

Delta-matroids are natural generalizations of matroids in which we replace each difference operator by the symmetric difference operator in the basis exchange axiom. I will briefly introduce (even) Delta-matroids and their representability. I will also discuss how they are related to the spinor varieties.

### Spectral Theory for Products of Many Large Gaussian Matrices

Series
CDSNS Colloquium
Time
Friday, October 29, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Boris HaninPrinceton University

Let X_{N,n} be an iid product of N real Gaussian matrices of size n x n. In this talk, I will explain some recent joint work with G. Paouris
(arXiv:2005.08899) about a non-asymptotic analysis of the singular values of X_{N,n} . I will begin by giving some intuition and motivation for studying such matrix products. Then, I will explain two new results. The first gives a rate of convergence for the global distribution of singular values of X_{N,n} to the so-called Triangle Law in the limit where N,n tend to infinity. The second is a kind of quantitative version of the multiplicative ergodic theorem, giving estimates at finite but large N on the distance between the joint distribution of all Lyapunov exponents of X_{N,n} and appropriately normalized independent Gaussians in the near-ergodic regime (N >> n).