Event Date: Monday April 25, 2022 - 2:00pm, GAB 461

Speaker: Jonathan Cohen (UNT)

Title: Equidistribution results in number theory

Abstract: We will consider some classical and modern results of equidistribution related to prime numbers. In particular, we will discuss Dirichlet's theorem, Chebotarev's density theorem, the Sato-Tate conjecture, and the intimate relation of these types of results to L-functions.

Event Date: Monday April 11, 2022 - 4:00pm, GAB 461

Speaker: Joseph Zielinski (UNT)

Title: The actions of some non-locally compact groups

Abstract:

The broader theme of this talk concerns the relationship between two notions of complexity in a topological group. On the one hand, there is the complexity of the topological group structure itself and, on the other, the complexities of the orbit equivalence relations of its continuous actions. This relationship has been explored for many types of topological group complexities by numerous mathematicians over the last few decades. We will also discuss, more specifically, work done on this matter when the topological complexity in question is the failure of local compactness in certain classes of Polish groups. This involves work with A.S. Kechris, M. Malicki, and A. Panagiotopoulos.

Event Date: Tuesday February 1, 2022 - 2:30pm

Special Millican Colloquium Talk

Event Date: Tuesday February 3, 2022 - 2:30pm

Special Millican Colloquium Talk

Event Date: Tuesday February 10, 2022 - 2:30pm

Special Millican Colloquium Talk

Event Date: Tuesday February 11, 2022 - 2:30pm

Special Millican Colloquium Talk

Event Date: Monday Novemeber 8, 2021 - 4:00 pm

Speaker: Houston Schuerger (Trinity College)

Title: Zero Forcing and Vertex Induced Subgraphs

Abstract: Zero forcing is a coloring propagation process on finite graphs, which can be considered a one player game. In this talk we will consider recent findings in zero forcing concerning monotonicity. While the zero forcing number of a graph is not monotone with respect to its subgraphs, we can still use certain graph substructures created during the propagation process to preserve a sense of monotonicty. We will consider this problem from two directions, first we will look at the vertex induced subgraphs associated with cut-sets of a graph, and second we will construct supergraphs from sequences of graphs in a way prescribed by another graph theoretical game with roots in the work of Erdos.

Event Date: Monday, November 1, 2021 - 4:00 pm

Speaker: Xuexia Wang (Associate Professor in Statistics, the University of North Texas)

Title: A Novel Powerful Gene Based Association Test Using GWAS Summary Data

Abstract: Gene-based association tests provide a useful alternative and complement for the traditional single variant association tests in genome-wide association studies (GWAS). Using appropriate weights (pre-specified or eQTL-derived) can boost statistical power, especially for detecting weak associations between genes and a trait. However, the sparsity level of a trait (e.g. the number of causal variants/sample size) or directions of the underlying associations in real data is often unknown. In addition, access to individual-level data is often limited. To resolve the existing limitations, we propose an optimally weighted combination (OWC) test based on summary statistics from GWAS. We analytically prove that aggregating the variants in one gene is the same as using the weighted combination of Z-scores for each variant based on the score test method. We also empirically illustrate that our proposed test outperforms several existing methods via simulation studies. A number of traditional gene based tests such as burden tests, the weighted sum of squared score (SSU) test, the weighted sum statistic (WSS), and the score test are the special cases of the proposed test. Lastly, we utilize schizophrenia GWAS data and a fasting glucose GWAS meta-analysis data to demonstrate that our method outperforms the existing methods in real data analyses.

Event Date: Friday, October 29, 2021 - 4:00 pm

Speaker: Mark Gockenbach (University of Delaware)

Title: Tikhonov regularization, parameter choice rules, and convergence

Abstract: Tikhonov regularization is the most popular general-purpose method for regularizing linear inverse problems. It requires the choice of a scalar regularization parameter, and methods for automatically choosing this parameter have been an active area of study for many years. I will describe the difficulties associated with choosing the regularization parameter and discuss my own work related to this question.

Event Date: Friday, October 22, 2021 - 4:30 pm

Speaker: Ignat Soroko (Florida State University)

Title: Divergence in Coxeter groups

Abstract: Divergence of a metric space is an interesting quasi-isometry invariant of the space which measures how geodesic rays diverge outside of a ball of radius r, as a function of r. Divergence of a finitely generated group is defined as the divergence of its Cayley graph. For symmetric spaces of non-compact type the divergence is either linear or exponential, and Gromov suggested that the same dichotomy should hold in a much larger class of non-positively curved CAT(0) spaces. However this turned out not to be the case and we now know that the spectrum of possible divergence functions on groups is very rich. In a joint project with Pallavi Dani, Yusra Naqvi, and Anne Thomas, we initiate the study of the divergence in the general Coxeter groups. We introduce a combinatorial invariant called the `hypergraph index', which is computable from the Coxeter graph of the group, and use it to characterize when a Coxeter group has linear, quadratic or exponential divergence, and also when its divergence is bounded by a polynomial.

Event Date: Monday, September 13, 2021 - 4:00pm

Speaker: Nam Trang

Title: Ideals and Determinacy

Abstract: We present some new results regarding the equiconsistency of strong ideals and strong determinacy theories. Ideals and determinacy are two foundational frameworks in set theory and these results give the bi-interpretability between one framework and the other (up to a certain complexity). In particular, one of our theorems answers a variation of a well-known conjecture by Woodin and completes a major research direction in descriptive inner model theory that started by R. Ketchersid in his thesis some 20 years ago. We will give background and history that lead up to these results as well as future research along this direction. This is joint work with G. Sargsyan and T. Wilson.