Spring 2026
Tuesday, March 17, 2026
12:00 pm | Nursing Research Building, G39
Student: Johnathon Taylor
Advisor: Nick Gurski
Title: Controlled Theories and Infinity Lawvere Theories
Abstract: In this talk, we introduce a category whose objects are called controlled theories: the objects provide generalized presentations for Lawvere theories. We build a functor, called generalized machinery, that sends a connected diagram of controlled theories to an infinity Lawvere theory whose models present the categorification of the axioms for a connected diagram of controlled theories whose higher morphisms are invertible. We finish by using generalized machinery to define a model for Picard infinity groupoids, i.e a categorification for Abelian groups.
Monday, March 17, 2026
9:00 am | Nord Hall 212
Student: Mengchun Cai
Advisor: Mark Meckes & Stainslaw Szarek
Title: Quantitative Convergence Rates and Mesoscopic Information in Random Matrix Theory
Abstract: The central focus of this dissertation is on the non-asymptotic mesoscopic rate of convergence (ROC) regarding classic models from random matrix theory (RMT). Primary attention is given to the unitary Wishart matrices (or LUE) and Haar matrices in various classical compact groups. Utilizing the determinantal point structures of their eigenvalues or eigenangles, with respect to the L1-Wasserstein distance, we obtain the rate of convergence for ensembles towards different point process when the dimension of matrices N is sufficiently large. Specifically, for ensembles on the compact groups, the convergence rate towards the sine process-the bulk limiting process-is roughly of order N−2 on the unitary group and of order N−1 on the orthogonal group and the compact symplectic group. Additionally, the left edge spectrum of the Wishart matrix converges to the Bessel processes at a rate of order N−2 under the hard-edge condition, and to the Airy processes at a rate of order N−2 3 under the soft-edge condition. Our method of quantitative estimates for the trace class norm directly applies to other classic unitary ensembles in RMT, such as the GUE and the JUE and can be extended to point processes with particular structure, including the permanent point process and the α-DPP.
Monday, March 16, 2026
9:00 am | Nord Hall 211
Student: Andrew Edwards
Advisor: David Singer
Title: Symmetric Minimal Hypersurfaces in H^2 x H^2
Abstract: This dissertation establishes examples of minimal hypersurfaces in the space H² x H² analogous to the familiar helicoid and catenoid in R³. These submanifolds share the property that they can be foliated by flat 2-manifolds which are the product of constant-curvature curves in each factor. They may be classified according to their symmetry type, and different symmetry classes admit different behaviors. We demonstrate the existence of immersed hypersurfaces in all cases, discussing embeddedness and uniqueness within each symmetry class.
Fall 2025
Thursday, December 4, 2025
4:00 pm | Rockefeller 304
Student: Yinhui Liu
Advisor: Peter Thomas
Title: On the Effects of Molecular Fluctuations on Digital Logic Circuits Engineered from Genetic Regulatory Systems
Abstract: Recent efforts in synthetic biology have implemented elements of digital logic circuits such as logical negation, logical NOR, and set-reset latch in genetic circuits in genetically engineered bacteria. In this thesis, we consider the effects of molecular fluctuations arising from small copy numbers of the DNA, RNA, and proteins constituting these circuits. We use stochastic simulation methods to investigate the behavior of model systems representing logical negation, logical NOR, and set-reset latch. We study the effects of noise on the performance of these systems using a combination of information theory measures and first-passage time distributions. We conclude that it may be important to take stochastic effects into account when designing synthetic genetic circuits.