Events for 11/15/2024 from all calendars

Combinatorial Algebraic Geometry

Time: 10:20AM - 11:10AM

Location: Bloc 302

Speaker: Suhan Zhong, Texas A&M University

Title: Polynomial Optimization in Data Science Under Uncertainty

Abstract: TBD

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Iulia Cristian, University of Bonn

Title: Coagulation equations describing rain and sedimentation

Abstract: Coagulation equations describe the evolution in time of a system of particles that are characterized by their volume. Multi-dimensional coagulation equations have been used in recent years in order to include information about the system of particles which cannot be otherwise incorporated. Depending on the model, we can describe the evolution of the shape, chemical composition or position in space of clusters. In this talk, we focus on a model that is inhomogeneous in space and contains a transport term in the spatial variable modeling the sedimentation of clusters. We prove local existence of mass-conserving solutions for a class of coagulation rates for which in the space homogeneous case instantaneous loss of mass occurs. This is based on a joint work with B. Niethammer and J J. L. Velázquez.

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 302

Speaker: Moxuan (Jasper) Liu, UCSD

Title: Matrix Loci and Orbit Harmonics

Abstract: Consider the affine space of n by n complex matrices with coordinate ring C[x_{n*n}]. We define graded quotients of C[x_{n*n}] where each quotient ring carries a group action. These quotient rings are obtained by applying the orbit harmonics method to matrix loci corresponding to the permutation matrix group S_n, the colored permutation matrix group S_{n,r}, the collection of all involutions in S_n, and the conjugacy classes of involutions in S_n with a given number of fixed points. In each case, we explore how the algebraic properties of these quotient rings are governed by the combinatorial properties of the matrix loci. Based on joint work with Yichen Ma, Brendon Rhoades, and Hai Zhu.

Departmental Colloquia

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Tao Mei

Title: Tossing Coins and the Khintchine Inequalities

Abstract: The simple act of tossing coins exemplifies one of the most fundamental models of independent and identically distributed (i.i.d.) random variables. In this talk, we will explore the classical Khintchine inequalities, which provide essential bounds on the moments of sums of i.i.d. symmetric random variables. These inequalities, rooted in probability theory, reveal unexpected depth in the behavior of random processes and serve as a bridge connecting probability, harmonic analysis, and number theory. We will journey through the historical development, key proofs, and significant implications of these inequalities, while also presenting some of my recent research contributions that extend and apply Khintchine's results. Portions of this talk are based on joint work with Chuah, Liu, Junge, and Parcet. No prior expertise in advanced probability theory will be assumed.