Events for 11/11/2024 from all calendars

Combinatorial Algebraic Geometry

Time: 11:00AM - 11:50AM

Location: Bloc 302

Speaker: CJ Bott, Texas A&M University

Title: Computation of Schubert Galois Groups

Abstract: While Galois Theory may be familiar in the contexts of solving equations and studying field extensions, many do not know that historically Galois Theory was deeply connected to enumerative geometry. We review Galois groups geometrically in this way, and describe our study of computing Galois groups in the setting of Schubert Calculus.
This is a practice talk for a job interview.

Mathematical Biology Seminar

Time: 1:00PM - 2:00PM

Location: BLOC 302

Speaker: Daniel Gomez, University of New Mexico

Title: Spikes and Small Targets with Lévy Flights

Abstract: The fractional order “s” of a Lévy flight controls the algebraic decay of its corresponding jump length distribution. When the fractional order s is s>1/2 , s=1/2, or s<1/2 the corresponding one-dimensional Lévy flights is qualitatively similar to Brownian motion in one-, two-, and three-dimensions. In this talk I will describe how this correspondence emerges in the asymptotic analysis of two fractional problems: the characterization of spike equilibrium solutions to singularly perturbed reaction-diffusion systems, and the analysis of the first hitting-time (FHT) for a Lévy flight to a small target. These two fractional problems are inspired by questions in pattern formation and optimal foraging theory. Our asymptotic results provide qualitative insights into how the fractional order affects the linear stability of spike solutions, as well as how target sparsity determines the optimal fractional order minimizing the first hitting-time.

Applied Math Seminar

Time: 1:00PM - 2:00PM

Location: BLOC 302

Speaker: Daniel Gomez, University of New Mexico

Title: Spikes and Small Targets with Lévy Flights

Abstract: The fractional order “s” of a Lévy flight controls the algebraic decay of its corresponding jump length distribution. When the fractional order s is s>1/2 , s=1/2, or s<1/2 the corresponding one-dimensional Lévy flights is qualitatively similar to Brownian motion in one-, two-, and three-dimensions. In this talk I will describe how this correspondence emerges in the asymptotic analysis of two fractional problems: the characterization of spike equilibrium solutions to singularly perturbed reaction-diffusion systems, and the analysis of the first hitting-time (FHT) for a Lévy flight to a small target. These two fractional problems are inspired by questions in pattern formation and optimal foraging theory. Our asymptotic results provide qualitative insights into how the fractional order affects the linear stability of spike solutions, as well as how target sparsity determines the optimal fractional order minimizing the first hitting-time.

Geometry Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Ian Anderson, Utah State University

Title: The DifferentialGeometry Software Project.

Abstract: The DG software consists of a comprehensive collection of Maple packages for computations in differential geometry, Lie theory and mathematical physics. It is particularly well-suited for the computation and analysis of symmetries of geometric structures; for coordinate-free calculations on homogeneous spaces; and for applications of the variational calculus. In this seminar, I provide an overview of the software project and demonstrate some of its important functionalities. The software is available at https://digitalcommons.usu.edu/dg/

Departmental Colloquia

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Wanlin Li

Title: Prime distribution and arithmetic of curves

Abstract: The distribution of primes among congruence classes is one of the most classical and influential problems in number theory. The question of whether there are more primes of the form 4k+1 or 4k+3 leads to the construction of Dirichlet characters, L-functions, and the study of analytic number theory. In this talk, I will discuss the study of Chebyshev's bias and the set of zeros of Dirichlet L-functions over global function fields. These studies can be viewed from a geometric perspective as studying the arithmetic of algebraic curves defined over finite fields. I will introduce the notion of ``supersingular'' and discuss the distribution of supersingular curves in algebraic families and in reductions of curves defined over number fields.