University of California, Santa Barbara
Fall 2022 - Seminar in Applied Mathematics
The UCSB student chapter of the Society for Industrial and Applied Mathematicians (SIAM) will host a weekly, interdisciplinary seminar to provide a forum for graduate students to discuss their research in an informal setting. This is a great outlet to polish your presentation skills in front of a general (technical) audience.
If you are interested in giving a talk during this seminar, please send an email to siam@math.ucsb.edu with a potential title, abstract, and when you would like to speak.
All are welcome to attend, cookies and coffee provided.
When: Mondays 2-3
Where: South Hall 6635
Date |
Fall 2022 Schedule |
September 26th | Organizational Meeting |
October 10th | Speaker: Rafael Lainez Reyes (Math) Title: Concentration Compactness Developed by P.L Lions in a series of papers, the Concentration Compactness Principle characterizes the convergence behavior of measures in L1. It has many important applications in problems arising in Calculus of Variations and Differential Equations. In this talk we will go over the main ideas of the principle. |
October 17th | Speaker: Joel Pion (Math) Title: Quantum Unconstrained Binary Optimization In this talk I will talk about problems we can solve on a quantum annealing device. We will treat the quantum annealer itself as a black box and will only consider the problem it solves, that of Quadratic Unconstrained Binary Optimization (QUBO). The main focus of the talk will be about how to take other problems we care about (mostly graph algorithm type problems) and convert them to QUBOs. The algorithm we will spend the most time on will be the Chinese Postman Problem (which is similar to the Traveling Salesman Problem). |
October 24th | Speaker: Rafael Lainez Reyes (Math) Title: Numerics and the Hartree-Fock Equations In this talk we will go over some of the numerical complications that arise when trying to obtain approximations to the Hartree-Fock equations. While this set of equations will be the focus of the talk, some of the ideas have extensions to other nonlinear problems. |
October 31th | Speaker: Micah Pedrick (Math) Title: Dissintigration of Measures |
November 7th | Speaker: Christian Hong (Math) Title: The Gagliardo-Nirenberg Inequality The Gagliardo-Nirenberg Inequality is a generalization of the usual Sobolev inequality. In this talk, we will focus on applications of the Gagliardo-Nirenberg Inequality to some nonlinear PDEs. In particular, we will discuss a regularity result for the Inviscid Burger's Equation and the Nonlinear Schrodinger Equation. |
November 14th | Speaker: Zach Wagner (Math) Title: Relativistic Quantum Mechanics Through Applications of Dirac Theory The Dirac Operator describes the motion of a relativistic particle. Its properties lead to interesting mathematical problems in relativistic quantum mechanics. In particular, one is led to study energy functionals analogous to the Hartree-Fock energy functional. We will discuss one such relativistic energy functional and methods which have been used to describe its critical points and derive their non-relativistic limit. We will then discuss extensions of these results to electrons in a self-generated magnetic field. |
November 21st | No Seminar |
November 28th | Speaker: Jimmie Adriazola (Math) Title: Applications of the Riemann-Hilbert Problems Riemann-Hilbert problems arise frequently in many different areas of applied analysis. During this talk, I will give a standard formulation of the Riemann-Hilbert problem and connect the framework with problems involving computation of special functions, the theory of orthogonal polynomials, and the inverse scattering transform for integrable equations. |
December 5th | No Seminar |