Friday October 19th - Saturday October 20th 2018
This is the first of an annual series workshop to showcase and celebrate excellence in research by women and other under-represented groups for the purpose of fostering and encouraging growth in the UC Riverside mathematical community.
After tea at 3:30 p.m. on Friday there will be two plenary talks, lasting until 5:00 pm, followed by a banquet in the Alumni Center 6:30 - 8:30 p.m. On Saturday there will be coffee and a poster session at 8:30 a.m., and then two parallel sessions on pure and applied mathematics, with talks at 9:30 a.m., 10:30 a.m., 11:30 a.m. , 1:00 p.m. and 2:00 p.m.
This program is co-sponsored by the University of California Office of President — Advancing Faculty Diversity and the Department of Mathematics, University of California at Riverside.
|Friday - Times||Event||Location|
|3:30 - 4:00 p.m.||Tea||HUB 260|
|4:00 - 5:00 p.m.||Catherine Searle||HUB 367|
|5:00 - 6:00 p.m.||Edray Goins||HUB 367|
|6:30 - 8:30 p.m.||Banquet at HUB Lawn||Bell Tower Lawn|
|Saturday - Times||Pure Math Event||Location||Saturday - Times||Applied Math Event||Location|
|8:30 - 9:30 a.m.||Coffee and Poster Session||Skye 282||8:30 - 9:30 a.m.||Coffee and Poster Session||Skye 282|
|9:30 - 10:30 a.m.||Jose Israel Rodriguez||Skye 268||9:30 - 10:30 a.m.||Bin Xu||Skye 284|
|10:30 - 11:30 a.m.||Pablo Solis||Skye 268||10:30 - 11:30 a.m.||Yuan Liu||Skye 284|
|11:30 a.m. - 1:00 p.m.||Lunch||Skye Patio||11:30 a.m. - 1:00 p.m.||Lunch||Skye Patio|
|1:00 - 2:00 p.m.||Xuwen Zhu||Skye 268||1:00- 2:00 p.m.||Tamar Shinar||Skye 284|
|2:00 - 3:00 p.m.||Christina Vasilakopoulou||Skye 268||2:00 - 3:00 p.m.||Betul Senay Aras||Skye 284|
Friday 4:00 p.m.
Title: Symmetries of Spaces with Lower Curvature Bounds
Abstract: The classification of manifolds of positive and non-negative sectional curvature is a long standing problem in Riemannian geometry. In particular, restricting our attention to closed, simply-connected manifolds, there are no topological obstructions that allow us to distinguish between positive and non-negative curvature, that is, we have no examples of manifolds that admit a metric of non-negative curvature that do not admit a metric of positive curvature. However, with the introduction of symmetries, we are able to distinguish between these two classes. In this context, I will discuss recent joint work with Christine Escher and work with Zheting Dong and Christine Escher on non-negatively curved manifolds with abelian symmetries.
Friday 5:00 p.m.
Title: Clocks, Parking Garages, and the Solvability of the Quintic: A Friendly Introduction to Monodromy
Abstract: Imagine the hands on a clock. For every complete the minute hand makes, the seconds hand makes 60, while the hour hand only goes one twelfth of the way. We may think of the hour hand as generating a group such that when we “move” twelve times then we get back to where we started. This is the elementary concept of a monodromy group.
In this talk, we give a gentle introduction to a historical mathematical concept which relates calculus, linear algebra, differential equations, and group theory into one neat theory called “monodromy”. We explore lots of real world applications, including why it’s so easy to get lost in parking garages, and present some open problems in the field. We end the talk with a discussion of how this is all related to solving polynomial equations, such as Abel’s famous theorem on the insolubility of the quintic by radicals.
Saturday, 8:30 a.m. - Coffee and Poster Session
Saturday, 9:30 a.m. - Pure Mathematics
Jose Israel Rodriguez, University of Chicago
Title: Numerical Descriptions of Algebraic Varieties
Abstract: Numerical algebraic geometry uses numerical algorithms to study sets defined by polynomials called algebraic varieties. It does this by representing a variety by a "witness set" which can be manipulated by a computer. I will discuss witness sets and examples relevant for chemistry, biology, and statistics. A background in algebraic geometry will not be assumed.
Saturday, 9:30 a.m. - Applied Mathematics
Title: Modeling Cell Polarity in Fission Yeast
Abstract: We present a mathematical model of the core mechanism responsible for the oscillatory dynamics of a signaling molecule (Cdc42) in fission yeast. The model is based on the competition of growth zones of Cdc42 localized at the cell tips for a common substrate that diffuses in the bulk. We analyze the bifurcations as the cell length increases and total amount of molecules increases. We find that a stable oscillation and a stable steady state can coexist, which is consistent with the experimental finding that only 50% of bipolar cells oscillate. Stochastic simulations suggest that noise can destabilize a steady state and quasi-cycles exist in the parameter regime where the deterministic model has a damped oscillation.
Saturday, 10:30 a.m. - Pure Mathematics
Title: Natural Cohomology on P1 x P1
Abstract: I’ll begin with a discussion of the classification of vector bundles on P1 and explain what natural cohomology means in this context. Then I’ll consider the case of vector bundles on P1 x P1. In general vector bundles on surfaces are more complicated but a useful tool allows one to reduce many problems about vector bundles to questions of linear algebra. This is the theory of monads. I’ll discuss monads and show how they are used to prove a conjecture of Eisenbud and Schreyer about vector bundles on P1 x P1 with natural cohomology.
Saturday, 10:30 am - Applied Mathematics
Title: Development of High Order Bound-Preserving Numerical Methods
Abstract: Hyperbolic equations have wide practical applications including fluid dynamics, astrophysics, biological sciences and many other areas. High order structure-preserving numerical methods, which can preserve certain properties of the underlying models are efficient for solving such partial differential equations. In this talk, we will discuss the bound-preserving property of hyperbolic equations, that is maximum-principle-preserving property for scalar conservation laws and positivity-preserving property for hyperbolic systems such as compressible Euler equations and ideal magnetohydrodynamic (MHD) equations. The first part of the talk is about a simple sweeping technique that can be generally used to construct high order bound-preserving finite difference/volume methods and spectral methods for scalar conservation laws. In the second part, we will utilize a parametrized flux limiter to develop high order finite difference/volume WENO schemes, which hold bound-preserving property for both scalar and system cases.
Saturday, 1:00 p.m. - Pure Mathematics
Title: Deformation Theory of Conical Metrics
Abstract: The problem of finding and classifying constant curvature metrics with prescribed singularities has a long history and has seen a lot of development. I will focus on the spherical conical metrics and describe recent work, joint with Rafe Mazzeo, which gives a new and broader existence theorem and shows that the nature of the moduli space of solutions has a different nature than had perhaps been anticipated. In particular, I will describe a new geometric construction of compactified configuration spaces that will enable us to tackle the obstructed analytic problem.
Saturday, 1:00 p.m. - Applied Mathematics
Title: Fluid-Structure Interaction: Numerical Algorithms and Applications
Abstract: Fluid-structure interaction problems arise in a variety of domains, including aerospace engineering, biomedical modeling, and physics-based animation. In this talk, I will give an overview of some approaches to simulation of fluid-structure interaction problems, highlighting recent work in my group on improved partitioned methods. I will also discuss some applications of numerical methods for fluid-structure interaction to the study of biological systems
Saturday, 2:00 p.m. - Pure Mathematics
Title: Hopf and Frobenius algebras: generalizations and the Larson-Sweedler Theorem
Abstract: Hopf and Frobenius algebras are of central importance in many branches of mathematics, especially representation theory and topology. The Larson-Sweedler theorem provides conditions under which a Hopf algebra is Frobenius. In this talk, we recall the concepts of Hopf and Frobenius algebra in the classical setting of vector spaces as well in any monoidal category. We also introduce their many-object generalizations: Hopf and Frobenius enriched categories. These let us prove a many-object version of the Larson-Sweedler theorem, which generalizes the classical one from vector spaces to broader contexts.
Saturday, 2:00 p.m. - Applied Mathematics
Betul Senay Aras, University of California, Riverside
Title: The Importance of the Eggshell During Polarization in the Early C. Elegans Embryo
Abstract: Polarization, whereby molecules and proteins are asymmetrically distributed throughout the cell, is a vital process for many cellular functions. In the early C. elegans embryo the asymmetric distribution of cell cytoskeleton during the initiation of polarization leads to asymmetric contractions which are higher in the anterior and lower in the posterior of a cell. The C. elegans embryo is surrounded by a rigid body, the eggshell, which functions in numerous cell processes. We investigate the structural support of the eggshell during the establishment phase by tracking the moving cell surface using phase field method. We incorporate reaction-diffusion model of protein dynamics involved in polarization into the membrane evolution. We conclude that the eggshell might have a role in cell polarization by preventing the distortion of cell surface.