Mathematics Colloquium Schedule

Fall 2019

 

Date: 10-11-2019 (12pm-1pm, F03-200A), Dr. Yunied Puig de Dios, University of California, Riverside.

Title: On the interplay of functional analysis and operator theory

Abstract: We overview some basic and striking facts concerning the theory of hypercyclic operators (considered to be born in 1982):

1. Hypercyclicity is a purely infinite-dimensional phenomenon: no finite dimensional space supports any hypercyclic operator;

2. It is not easy at all to determine whether a linear operator is hypercyclic. However, the set of hypercyclic operators is dense for the Strong Operator Topology in the algebra of linear and bounded operators;

3. Hypercyclicity is far from being an exotic phenomenon: any infinite-dimensional separable Frechet space supports a hypercyclic operator.

 

 

Summer 2019

 

Date: 06-03-2019 (2pm-3pm, F03-200A), Dr. Sudip Acharyya, University of Calcutta, India.

Title: Pseudocompact spaces -- Various Characterizations

Abstract: A topological space X for which C(X) = C*(X) is known as a pseudocompact space.  There are several equivalent descriptions of these spaces in terms of ideals, minimal ideals in the two rings C(X) and C*(X), and also certain subrings of C(X). Since these characterizations are of various types, it appears that there is possibly an unending flow of necessary and sufficient conditions, each equivalent to pseudocompactness.

 

 

Spring 2019
 

Date: 05-03-2019 (2pm-3pm, F03-200A), Dr. Jørgen Ellegaard Anderson, Aarhus University, Denmark.

Title: The Teichmüller TQFT

Abstract: After a five minute introduction to Topological Quantum Field Theory (TQFT), the talk will first cover a new diagrammatic way of representing triangulated three manifolds. Following this, the construction of the "Teichmüller TQFT" will be presented and in the particular case of knot complements, we will explain how the Teichmüller TQFT gives rise to a new knot invariant, which is a family (depending on Planck's constant) of functions defined on the real line. The talk will end with a discussion of our conjecture that the value of these functions at zero decays exponentially as Planck's constant goes to zero with the rate equal to the hyperbolic volume of the complement of the knot in the case of hyperbolic knots. This work was also presented at the ICM in Rio in 2018 and it is joint with Rinat Kashaev.

 

Date: 04-19-2019 (2pm-3pm, FO3-200A), Dr. Peyam Tabrizian, University of California, Irvine.

Title: Chemical Reactions and Diffusions

Abstract: In this colloquium talk, I present two PDE (Partial Differential Equations) models of a chemical reaction, and I will show that they are two different sides of the same coin: namely, the solutions of the one PDE converge to the solutions of the other. The proof of this fact is surprisingly elementary (but not easy!), because it just requires some integration by parts. If time permits, I will discuss some neat variations. This is based on joint work with Lawrence C. Evans.

 

Date: 04-12-2019 (12pm-1pm, F03-200A), Dr. David Wiygul, Department of Mathematics and Statistics, CSULB.

Title: Free-boundary Minimal Surfaces in the 3-ball with Connected Boundary

Abstract: After an overview of minimal surfaces and some associated boundary-value problems, I will briefly survey some existence and uniqueness results for free-boundary minimal surfaces in the three-dimensional ball and then focus on the first nontrivial construction (joint work with Nicos Kapouleas) of such surfaces having connected boundary.

 

Date: 03-08-2019 (12pm-1pm, F03-200A), Dr. Nick Johnson, Senior Researcher, DREME (Development and Research in Early Mathematics Education) Teacher Education at UCLA.

Title: Expanding Competence: Uncovering the Possibilities of Children’s Mathematical Thinking

Abstract: Young children are remarkably capable of making sense of and engaging in sophisticated mathematics. However, these rich understandings—which often present as partial, incomplete, or otherwise fragile—are often overlooked in research and practice. This presentation will explore how research on children’s thinking offers potential to broaden what is recognized as knowing and doing mathematics. Findings from studies of young children’s counting and teachers’ positioning of student contributions in classroom interactions will illustrate the socially constructed nature of competence, and how collective notions of competence shape opportunities for participation and learning.

 

 

 

 

Fall 2018
 

Date: 10-19-2018 (12pm-1pm, F03-200A), Dr. Naveen Vaidya, San Diego State University.

Title: Mathematical Models of Human Immunodeficiency Virus Reservoirs

Abstract: Despite the tremendous success of highly active antiretroviral therapy (HAART) for the treatment of Human Immunodeficiency Virus (HIV), there is no cure for HIV yet due to presence of viral reservoirs such as latently infected CD4+ memory T cells and infected brain cells. In this talk, I will present mathematical models of HIV reservoirs that accurately predict observations in experimental data from HIV infected humans and SIV (Simian Immunodeficiency Virus) infected macaques. First, I use the models to show that the latent infection can be limited by early ART during acute HIV infection. However, this effect can be influenced by the drug pharmacodynamics properties showing that the choice of drugs in ART is a key to successful cure via early therapy. Second, I use the models to estimate key parameters related to the brain infection, including virus-transfer across blood-brain barrier. The model analysis helps to provide a threshold for the establishment of infection, and to compare the viral infection dynamics in the brain with that in the plasma.

Date: 10-12-2018 (12pm-1pm, F03-200A), Dr. Curtis Bennett, Dean, CNSM, CSULB.

Title: Fibonacci and Lucas Analogues of Binomial Coefficients and What They Count

Abstract: In this talk we will first introduce and provide a little history of the Fibonomials. Next we provide a simple (and more useful than previous interpretations) description of an object the Fibonomials enumerate. We will use this new object to prove various Fibonomial analogues of standard identities on binomial coecients and discuss further generalizations using the Lucas numbers. Full Abstract