Proposed Activities
Presentations at California State University, Fresno
- Colloquium speaker: Dr. Michael Bishop (6/12/2018) (Fresno State).
Title: Quantum Mechanics and the Riemann Hypothesis
Abstract: The Riemann Hypothesis states that all the non-trivial zeros of the Riemann Zeta function
lie on the line 1/2 + it in the complex plane. This has great implications for the distribution
of prime numbers and all of mathematics. The Hilbert-Polya approach to the Riemann Hypothe- ´
sis suggests that zeros of the Riemann Zeta function correspond to energies and trajectories of a
physical system. In a quantum mechanical context, this means the eigenvalues of an operator. I
will present a recent fascinating attempt by Bender, Brody, and Muller at the Riemann Hypothesis
using PT symmetry.
- Colloquium speaker: Dr. Erin Pearse (6/19/2018) (Cal Poly San Luis Obispo).
Title: Optimal transport, coarse curvature, and some applications
Abstract: I will discuss the optimal transport problem, its origins, and some different formulations.
Optimal transport makes it possible to develop a synthetic notion of Ricci curvature and
I will compare two recent approaches to this problem, and discuss how they provide a notion of
curvature which is valid for metric measure spaces which may carry no differentiable structure;
this includes graphs and Markov chains. We will discuss some applications of optimal transport
(and coarse Ricci curvature) to problems in computer science and machine learning
- Colloquium speaker: Dr. Tamer Oraby (6/26/2018) (University of Texas Rio Grande Valley)
Title: Mathematical Models in Epidemiology
about outbreaks; such as their potential to spread and become endemic, and the effect of different
control measures on that spread and on the population (in case of animal diseases). It also
explains human behavior towards some control measures like vaccination. In my presentation, I
will talk about some of those questions and show how mathematical modeling supported with data
has answered them.
- Colloquium speaker: Dr. Vincent Bonini (7/3/2018) (California Polytechnic State University, San Luis Obispo)
Title: Nonnegatively Curved Hypersurfaces in Hyperbolic Space
Abstract: The embedded and immersed hypersurfaces with various nonnegative
curvature conditions in Euclidean space and hyperbolic space are classical objects that
are studied in differential geometry. In this student centered talk, we will discuss the
setting and some of the basic tools that can be used to study hypersurfaces immersed
in hyperbolic space. In particular, we will discuss the geometry of horospheres in
hyperbolic space and the global correspondence theorem, which we have used to
extend classification theorems for nonnegatively curved embedded hypersurfaces in
hyperbolic space to the immersed setting.
- Colloquium speaker: Dr. Erwin Suazo (7/10/2018) (University of Texas Rio Grande Valley)
Title: On closed solutions for inhomogeneous linear and nonlinear Schrodinger equations and ¨
applications to optics.
Abstract: The mathematical analysis of Partial Differential Equations (PDEs) has been fundamental
to understanding how we can apply several PDEs to model real-life problems coming from
physics, chemistry, biology and the social sciences. In this presentation we will discuss multiparameter
solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation
which include oscillating laser beams in a parabolic waveguide. Also, by means of similarity
transformations we study exact analytical solutions for a generalized nonlinear Schrodinger
equation with variable coefficients. This equation appears in literature describing the evolution
of coherent light in a nonlinear Kerr medium, Bose-Einstein condensates phenomena and highintensity
pulse propagation in optical fibers. By restricting the coefficients to satisfy Ermakov-Riccati
systems with multi-parameter solutions, we present conditions for existence of explicit
solutions with singularities and a family of oscillating periodic soliton-type solutions. Also, we
show the existence of bright-, dark- and Peregrine-type soliton solutions, and by means of a computer
algebra system we exemplify the nontrivial dynamics of the solitary wave center of these
solutions produced by our multi-parameter approach.