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# Mathematics Colloquium Schedule

**Fall 2015 **

**Date: 9-11-2015 (12-1pm, F03-200A), Dr. Hui Sun, UCSD**

**Title:** Numerical Simulation of Solvent Stokes Flow and Solute-Solvent Interface Dynamics

**Abstract:** Fundamental biological molecular processes, such as protein folding, molecular recognition, and molecular assemblies, are mediated by surrounding aqueous solvent (water or salted water). Continuum description of solvent is an efficient approach to understanding such processes. In this work, we develop a solvent fluid model and computational methods for solvent dynamics and solute-solvent interface motion. The key components in our model include the Stokes equation for the incompressible solvent fluid which governs the motion of the solute-solvent interface, the ideal-gas law for solutes, and the balance on the interface of viscous force, surface tension, van der Waals type dispersive force, and electrostatic force. We use the ghost fluid method to discretize the flow equations that are reformulated into a set of Poisson equations, and design special numerical boundary conditions to solve such equations to allow the change of solute volume. We move the interface with the level-set method. To stabilize our schemes, we use the Schur complement and least-squares techniques. Numerical tests in both two and three-dimensional spaces will be shown to demonstrate the convergence of our method, and to demonstrate that this new approach can capture dry and wet hydration states as observed in experiment and molecular dynamics simulations.

**Date: 10-09-2015 (12-1pm, F03-200A), Dr. Andrew J. Bernoff, Harvey Mudd College**

**Title:** Energy driven pattern formation in thin fluid layers: The good, the bad and the beautiful

**Abstract:** A wide variety of physical and biological systems can be described as continuum limits of interacting particles. Their dynamics can often be described in terms of a monotonically decreasing interaction energy. We show how to exploit these energies numerically, analytically and asymptotically to characterize the observed behavior. Examples are drawn from the dynamics of thin fluid layers including ferrofluids.

**Date: 10-16-2015 (2-3pm, F03-200A), Dr. Peter Jipsen, Chapman University Center of Excellence in Computation, Algebra and Topology (CECAT)**

**Title:** From Residuated Lattices to Boolean Algebras with Operators

**Abstract:** This general audience talk introduces lattices and residuated operations on them, and explains how these algebraic structures are related to substructural logics. Adding some natural axioms defines Heyting algebras (corresponding to intuitionistic logic) and Boolean algebras (corresponding to classical propositional logic). No special background in abstract algebra or logic is assumed for this talk.

For many applications in logic and computer science additional operations are introduced, leading to the classical theory of Boolean algebras with operators (BAOs) as well as the still largely unexplored theory of Heyting algebras with operators (HAOs). As an example of BAOs, I will define Boolean semilattices and present some recent results about them. In the area of HAOs, generalized bunched implication algebras (GBI-algebras) are Heyting algebras expanded with a residuated monoid operation, and they have found interesting applications in the past decade in the form of separation logic for reasoning about pointers, data structures and parallel resources.

I will indicate why BAOs with a monoid operator generally lack decision procedures for their equational theories, whereas GBI-algebras, residuated lattices and several of their subclasses are equationally decidable. Some algorithms for enumerating finite algebras in these classes will be presented, as well as computational tools that are useful for exploring research questions in these areas.

**Date: 10-23-2015 (12-1pm, F03-200A), Dr. Christian Rose, Technische Universität Chemnitz**

**Title:** Compact manifolds with integral bounds on the negative part of Ricci curvature and the Kato class

**Abstract:** Bochner’s theorem states that a compact manifold with non-negative Ricci curvature and positive somewhere admits a trivial first cohomology group. Starting from a generalization by Elworthy and Rosenberg we show using Kato conditions for certain Schrödinger operators that L^p criteria for the part of curvature below a certain depth is sufficient that Bochner still holds.

**Date: 10-30-2015 (12-1pm, F03-200A), Dr. Jasbir Chahal, Brigham Young University**

**Title:** Two Applications of the Arithmetic of Elliptic Curves

**Abstract:** We will explain everything about elliptic curves needed to show how the arithmetic of elliptic curves can be used to solve two ancient problems. One is: what whole numbers are the areas of right triangles when the side lengths are allowed to be rational numbers and not just the whole numbers? The second problem is: for what triangles with all side lengths rational, an altitude, an angle bisector and the median are concurrent? No knowledge beyond high school math is required. However, the topics are very beautiful and lie at the frontier of research in number theory.

**Date: 11-13-2015 (12-1pm, F03-200A), Applied Math and Statistics Graduate Students, CSULB**

**Title:** Part I: Collaborative Filtering and the Yelp Dataset Part II: Python Introduction

**Abstract:** We will have a special colloquium featuring two presentations from our Applied Math and Statistics Master's students. Maike Scherer and Daniel Hallman will speak on collaborative filtering techniques for predicting user ratings of restaurants on Yelp. Juan Apitz and Truong Tran will then give an introduction to Python and the Jupyter Notebook project.