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# Mathematics Colloquium Schedule

**Spring 2018**

**Date: 2-2-2018 ( 12pm-1pm, F03-200A), Dr. Curtis Bennett, Dean, CNSM, CSULB**

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**Title: TBA**

**Abstract: TBA**

**Fall 2017**

**Date: 12-1-2017 ( 12pm-1pm, F03-200A), Dr. Chiu-yen Kao, Department of Mathematics and Computer Science at Claremont McKenna College**

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**Title: Minimization of inhomogeneous biharmonic eigenvalue problems**

**Abstract:** Biharmonic eigenvalue problems arise in the study of the mechanical vibration of plates. In this paper, we study the minimization of the first eigenvalue of a simplified model with clamped boundary conditions and Navier boundary conditions with respect to the coefficient functions which are of bang-bang type (the coefficient functions take only two different constant values). A rearrangement algorithm is proposed to find the optimal coefficient function based on the variational formula of the first eigenvalue. On various domains, such as square, circular and annular domains, the region where the optimal coefficient function takes the larger value may have different topologies. An asymptotic analysis is provided when two different constant values are close to each other. In addition, a symmetry breaking behavior is also observed numerically on annular domains.

**Date: 11-3-2017 (12pm-1pm, FO3-200A), Gene Kim****, Department of Mathematics, USC.**

**Title: Distribution of Descents in Matchings**

**Abstract:** The distribution of descents in a fixed conjugacy class of $S_n$ is studied, and it is shown that its moments have an interesting property. A particular conjugacy class that is of interest is the class of matchings (also known as fixed point free involutions). This paper provides a bijective proof of the symmetry of the descents and major indices of matchings and uses a generating function approach to prove an asymptotic normality theorem for the number of descents in matchings.

**Date: 10-27-2017 (11am-12pm, LA5-154), Dr. Donald Saari****, UC Irvine.**

**Title: From Arrow's Social Choice Theorem to the compelling "dark matter" mystery**

**Abstract:** In this expository, general talk, it is shown how the muscle power of mathematics explains a major result in elections and group decision making (which asserts that what is obviously possible to do is, in fact, impossible), and connects it to a compelling mystery in astronomy--dark matter.

**Date: 10-20-2017 ( 12pm-1pm, F03-200A), Dr. Alfonso Castro, Department of Mathematics, Harvey Mudd College**

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**Title: **Shooting from singularity to singularity and a semilinear Laplace-Beltrami equation

**Abstract:** Rotationally symmetric solutions to semilinear Laplace-Beltrami equation defined on a manifold of revolution is considered. We will show how such a problem becomes an ordinary differential equation with two singularities. We will study the singular differential equations using the shooting method and conclude that when the nonlinearity is *superlinear *and *subcritical *the problem has infinitely many solutions.

**Date: 10-6-2017 (12pm-1pm, F03-200A), Dr. Stacy Musgrave, Department of Mathematics & Statistics, Cal Poly Pomona **

**Title:** Mathematical Structures: Up Close and Afar

**Abstract:** Reasoning structurally has been identified as a key component of mathematical activity, so much so that national documents like the Common Core State Standards highlight this way of reasoning as a mathematical practice (MP7) we ought to foster in students in K-12 classrooms. In this talk, I define reasoning structurally and demonstrate what it looks like to reason structurally with algebraic expressions and equations. We will explore structural and non-structural response types to tasks from a diagnostic tool, the Mathematical Meanings for Teaching secondary mathematics (MMTsm), used to characterize high school teachers’ meanings for foundational ideas in the secondary curriculum.

**Date: 9-22-2017 (11am-12pm, F03-200A), Dr. Matteo Mori, Department of Physics, UC San Diego **

**Title:** *From Macro to Micro and Back: Complexity, Simplicity and Optimality of Bacterial Cells*

**Abstract:** Understanding how living cells work as a system requires to unravel how simple behaviors emerge from the complexity of the cell's molecular machinery. At the macroscopic level, coarse descriptions and simple "growth laws" can be used to understand the physiology of the cell. On the other hand, genome-scale models can be used to understand how simple "macro" behaviors emerge from the complexity of cellular metabolism. I will discuss a couple of examples of (only apparently) sub-optimal performances of bacterial cells, and the role of protein allocation models as a unifying framework for understanding cell physiology.