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# Mathematics Colloquium Schedule

**Spring 2018**

**Date: 3-16-2018 ( 12pm-1pm, F03-200A), Dr. Jim Stein, Professor Emeritis, Department of Mathematics and Statistics, CSULB**

**.**

**Title: How to Predict the Fate of Schrodinger's Cat**

**Abstract: **Let's face it, nobody really cares if Schrodinger's Cat is in a half-alive, half-dead state -- whatever that is. The interesting question, at least to cat lovers (or haters), is whether, when we open the box, we'll find that the cat is alive -- or dead.

We'll describe an experimental setup in which poison gas is released on the decay of a radioactive atom which decays with probability 1/2, but which has the curious property that we can correctly predict more than half the time, even before the experiment begins, the fate of the cat.

We'll also take a side trip to the town Willoughby, featured in the Twilight Zone episode "A Stop at Willoughby".

**Date: 2-23-2018 ( 12pm-1pm, F03-200A), **

**Dr. Jonas Cremer**, UCSD**.**

**Title: TBA**

**Abstract: TBA**

**Date: 2-16-2018 ( 12pm-1pm, F03-200A), **

**Dr.****Jørgen Ellegaard Andersen, Director of the Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Denmark**

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**Title: RNA secondary structures enumeration and prediction and their relation to moduli spaces**

**Abstract: **In molecular biology a very important problem is to predict from the primary sequence of an RNA strand, how it will fold. In particular, to predict its secondary structure, e.g. which base pair bonds to which, is a very interesting and challenging problem with a long history with close ties to mathematics. I shall try to review this problem and some of the history of how this problem has been addressed mathematically. Following this I shall explain how a more modern approach to this theory now involved techniques from pure mathematics, such a combinatorial structure on the classical moduli spaces of Riemann Surfaces introduced first by Riemann a couple of centuries ago, can be combined with techniques from quantum field theory and matrix models to improve the predictability of the secondary structure from the primary.

**Date: 2-9-2018 ( 12pm-1pm, F03-200A), Dr. Evan Gawlik, UCSD**

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**Title: Interpolation of Manifold-Valued Functions**

**Abstract: **Manifold-valued data and manifold-valued functions play an important role in a wide variety of applications, including mechanics, computer vision and graphics, medical imaging, and numerical relativity. This talk will describe a family of interpolation operators for manifold-valued functions, with an emphasis on functions taking values in symmetric spaces and Lie groups. A key role in our construction is played by the polar decomposition -- the well-known factorization of a real nonsingular matrix into the product of a symmetric positive-definite matrix times an orthogonal matrix -- and its generalization to Lie groups. We demonstrate that this factorization can be leveraged to carry out a number of seemingly disparate tasks, including the design of finite elements for numerical relativity, the interpolation of subspaces for reduced-order modeling, and the approximation of acceleration-minimizing curves on the special orthogonal group.

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

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**Title: Discrete Means: generalizing a theorem of Kolmogorov and social choice.**

**Abstract: **According to the U.S. Census Bureau, the "average" American household consists of 2.53 people and while this number is understood to be an average over all households in the U.S., it also leaves us unable to select an example of such a family. This is a problem of discrete means. In 1930, Kolmogorov gave an elegant axiomatization and classification of all means on the real numbers, and in this talk we will discuss Kolmogorov's theorem and discuss different generalizations to his axioms when we restrict the mean to map on and into the integers. We will also discuss how the issues raised by discrete means confront us in a variety of settings.

This talk will be accessible to a wide audience (including undergraduate mathematics majors).

**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.