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# Mathematics Colloquium Schedule

**Spring 2018**

**Date: 4-27-2018 (12pm-1pm, F03-200A), Dr. Yi-Ming Zou, Department of Mathematical Sciences, University of Wisconsin-Milwaukee.**

**Title: Study Gene Regulatory Networks Using Boolean Models**

**Abstract:** A gene regulatory network is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expressions of mRNA and proteins. Different mathematical models can be built based a gene regulatory network to investigate the behaviors of the underlying biological system. Boolean models offer a relatively simple and effective method for this purpose. In this talk, I will give a brief introduction to the construction of these gene regulatory networks, explain why Boolean models are suitable for the study of these networks, and discuss how to construct Boolean models from the interaction networks. I will discuss our recent effort to compute the stable states of a Boolean network and discuss its application to the study of these gene regulatory networks. I will also discuss a prostate cancer regulatory network we constructed recently and the result of applying a Boolean model to the study this network.

**Date: 4-20-2018 (12pm-1pm, F03-200A), Dr. Adolfo Escobedo, School of Computing, Informatics, and Decision Systems Engineering, Arizona State University****.**

**Title: New Ranking Measures and Algorithms for Expanding Robust Group Decision-Making Frameworks**

**Abstract:** The consensus ranking problem is central to group decision-making. It involves finding an ordinal vector that minimizes collective disagreement with respect to a set of individually stated preferences over a list of competing objects. Common examples include university rankings, corporate project selection, and metasearch engines. Although different measures for quantifying disagreement between rankings can be employed, those founded on axiomatic distances are regarded as the most robust due to their rigorous mathematical underpinnings and intuitive social choice-related properties. In this presentation, we introduce ranking measures specifically designed to ensure fairness and mitigate individual bias/manipulation when handling problematic types of input ranking data. The adequacy of these measures is exhibited through computational comparisons with alternative axiomatic and ad hoc approaches, which are facilitated through tailor-made aggregation algorithms. In all, the featured contributions can be regarded as generalizations of the Kemeny distance and Kendall Tau correlation coefficient frameworks, which have been applied to several application areas outside of group decision-making including informatics, computer vision, and biostatistics.

Dr. Adolfo Escobedo would also like to meet our faculty and our students to talk about opportunities in their Industrial Engineering PhD program, whose core strengths are in industrial statistics and operations research.

Pizzas and soft drinks will be provided at 11am.

**Date: 4-18-2018 ( Wednesday, 5:30pm-6:30pm, F03-200A), **

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

**.**

**Title: Geometric Recursion**

**Abstract: **Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract setup we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and if time permits the Goldman symplectic form on moduli spaces of flat connections for general compact simple Lie groups. The work presented is joint with G. Borot and N. Orantin.

**Date: 4-13-2018 (12pm-1pm, F03-200A), A Panel of CNSM Students, CSULB****.**

**Title: CNSM Munch N' Learn. Students Speak: What Professors Should Know**

**Abstract:** What can instructors do to help students succeed? What do instructors do that hinders success? What are some of the non-academic challenges that students wish instructors knew about? How do students choose their classes? How do they choose their major? Why do students miss classes? What motivates them to attend? What do students make of all the growth mindset messaging? How do students use ratemyprofessor?

*So many questions! *Come, ask some questions of your own, and hear some students’ perspectives.

**Date: 4-6-2018 (12pm-1pm, F03-200A), Adam D. Richardson, Department of Mathematics and Statistics, CSULB****.**

**Title: Finitely Additive Invariant Set Functions and Paradoxical Decompositions, or: How I Learned to Stop Worrying and Love the Axiom of Choice**

**Abstract:** This talk introduces the historic sigma-additive measure problem in n-dimensional Euclidean space and describes how the existence of nonmeasurable sets provided an answer to this problem that led mathematicians to explore the consequent finitely additive measure problem in n-dimensional Euclidean space. The Axiom of Choice plays an inextricable role in these problems. The existence of a finitely additive measure on the unit circle is developed carefully using results from functional analysis before the problem is explored in general. The application of the Axiom of Choice in these problems can yield paradoxical decompositions of subsets of Euclidean space (and by extension Euclidean space itself) such as the seminal Hausdorff half-third paradox as well as the eponymous Banach-Tarski paradox. The development of these paradoxes is group theoretic in nature, and some of the group properties which yield such decompositions are discussed. This talk seeks to tell the mathematical origin story of such paradoxes, including detailing the Hausdorff half-third paradox, while highlighting how the controversial Axiom of Choice led to these wholly counterintuitive yet absolutely fascinating measure-theoretic results.

**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: Expansion Dynamics of Bacterial Populations**

**Abstract: **Many bacterial species can swim and are capable to sense and actively follow chemical gradients. For Escherichia coli, the cellular implementation of this chemotactic response belongs to the best-characterized subjects of molecular biology. However, much less is known about the collective swimming dynamics of multiple cells and their fitness consequences for growing bacterial populations. Here I discuss the collective motion of cells along self-generated chemotactic gradients. Presenting experiments and a theoretical analysis, I describe how the interplay of metabolite sensing, proliferation, metabolite uptake, and swimming leads to the spreading and growth of an initially localized population. The collective migration dynamics of cells along ring-shaped fronts is described by a modified Keller-Segel model, emphasizing the crucial role of bacterial growth and nutrient utilization. Coupled to the front propagation via pushed waves, proliferation of cells in the back drives overall population growth. By the integration of chemoattractant sensing into directed movement, the cue-driven form of range expansion described here is fast (speed of order 1 cm/h) and easily outcompetes the canonical form of range-expansion via pulled waves and Fisher-Kolmogorov dynamics.

**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**

**.**

**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**

**.**

**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**

**.**

**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**

**.**

**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**

**.**

**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.