## September 2018

### Pre-Colloquium Non-Colloquium Party

The traditional year-opening social event for the Claremont Colleges Mathematics Community will be held in the Millikan Courtyard. Spouses, partners, and family are welcome. Professors Ali Nadim (CGU) and Blerta Shtylla (POM), co-chairs, hope to see everyone there for refreshments, and other pleasant pursuits.

Find out more »### An Algebra of Arcs and Knots on a Surface (Helen Wong, CMC)

The end of the previous century saw radical changes to three-dimensional topology, which arose from two completely different approaches. One breakthrough came from Bill Thurston's introduction of hyperbolic geometry into the field. The second one came from the Vaughn Jones’s discovery of a new "quantum" invariant for knots that brought in insight and techniques from mathematical physics and non-commutative algebra. It is widely believed that the two approaches are related. In this talk, we will focus on a point of…

Find out more »### Fall 2018 Poster Session

CLAREMONT CENTER for MATHEMATICAL SCIENCES Fall 2018 Poster Session Computing Eigenmodes of the Laplace-Beltrami Operator by Using Radial Basis Functions by Vladimir Delengov, Chiu-Yen Kao Claremont Graduate University Covariance-based Dissimilarity Measures Applied to Clustering Wide-sense Stationary Ergodic Processes by Nan Rao, Qidi Peng, Ran Zhao Claremont Graduate University Generalized Covariation of Symmetric -stable Distributions by Yujia Ding, Qidi Peng Claremont Graduate University Learning to Fail: Predicting Fracture Evolution in Brittle Materials using Recurrent Graph Convolutional Neural Networks by Yadong Ruan,…

Find out more »### Snow Business: Scientific Computing in the Movies and Beyond (Joseph Teran, UCLA)

New applications of scientific computing for solid and fluid mechanics problems include simulation of virtual materials in movie visual effects and virtual surgery. Both disciplines demand physically realistic dynamics for materials like water, smoke, fire, and soft tissues. New algorithms are required for each area. Teran will speak about the simulation techniques required in these fields and will share some recent results including: simulated surgical repair of biomechanical soft tissues; extreme deformation of elastic objects with contact; high resolution incompressible flow; and…

Find out more »## October 2018

### Modeling Mechanisms of Ovulatory (Dys)Function (Erica Graham, Bryn Mawr College)

A normally functioning menstrual cycle requires significant crosstalk between hormones originating in ovarian and brain tissues. Reproductive hormone dysregulation may disrupt function and can lead to infertility, as occurs in the common endocrine disorder polycystic ovarian syndrome (PCOS). In this talk, I will discuss a mathematical model of the ovulatory cycle that accounts for mechanisms of ovarian testosterone production and explore insulin-mediated ovulatory dysfunction. I will also explore additional model characteristics, via bifurcations and parameter sensitivity, and their respective clinical…

Find out more »### Applications of Cayley Digraphs to Waring’s Problem and Sum-Product Formulas (Yesim Demiroglu, Harvey Mudd)

Abstract: In this talk, we first present some elementary new proofs (using Cayley digraphs and spectral graph theory) for Waring's problem over finite fields, and explain how in the process of re-proving these results, we obtain an original result that provides an analogue of Sarkozy's theorem in the finite field setting (showing that any subset E of a finite field Fq for which |E| > (qk)/sqrt{q - 1}must contain at least two distinct elements whose difference is a kth power).…

Find out more »### Great Expectations (Matthew Junge, Duke Univ.)

The mean of a random quantity is supposed to confirm our expectations. What happens when it defies them? We will look at a few famous expected values; some old, some new, all great.

Find out more »### Isometric Circle Actions (Catherline Searle, Wichita State)

I will begin by describing a number of important examples of isometric actions of circles in Euclidean space and their restrictions to subspaces of Euclidean space. The goal of the talk will be to see how isometric actions of circles and tori can be used to "recognize" the space on which they are acting.

Find out more »### Saving Bats from Fungal Diseases with Linear Algebra (Nina Fefferman, U of Tennessee-Knoxville)

Abstract: Bats in North America have been dying off due to the invasion of a fungal disease (White Nose Syndrome). In this talk, I'll present a very simple linear algebraic model to predict the magnitude of the die-offs. By comparing these models to some data about actual bat survival, my collaborator and I also hypothesized that the disease might be causing rapid evolution in the bat populations and this could give some populations better hope of surviving. I'll go through…

Find out more »## November 2018

### The Legacy of Rudolph Kalman (Andrew Stuart, Caltech)

Abstract: In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography, oil recovery, medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to…

Find out more »### Coupled Mechanochemical Multiscale Model to Study the Growth Regulation and Morphogenesis during Tissue Development (Weitao Chen, UCR)

Growth regulation and pattern formation are two main problems in developmental biol- ogy. How cells know when to stop growing at certain tissue size with specic shape is an important question in both developmental biology and regenerative medicine, and it is still an unsolved mystery in many systems. During the growth, tissues and organs always exhibit self-government to some extent. Cells stop proliferation precisely when the intended size of the tissue or organ is achieved. Meanwhile, dierential cell shapes in…

Find out more »### Convolutional Dictionary Learning for Tomographic Reconstruction (Cristina Garcia-Cardona, LANL)

Convolutional sparse representation is an efficient tool for computing sparse representations for entire signals in terms of sums of a set of convolutions with dictionary filters. Unlike representations that are based on overlapping image patches, the convolutional representation optimizes over the entire image, yielding representations that are very sparse both spatially and across the filters. This technique has been successfully applied to natural images, video and speech in tasks as diverse as denoising, classification or superresolution. In this work, we…

Find out more »## December 2018

### The kissing number and related problems (Oleg Musin, University of Texas Rio Grande Valley)

Abstract: The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size. This problem in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was finally solved only in 1953 by Schutte and van der Waerden. In this talk we are going to give an overview of this problem and to present…

Find out more »### Defining Ada: On The Legacy of Augusta Ada Byron King Lovelace (Gizem Karaali, Pomona College)

Abstract: Augusta Ada, Countess of Lovelace, is today viewed as the rst person to recognize the power of algorithmic machines and a pioneer in computer programming. Her biographers have often disagreed on her mathematical talents, her mathematical contributions, and her legacy. In this talk I explore the various approaches taken towards her, focusing explicitly on how the men in her life have been used to dene her. I conclude with some thoughts on Adas impact and legacy. problems.

Find out more »## January 2019

### Mathematics: Pure, Applied, A Liberal Art ( Al Erisman, Seattle Pacific University)

From the view of a pure mathematician, those working in pure mathematics produce pure knowledge. Whether used or not, it has a great elegance and value in and of itself. Those in applied mathematics simply pick up what has been done and use it in designing or building things. Number theory is often used to illustrate this, where work done decades ago in pure mathematics is now central to encryption. However, the relationship between pure and applied mathematics is a…

Find out more »## February 2019

### Algebraic and Polyhedral Perspectives on Combinatorial Neural Codes (Robert Davis, Harvey Mudd)

In the 1970s, James O’Keefe and his team observed that certain neurons in the brain, called place cells, spike in their firing rates when the animal is in a particular physical location within its arena. If a place cell is thought of as either “active” or “silent,” then one may represent the co-firing patterns of place cells by a combinatorial neural code: a set of 0/1 vectors whose coordinates represent that status of distinct place cells. From the code, we…

Find out more »### Cracking the Code: Predicting Properties of Material Fracture Networks using Machine Learning (Allon Percus, CGU)

Understanding how fluid flows through heterogeneous materials, and how it can make these materials fail, are among the hardest challenges in materials science. Experiments and simulations show that flow through subsurface rock is mostly limited to a small subnetwork, or backbone, of fractures. Identifying this backbone would allow for a large speedup in flow and transport simulations, but the process of identifying it can itself be computationally intensive. I will discuss a machine learning approach, developed in a CGU Math…

Find out more »### Personal Perspectives on m-ary Partitions (James Sellers, Penn State)

Abstract: A great deal of my research journey has involved the study of m-ary partitions. These are integer partitions wherein each part must be a power of a fixed integer m > 1. Beginning in the late 1960s, numerous mathematicians (including Churchhouse, Andrews, Gupta, and Rodseth) studied divisibility properties of m-ary partitions. In this talk, I will discuss work I completed with Rodseth which generalizes the results of Andrews and Gupta from the 1970s. Time permitting, I will then discuss several problems related to m-ary partitions, including…

Find out more »### Pull Out All The Stops: Textual Analysis via Punctuation Sequences (Mason Porter, UCLA)

Abstract: Whether enjoying the lucid prose of a favorite author or slogging through some other writer's cumbersome, heavy-set prattle (full of parentheses, em-dashes, compound adjectives, and Oxford commas), readers will notice stylistic signatures not only in word choice and grammar, but also in punctuation itself. Indeed, visual sequences of punctuation from different authors produce marvelously different (and visually striking) sequences. Punctuation is a largely overlooked stylistic feature in "stylometry", the quantitative analysis of written text. In this paper, we examine…

Find out more »## March 2019

### Accidental Mathematics (Matt Stamps, Yale-NUs College)

Abstract: Growing up, I always loved learning about world-changing scientific breakthroughs that were discovered by accident. Penicillin, artificial sweeteners, X-rays, and synthetic dyes are just a few of the discoveries that were stumbled upon by scientists who had other goals in mind. More recently, I have come to wonder why anecdotes about accidental discoveries in mathematics are not as commonplace. Is it a fundamental difference in they way mathematicians and natural scientists view their work? Are such stories too contrary…

Find out more »### Some Unexpected Mathematics Arising From Research at NIST ( Hunt, NIST)

A lot of the mathematics done at NIST supports the research on and measurement of advanced materials and technology. In this rather applied context. surprising mathematics makes an appearance. We present a few examples.

Find out more »### Reasoning about Liability of Intelligent Agents ( Naumov, CMC)

Abstract: As intelligent agents assume larger role in our daily lives, reasoning by humans about liability of such agents as well as reasoning by the intelligent agents themselves about liability becomes more important. The existing laws, written with humans in mind, will eventually need to be re-interpreted in terms of their applicability in a hybrid environment that consists of humans and intelligent agents. In some cases, new laws will need to be written to redefine liability in the context involving…

Find out more »## April 2019

### On the interplay of functional analysis and operator theory (Puig de Dios, UCR)

Abstract: We overview some basic and striking facts concerning the theory of hypercyclic operators (considered to be born in 1982): 1. Hypercyclicity is a purely infinite-dimensional phenomenon: no finite dimensional space supports any hypercyclic operator; 2. It is not easy at all to determine whether a linear operator is hypercyclic. However, the set of hypercyclic operators is dense for the Strong Operator Topology in the algebra of linear and bounded operators; 3. Hypercyclicity is far from being an exotic phenomenon:…

Find out more »### A General Bayesian Discrete Time Survival Model (King, CPP)

Abstract: "We present a general Bayesian statistical model for discrete time, discrete state space stochastic processes. Applications include the modeling of recurrent and episodic disease processes, such as episodes of illicit drug use, as well as social processes such as educational enrollment and employment. We also present Markov chain Monte Carlo inference algorithms for our model, along with a freely available software package called "brea" which implements these methods in the R programming language."

Find out more »### Unravelling Biochemistry Mysteries: Knot Theory Applied to Biochemistry (Price, University of San Diego)

Abstract: Mathematical modeling is an effective resource for biologists since it provides ways to simplify, study and understand the complex systems common in biology and biochemistry. Many mathematical tools can be applied to biological problems, some traditional and some more novel, all innovative. This presentation will review the mathematical tools that are used to model and study biological issues of DNA-protein interactions.

Find out more »### A Conformal Mapping Approach to Shape Optimization Problems. (Kao, CMC)

Abstract: In this talk, a conformal mapping approach to shape optimization problems on planar domains will be discussed. In particular, spectral methods based on conformal mappings are proposed to solve Steklov eigenvalues and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov eigenvalue problem in the complex domain via conformal mappings. The eigenfunctions are expanded in Fourier series so the discretization leads to an eigenvalue problem for coefficients of Fourier series. For shape…

Find out more »## May 2019

### Is My Subgroup Normal? How Math Communities Differand Why it Matters (Sinclair, Google)

Mathematics isnt done in a void: its done by groups of people. Those groups have different norms and values, which affect both who wants to engage in math and the mathematics itself being done. When thinking about diversity and inclusion, explicitly examining norms within our communities can get us a long way. Through a Thomas J Watson Fellowship, I had the opportunity to experience mathematics competitions communities in Brazil, Argentina, Senegal, Singapore and England. Come hear about the differences I…

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