Talks (unless otherwise indicated) are in Davis 301 from 4–5 PM on Mondays. Refreshments begin at 3:30 on the second floor of Davis.
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SUNY New Paltz
Differential Operators on the Superline, Berezinians and Darboux Transformations
Supermathematics is a standard tool for Quantum Physics that allows us to describe both fermions and bosons. The name comes from “supersymmetry.” Darboux transformations are a tool in integrable systems theory, which seeks exact solutions of nonlinear and linear partial and ordinary differential equations. In this talk I shall present my results on developing Darboux transformations in supergeometry. I shall touch on my results about superdeterminants, such as a non-trivial analogue of row (column) expansion. Overall I aim to introduce the audience to the world of supermathematics, show analogues of familiar concepts and give some idea of my work. I shall not be assuming any prior knowledge besides Linear Algebra and Calculus.
Network Data Analysis: Inference and Characterization
The analysis of network data is widespread across scientific disciplines. In applied network analysis, a common approach is to gather basic measurements on the interactions among elements in the system, construct a network-based representation of the system, and numerically summarize the structure of the resulting network graph. We address the empirically relevant problem that errors made in assigning links between nodes accumulate in the reporting of motif count statistics in characterizing the network as a whole. We demonstrate the utility of network characterization in two clinically relevant applications: (i) the high-order interactions among microbes constituting the ecological network of the human gut microbiome and (ii) the rate of percolation in the human brain network at the onset of an epileptic seizure.
Dizzy Patients and a Mathematical Playground of Probabilities on Spheres
Interesting mathematical topics often arise in real-life problems. This talk will begin with a description of research on vestibular patients at Baylor College of Medicine and a comparison with previously published data on eye movements, and then will dive into mathematical questions—and even some answers—that arose. Above all, this talk will point out some intriguing questions about probabilities on spheres that lead to a whole playground of mathematical (and statistical) questions.
Constrained Flexibility: Some Surprising Connections between Geometry and Topology
Length, area, curvature are geometric properties. An object’s topological properties, on the other hand, are those which don’t change when the object is stretched, twisted, or bent. Curves in the plane or in 3-dimensional space exhibit an interesting variety of both geometric and topological properties. I’ll survey they ways these properties are related to each other, tracing a line of investigation which begins in the early 20th century and extends to very recent results concerning how twisted knots can be. (Image by Conan Wu)
Inclusion, Exclusion, and the Theory and Practice of “Truly International” Mathematics
In theory, just about anyone can be a mathematician. Theorems and proofs, for the most part, don’t discriminate based on race, class, gender, disability, national origin, or anything else, at least in princniple. Historically, however, the field and profession has been open to very few. Mathematicians have grappled in many different ways with this gap between an ideal of openness and and a reality of exclusion and even outright discrimination. I will show how American mathematicians took leadership of the international mathematics community over the period between 1920, when they first proposed to host an International Congress of Mathematicians, and 1950, when they finally brought one to fruition. American mathematicians tried to reshape mathematics as a more interconnected and inclusive discipline, succeeding in some ways and failing in others. In particular, they tried to create what they called a “truly international” discipline. I will explain how this ambiguous and shifting phrase helped them navigate a wide range of political, financial, and other obstacles, while covering over persistent problems and blindspots.
FAst Matrix Multiplication: An Adventure in Machine Learning
Neural nets have been used to attack a variety of problems, including image classification, speech recognition, and autonomous driving. After detailing how neural nets can be used in settings of this sort, we will use them to solve a problem in algebra instead.
Square Pegs in a Round Circle Problem
In this talk we’ll introduce Gauss’s Circle Problem, the centuries-old conjecture concerning estimates of the number of integer-coordinate points inside a circle as we vary the radius. We’ll also discuss variants on this problem in higher dimensions, and how we can get information from the Fourier coefficients of a particular theta function with interesting analytic properties. Some joint work with Chan Ieong Kuan, David Lowry-Duda, and Alexander Walker may also be presented.
Mathematics and Statistics Alumni Panel
Malia Kawamura ’14, Anne Crumlish ’98, Ben Hauptman ’09, Tom Hulse ’07
Japanese Temple Geometry
During the period of Japanese history known as the Edo period, Japan followed a strict isolationist foreign policy in which travel outside the country was forbidden and cultural exchange with European nations was effectively cut off. Coupled with the peace and economic prosperity enjoyed during the Edo period, this “closed country” policy led to a flourishing of uniquely Japanese arts and culture. One of the curious practices that developed during this time was a tradition of hanging wooden tablets inscribed with geometry problems in Buddhist temples and Shinto shrines. In this talk we will discuss the Japanese mathematics of the Edo period generally and the sangaku tablets in particular, including the one problem from these tablets that remains unsolved.