We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Iris Yoon (Wesleyan University) Title: Dowker duality, profunctors, and spectral sequences Abstract: I will present three short, new proofs of Dowker duality using various poset fiber lemmas. I will introduce modifications of joins and products of simplicial complexes called relational join and […]
Speaker: Iris Yoon, Professor of Mathematics, Wesleyan University Title: How Topology Reveals Structure in Neuroscience Data Abstract: We live in an exciting time where new data is generated at an exponential rate. Such data explosion necessitates the development of novel methods for studying large, noisy, and complex data. One interesting aspect of data is its shape and […]
No seminar this week due to Spring break!
Title: Learning on manifolds without manifold learning Abstract: Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional Euclidean space. A great deal of research deals with obtaining information about […]
I will present an integral — requiring no character twists — converse theorem for recognizing when is a Dirichlet series with algebraic integer coefficients equal to the L-function of a modular form. This refines the unbounded denominators conjecture of Atkin and Swinnerton-Dyer. Analogies with basic function field arithmetic then suggest a quantitative refinement which precludes a pair of GL(2) automorphic L-functions […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Reginald Anderson (Claremont McKenna College) Title: Kontsevich's Recursive Formula for Rational Plane Curves Abstract: Gromov-Witten theory was developed in the 1990s as a curve-counting theory by integrating cohomology classes against a virtual fundamental class for a moduli space of stable maps. One […]
Speaker: Yimin Xiao, Professor of Statistics and Probability, Michigan State University Title: Brownian Motion, Random Fractals, and Beyond Abstract: Brownian motion is not only a fascinating object in mathematics but also a powerful stochastic model that has been applied in many scientific fields, from physics to finance, to biological sciences. The sample function of Brownian […]
A big area in combinatorics over the last several decades has been the study of pattern-avoiding permutations, whose enumeration is exciting and mysterious. Alternating sign matrices (ASMs) are a generalization of permutations whose study in combinatorics has also been exciting and mysterious. In this talk, I will explain some new asymptotic results involving the number […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Scott Taylor (Colby College) Title: Genus 1 Bridge Number of Satellite Knots in Lens Spaces Abstract: In the mid-1950s, Horst Schubert introduced two ideas which turned out to have lasting impact in knot theory: satellite knots and bridge number. A Satellite knot […]
Speaker: Scott Taylor, Professor of Mathematics, Colby College, Maine Title: Sums and Symmetries Abstract: Adding is one of the fundamental mathematical operations and we like it so much, we can't […]
This GEMS session will be facilitated by Professor Bahar Acu from Pitzer College. Title: The Hole Truth: When is a Coffee Mug a Donut? Abstract: In mathematics, topology is the study of properties […]
