Speaker:Jesse Wolfson, UC Irvine Title: Braids, Polynomials, and Hilbert’s 13th Problem Abstract: There are still completely open fundamental questions about polynomials in one variable. One example is Hilbert’s 13th Problem, a conjecture going back long before Hilbert. Indeed, the invention of algebraic topology grew out of an effort to understand how the roots of a […]
Title: Exceptional Sets for Divergent Fourier Series Abstract: A survey of some old and newer results on divergent Fourier series with some comments on how they relate to undergraduate analysis courses and (time permitting) leading to a brief discussion of an open question on the size of exceptional sets in divergence examples and some progress […]
This GEMS session will be facilitated by Professor David Bachman from Pitzer College. Title: How does ChatGPT work? Abstract: In 2022 ChatGPT took the world by storm and challenged our ideas of what computers are capable of. However, few people have any sense of how this technology works. Through hands-on activities participants will learn about […]
The classical Noether-Lefschetz Theorem states that a suitably general algebraic surface S of degree d ≥ 4 in complex projective 3-space P3 contains no curves besides complete intersections, that is, curves of the form S ∩ T where T is another surface. After discussing briefly Noether’s non-proof of this theorem and hinting at the idea […]
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Vijay Higgins (UCLA) Title: Webs and skein algebras Abstract: The Jones polynomial of a link can be computed diagrammatically by using skein relations, which encode the representation theory of SL(2). By considering the vector space spanned by links drawn on a surface and […]
Speaker: Michelle Manes, AIM Title: Dynamical Systems and the Period 3 Implies Chaos Theorem Abstract: Sharkovskii’s theorem, sometimes called "period 3 implies chaos," concerns a one-dimensional real dynamical system: a function from the real line to itself that you iterate and study the orbits of points. This theorem is fascinating because of its very simple […]
Integer partitions are ubiquitous in mathematics, arising in subjects as disparate as algebraic combinatorics, algebraic geometry, number theory, representation theory, to mathematics physics. Many of the deepest results on partitions have their origin in the work of Ramanujan. In this lecture, we will describe a completely new and unexpected role for partitions that also arises […]
We welcome all undergraduate/graduate students and faculty to attend the Topology Seminar! Speaker: Claudio Gomez-Gonzales (Carleton College - UC Irvine) Title: How hard could it be? A tour of resolvent degree Abstract: Solving algebraic equations are among the oldest problems in mathematics. In this talk, we offer a concrete, visual, and historical introduction to resolvent […]
Speaker: Dorothy Buck, Professor of Mathematics, Duke University Title: Molecular Pasta: Complex Entanglement in Biopolymers Abstract: If you’ve cooked spaghetti, you’ve probably noticed how the pasta becomes entangled in the pot (especially in a small volume of water) or in your bowl afterwards. This is a macro example of what I like to think about: […]
Speaker: Iris Clever, University of Chicago Title: The Making of the Modern Statistical Identity: From Skull Science to Biometrics Abstract: In this presentation, I uncover an overlooked genealogy of biometrics, tracing it back to early 20th-century race science and the rise of statistical thinking about human identity. Before biometrics became a technology of controlling human identity, […]
