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, […]
Title: Designing Robust Networks of Coupled Phase Oscillators with Applications to the High-Voltage Electric Grid Abstract: A network is any collection of objects, called nodes, in which some pairs of these objects are connected by links, called edges. In a network of coupled phase-oscillators, each node represents a phase-angle (or an angle with periodicity) whose […]
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Heather Lee Title: Some examples of homological mirror symmetry Abstract: Mirror symmetry is a duality phenomenon between symplectic geometry and complex geometry. The homological mirror symmetry (HMS) conjecture was originally formulated by M. Kontsevich in 1994 to fully capture this phenomenon for mirror […]
Speaker: Kobi Abayomi, Head of Science, Gumbel Demand Acceleration Title: Sound Information is All You Need Abstract: It turns out that affinity for a song is predictable from its sound. We explore the statistical predictability of aggregate song demand from an informational representation. ___________________________ Bio: Dr. Abayomi is the Head of Science for Gumbel Demand […]
