11am, Steven Bradlow, Geometric Structures on Pretzels and Other Surfaces: What Goes on in a Mathematics Research Institute
As a CAS Fellow, Professor Bradlow spent three months in Fall 2019 at the Mathematical Sciences Research Institute, a remarkable place at the top of the Berkeley hills overlooking the San Francisco Bay. He was there for a program devoted to the mathematics of surfaces, a subject where geometry is no longer governed by Euclid’s postulates and exotic structures play a role in questions as varied as how to find the best way to avoid the corners of a polyhedron and questions in quantum field theories in physics. He will describe some of the themes of the program but will leaven the mathematics with some digressions about the hosting institute and its history.
Noon, Vesna Stojanoska, Solving Polynomial Equations with Homotopy Theory
Given a general polynomial, it can be hard or impossible to solve it, or even to tell if solutions exist within a fixed number system. The set of solutions is rather rigid: numbers that are “close” to a solution usually are not themselves solutions. So how can homotopy theory, the study of shapes that can be continuously deformed without changing their nature, help in solving polynomials? Professor Stojanoska will sketch some old ideas and new developments in the world of homotopical approaches to arithmetic questions.
