2024 Distinguished Lecture Series

Department of Mathematics, University of Hawai'i at Manoa







Benson Farb

University of Chicago



Public Lecture: Polynomials, Braids, and You

Tuesday, April 23 at 5:30pm (PSB 217)

Target Audience: Curious people of any age!

Abstract: Whether you like it or not, polynomials run your life : almost every equation that describes the world is either a polynomial or is well-approximated by a polynomial. In 2500 years of studying polynomials, we've learned a lot, but they still have mysteries to reveal. Mathematicians continue to understand solutions to polynomial equations in new ways. They are doing this by relating polynomials to spaces of configurations of objects (e.g. of satellites orbiting the Earth, or of robots on a factory floor), to braids, to hyperplanes, and more. Most remarkably, these seemingly disparate topics are all part of one beautiful, profound, intertwined picture.

Registration:

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Colloquium: Hilbert's 13th Problem and geometry

Thursday, April 25 at 3:30pm (PSB 217)

Target Audience: Much of this talk should be accessible to undergraduate math majors

Abstract: Hilbert's 13th Problem is a fundamental open problem about 1-variable polynomials. In this talk I will explain how Hilbert's 13th (and related problems) fits into a wider framework that includes, for example, problems in enumerative algebraic geometry and the theory of modular functions. I will then report on some recent progress, joint with Mark Kisin and Jesse Wolfson.

Colloquium will be followed by a department tea.





Seminar: Rigidity of moduli spaces and algebro-geometric constructions

Friday, April 26 at 3:30pm (Keller 303)

Target Audience: Much of this talk should be understandable to advanced undergraduates.

Abstract: Algebraic geometry contains an abundance of miraculous constructions, from ``resolving the quartic'' to the 9 flex points on a smooth cubic curve to the Jacobian of a genus g curve. In this talk I will explain some ways to systematize and formalize the idea that such constructions are special: conjecturally, they should be the only ones of their kind. I will state a few of these (mostly open) conjectures, and describe some methods used to solve some of them (coming from e.g. topology, geometric group theory, complex geometry). These conjectures can be viewed as forms of rigidity (a la Mostow and Margulis) for various moduli spaces and maps between them. They can also be viewed as a call for a "systematic search" for miracles.