Title: Ways to write a positive integer into sums of positive integers Abstract: Take a positive integer, say 4; we can write it as a sum of positive integers in the following five ways: 4, 3+1, 2+2, 2+1+1, 1+1+1+1. Among these five ways, how many have only odd numbers as summands? How many of them […]
Title: K-Theory of Adic SpacesAbstract: We will explain a new approach to the K-theory of analytic adic spaces via condensed mathematics. Its main advantage is that it allows us to define K-theory in that context as the (continuous) K-theory of a certain dualizable stable infty-category associated to an analytic adic space (as opposed to previous […]
Title: The Geometry of the Hitchin Fibration for Symmetric Spaces Abstract: Motivated by questions in relative Langlands and relative endoscopy, we study generalized Hitchin systems associated to symmetric spaces. We will use two new techniques in invariant theory, the regular quotient and the parabolic cameral cover, in an effort to describe the geometry of such […]
Title: Frieze Patterns Abstract: As we are in the midst of a cold, dark winter... there is no better time to learn about frieze patterns. Frieze patterns were first defined by mathematicians to classify certain symmetries in ancient art and architecture. In this talk, we will explore arrays of mathematical objects that obey these classified frieze pattern […]
Title: The role of curvature in the production of sound: Music, Geometry and BeyondAbstract: When a string vibrates, it produces different pitches depending on its length. This is how guitarists can play several notes using only one string. But what happens when we have surfaces or 3D objects that vibrate, like when playing a flute, […]