Video Lectures

An Anosov flow Φ on a closed 3-manifold M gives rise to a non-Weinstein Liouville structure on V:=[−1,1]×M. Building upon the work of Hozoori, we establish a homotopy correspondence between Anosov flows and certain pairs of contact forms. Moreover...

Noetherianity is a fundamental property of modules, rings, and topological spaces that underlies much of commutative algebra and algebraic geometry. This talk concerns algebraic structures such as the infinite-dimensional polynomial ring K[x_1,x_2...

In interactive coding, Alice and Bob wish to compute some function f of their private inputs x and y. They do this by engaging in a non-adaptive (fixed speaking order, fixed length) protocol to jointly compute f(x,y). The goal is to do this in an...

In Hamiltonian Floer theory one needs to regularize infinitely many moduli spaces. It is convenient to formalize the discussion using the language of flow categories and bimodules. In this lecture I will explain how to use the notion of "derived...

The XY and the Villain models are models which exhibit the celebrated Kosterlitz-Thouless phase transitions in two dimensions. The spin wave conjecture, originally proposed by Dyson and by Mermin and Wagner, predicts that at low temperature, spin...

I will introduce a new version of symplectic homology that resembles the relative symplectic homology and that is related to the symplectic homology of a Liouville sector. This version, called selective symplectic homology, is associated with a...

J. Duncan will explain how the works of Andrew Ogg—especially his questions—have guided the maturation of moonshine from its inception to the present, and continue to shape its future perspective.

Ogg’s celebrated conjecture can be paraphrased as saying that rational points (on the modular curves that parametrize torsion points on elliptic curves) exist if and only if there is a good geometric reason for them to exist. Ogg’s mathematical...

Ogg’s celebrated conjecture can be paraphrased as saying that rational points (on the modular curves that parametrize torsion points on elliptic curves) exist if and only if there is a good geometric reason for them to exist. Ogg’s mathematical...