Video Lectures

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 contrast to symmetry breaking phases of matter, unconventional phases like spin liquids feature long-range quantum entanglement and relate to the deconfined phases of gauge theories. However, the realization of these states  in materials has...

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 the year AD 79, Mount Vesuvius erupted with devastating force, burying the nearby town of Pompeii under more than thirty feet of volcanic debris. Pompeii was wiped off the map, yet below the surface the material remains of the town were preserved...

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...

For a political scientist, the contradictory themes surrounding the Arabs and their region before the coming of Islam often seem strange and incomprehensible. Although there are no major barriers posed by rivers or mountain ranges, numerous...

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...