Homological mirror symmetry is a deep mathematical conjecture

proposed by Maxim Kontsevich at the 1994 ICM in Zürich, and it is about

a certain relationship between the two mathematical areas of symplectic

geometry and algebraic geometry. More precisely, the conjecture states

that there is a derived equivalence between the so-called Fukaya

category in symplectic geometry, and the category of...

A typical game theoretic question is this: given some set of information and available memory, what conditions can an agent force? This talk will tackle the converse: given a class of conditions, what information and memory does an agent need to force the conditions? Specifically, I present the logic ATL* for reasoning about strategic ability in a multi-agent settings, and show that for...

The two-dimensional Gaussian free field is the canonical model for a random surface and is important in many different areas of mathematics and physics. It is the two-dimensional time analog of Brownian motion and enjoys many similar properties, such as a certain domain Markov property and local sets, i.e., higher-dimensional versions of stopping times. In this talk, we introduce these...

Percolation studies the behaviour of clusters in random graphs. It has applications to modeling phenomena as diverse as magnetism, spread of infectious diseases, and the adaption of new technologies in society. This talk will give a brief overview of the theory of percolation, starting from the celebrated Harris-Kesten theorem on percolation in the square lattice in two dimensions. We will...