Resilient functions

Eshan Chattopadhyay
Member, School of Mathematics
September 20, 2016
A resilient function $f: X^n to \{0,1\}$, for some set $X$, is such that every subset of coordinates of bounded size has small influence on the function. Such functions have applications in computer science, and are of independent interest of study as well. In this talk, I will motivate resilient functions from an application in distributed computing, present some known results on resilient functions and open directions for future work.

Lagrangian cell complexes and Markov numbers

Jonny Evans
University College London
September 20, 2016
Joint work with Ivan Smith. Let p be a positive integer. Take the quotient of a 2-disc by the equivalence relation which identifies two boundary points if the boundary arc connecting them subtends an angle which is an integer multiple of ($2 \pi / p$). We call the resulting cell complex a '$p$-pinwheel'. We will discuss constraints on Lagrangian embeddings of pinwheels. In particular, we will see that a p-pinwheel admits a Lagrangian embedding in $CP^2$ if and only if $p$ is a Markov number.

Non-archimedean geometry for symplectic geometers

Mohammed Abouzaid
Columbia University; Member, School of Mathematics
September 21, 2016
I will explain basic tools for thinking about derived categories of coherent sheaves on rigid analytic spaces that are conducive to the study of homological mirror symmetry. A particular focus will be placed on the case of curves, and on methods that help get around problems of coherence in derived constructions.