# Recently Added

## Edward T Cone Concert Series Post Concert Discussion

## High Dimensional Expansion and Error Correcting Codes

High dimensional expansion generalizes edge and spectral expansion in graphs to higher dimensional hypergraphs or simplicial complexes. Unlike for graphs, it is exceptionally rare for a high dimensional complex to be both sparse and expanding. The only known such expanders are number-theoretic or group-theoretic.

## Constraint Satisfaction Problems and Probabilistic Combinatorics I

The tasks of finding and randomly sampling solutions of constraint satisfaction problems over discrete variable sets arise naturally in a wide variety of areas, among them artificial intelligence, bioinformatics and combinatorics, and further have deep connections to statistical physics.

## TMF and SQFT

## Deforming Holomorphic Chern-Simons at Large N

We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira-Spencer gravity. This gives a complete description of open-closed string field theory in the topological B-model. We explain an anomaly cancellation mechanism at all loops in perturbation theory in this model. At one loop this anomaly cancellation is analogous to the Green-Schwarz mechanism. This is joint work with Kevin Costello.

## An isoperimetric inequality for the Hamming cube and some consequences

I will introduce an isoperimetric inequality for the Hamming cube and some of its applications. The applications include a “stability” version of Harper’s edge-isoperimetric inequality, which was first proved by Friedgut, Kalai and Naor for half cubes, and later by Ellis for subsets of any size. Our inequality also plays a key role in a recent result on the asymptotic number of maximal independent sets in the cube.

This is joint work with Jeff Kahn.

## The singular set in the fully nonlinear obstacle problem

For the Obstacle Problem involving a convex fully nonlinear elliptic operator, we show that the singular set of the free boundary stratifies. The top stratum is locally covered by a $C^{1,\alpha}$-manifold, and the lower strata are covered by $C^{1,\log^\eps}$-manifolds. This essentially recovers the regularity result obtained by Figalli-Serra when the operator is the Laplacian.