## Near-coherent Scrambling

Alexei Kitaev

December 5, 2017

Alexei Kitaev

December 5, 2017

Jun Su

Princeton University

December 5, 2017

We consider the coherent cohomology of toroidal compactifications of Shimura varieties with coefficients in the canonical extensions of automorphic vector bundles and show that they can be computed as relative Lie algebra cohomology of automorphic representations. Consequently, any Galois representation attached to these coherent cohomology should be automorphic. Our proof is based on Franke’s work on singular cohomology of locally symmteric spaces and via Faltings’ B-G-G spectral sequence we’ve also strengthened Franke’s result in the Shimura variety case.

Daniel Jafferis

December 5, 2017

Daniel Holz

The University of Chicago

December 5, 2017

Leonard Susskind

December 5, 2017

Steve Shenker

December 5, 2017

Xiaoliang Qi

December 5, 2017

Madhu Sudan

Harvard University

December 4, 2017

Greta Panova

University of Pennsylvania; von Neumann Fellow, School of Mathematics

December 4, 2017

We will give a brief overview of the classical topics, problems and results in Algebraic Combinatorics. Emerging from the representation theory of $S_n$ and $GL_n$, they took a life on their own via the theory of symmetric functions and Young Tableaux and found applications into new fields. In particular, these objects can describe integrable lattice models in statistical mechanics like dimer covers on the hexagonal grid, aka lozenge tilings.

Amitai Zernik

Member, School of Mathematics

December 4, 2017

In joint work with Buryak, Pandharipande and Tessler (in preparation), we define equivariant stationary descendent integrals on the moduli of stable maps from surfaces with boundary to $(\mathbb{CP}^1,\mathbb{RP}^1)$. For stable maps of the disk, the definition is geometric and we prove a fixed-point formula involving contributions from all the corner strata. We use this fixed-point formula to give a closed formula for the integrals in this case.