## Extraordinary Physics with Millisecond Pulsars

Scott Ransom

National Radio Astronomy Observatory

November 22, 2016

Scott Ransom

National Radio Astronomy Observatory

November 22, 2016

Emmanuel Abbe

Princeton University

November 28, 2016

The stochastic block model (SBM) is a random graph model with planted clusters. It has been popular to model unsupervised learning problems, inhomogeneous random graphs and to study statistical versus computational tradeoffs. This talk overviews the recent developments that establish the thresholds for SBMs, the algorithms that achieve the thresholds, and the techniques (genie reduction, graph splitting, nonbacktracking propagation) that are likely to apply beyond SBMs.

Thomas Church

Stanford University; Member, School of Mathematics

November 28, 2016

Representation theory over $\mathbb Z$ is famously intractable, but "representation stability" provides a way to get around these difficulties, at least asymptotically, by enlarging our groups until they behave more like commutative rings. Moreover, it turns out that important questions in topology/number theory/representation theory/... correspond to asking whether familiar algebraic properties hold for these "rings".

Orit Raz

Member, School of Mathematics

November 29, 2016

In this talk I will review some of the classical (and fundamental) results in the theory of graph rigidity.

Claude Viterbo

Ecole Normale Supérieure

November 29, 2016

We shall give a construction of the quantized sheaf of a Lagrangian submanifold in $T^*N$ and explain a number of features and applications.

Sobhan Seyfaddini

Member, School of Mathematics

November 29, 2016

After introducing Hamiltonian homeomorphisms and recalling some of their properties, I will focus on fixed point theory for this class of homeomorphisms. The main goal of this talk is to present the outlines of a $C^0$ counterexample to the Arnold conjecture in dimensions four and higher. This is joint work with Lev Buhovsky and Vincent Humiliere.

Sheel Ganatra

Member, School of Mathematics

November 30, 2016

Noncommutative geometry, as advocated by Konstevich, proposes to replace the study of (commutative) varieties by the study of their (noncommutative) dg/A-infinity categories of perfect complexes. Conveniently, these techniques can then also be applied to Fukaya categories. In this mini-course, we will review some basic properties and structures in noncommutative geometry, with an emphasis on the notion of "smoothness" of a category and its appearance in topology and both sides of homological mirror symmetry.

Jean Bourgain

IBM von Neumann Professor, School of Mathematics

November 30, 2016

Marie-France Vignéras

Institut de Mathématiques de Jussieu

November 30, 2016

Let $F$ be a local field with finite residue characteristic $p$, let $C$ be an algebraically closed field of characteristic $p$, and let $\mathbf G$ be a connected reductive $F$-group. With Abe, Henniart, Herzig, we classified irreducible admissible $C$-representations of $G=\mathbf G(F)$ in terms of supercuspidal representations of Levi subgroups of $G$. For a parabolic subgroup $P$ of $G$ with Levi subgroup $M$ and an irreducible admissible $C$-representation $\tau$ of $M$, we determine the lattice of subrepresentations of $\mathrm{Ind}_P^G \tau$.

Sheel Ganatra

Member, School of Mathematics

December 2, 2016

Noncommutative geometry, as advocated by Konstevich, proposes to replace the study of (commutative) varieties by the study of their (noncommutative) dg/A-infinity categories of perfect complexes. Conveniently, these techniques can then also be applied to Fukaya categories. In this mini-course, we will review some basic properties and structures in noncommutative geometry, with an emphasis on the notion of "smoothness" of a category and its appearance in topology and both sides of homological mirror symmetry.