## Friends Lunch with a Member

Reuben Jonathan Miller, Friends of the Institute for Advanced Study Member

School of Social Science

February 10, 2017

Reuben Jonathan Miller, Friends of the Institute for Advanced Study Member

Yve-Alain Bois

Pablo Picasso did not speak often about abstraction, but when he did, it was either to dismiss it as complacent decoration or to declare its very notion an oxymoron. The root of this hostility is to be found in the impasse that the artist reached in the summer 1910, when abstraction suddenly appeared as the logical development of his previous work, a possibility at which he recoiled in horror. But though he swore to never go again near abstraction, he could not prevent himself from testing his... Read more

Reuben Jonathan Miller, Friends of the Institute for Advanced Study Member

School of Social Science

February 10, 2017

Reuben Jonathan Miller, Friends of the Institute for Advanced Study Member

Tony Yue Yu

Visitor, School of Mathematics

February 13, 2017

Berkovich geometry is an enhancement of classical rigid analytic geometry. Mirror symmetry is a conjectural duality between Calabi-Yau manifolds. I will explain (1) what is mirror symmetry, (2) what are Berkovich spaces, (3) how Berkovich spaces appear naturally in the study of mirror symmetry, and (4) how we obtain a better understanding of several aspects of mirror symmetry via this viewpoint. This member seminar serves also as an overview of my minicourses in the same week.

Ilya Razenshteyn

Massachusetts Institute of Technology

February 13, 2017

I will show a new efficient approximate nearest neighbor search (ANN) algorithm over an arbitrary high-dimensional *symmetric* norm. Traditionally, the ANN problem in high dimensions has been studied over the $\ell_1$ and $\ell_2$ distances with a few exceptions. Thus, the new result can be seen as a (modest) step towards a "unified theory" of similarity search.

Mariusz Mirek

University of Bonn; Member, School of Mathematics

February 8, 2017

Given $d, k\in\mathbb N$, let $P_j$ be an integer-valued polynomial of $k$ variables for every $1\le j \le d$. Suppose that $(X, \mathcal{B}, \mu)$ is a $\sigma$-finite measure space with a family of invertible commuting and measure preserving transformations $T_1, T_2,\ldots,T_{d}$ on $X$. For every $N\in\mathbb N$ and $x \in X$ we define the ergodic Radon averaging operators by setting \[ A_N f(x) = \frac{1}{N^{k}}\sum_{m \in [1, N]^k\cap\mathbb Z^k} f\big(T_1^{ P_1(m)}\circ T_2^{ P_2(m)} \circ \ldots \circ T_{d}^{ P_{d}(m)} x\big).

Dmitry Orlov

Steklov Mathematical Institute, Russian Academy of Sciences; Member, School of Mathematics

February 8, 2017

David Lang

IAS

February 3, 2017

Amir Ali Ahmadi

Princeton University

February 7, 2017

In recent years, there has been a surge of exciting research activity at the interface of optimization (in particular polynomial, semidefinite, and sum of squares optimization) and the theory of dynamical systems.

Alexandru Oancea

Université Pierre et Marie Curie; Member, School of Mathematics

February 6, 2017

The Hofer-Zehnder capacity of a symplectic manifold is one of the early symplectic invariants: it is a non-negative real number, possibly infinite. Finiteness of this capacity has strong consequences for Hamiltonian dynamics, and it is an old question to decide whether it holds for small compact neighborhoods of closed Lagrangians. I will explain a positive answer to this question for a class of manifolds whose free loop spaces admit nontrivial local systems.

Prasad Raghavendra

University of California, Berkeley

February 6, 2017

Random constraint satisfaction problems (CSPs) are known to exhibit threshold phenomena: given a uniformly random instance of a CSP with $n$ variables and $m$ clauses, there is a value of $m = \Omega(n)$ beyond which the CSP will be unsatisfiable with high probability. Strong refutation is the problem of certifying that no variable assignment satisfies more than a constant fraction of clauses; this is the natural algorithmic problem in the unsatisfiable regime (when $m/n=\omega(1)$).

Klaus Larres

January 27, 2017

followed by a Member talk and dinner with spouses at 7:00 p.m.