Seminars Sorted by Series

The PCP theorem says that any mathematical proof can be written in a special "PCP" format such that it can be verified, with arbitrarily high probability, by sampling only a few symbols in the proof. Hence the name, Probabilistically Checkable...

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...

The unique games conjecture gives a very strong PCP theorem, which, if true, leads to a clean understanding of a broad family of approximation problems. We will describe recent progress on the conjecture and how certain type of expansion and...

The 4th Clay Millenium problem has a very simple formulation: may viscous incompressible fluids form a singularity in finite time? The answer is no in dimension two as proved by Leray in 1932, but the three dimensional problem is out of reach. More...

In the last forty years, the study of singularity formation has mostly concerned model problems and focusing non linearities. In this second lecture, we will try to give a unified overview on the known mechanisms of singularity formation, with in...

The defocusing Non Linear Schrödinger equation $iu_{t} = \Delta {u-u}|u|^{p-1}$ is a classical model of mathematical physics. For energy subcritical non linearities, Ginibre and Velo proved in the ’80s that all solutions are global in time and...

Given several real numbers $\alpha_1,...,\alpha_k$, how well can you simultaneously approximate all of them by rationals which each have the same square number as a denominator? Schmidt gave a clever iterative argument which showed that this can be...

Given any non-negative function $\f:\mathbb{Z}\rightarrow\mathbb{R}$, it follows from basic ergodic ideas that either 100% of real numbers $\alpha$ have infinitely many rational approximations $a/q$ with $a,q$ coprime and $|\alpha-a/q|

I'll describe a recent resolution of this conjecture, which recasts the problem in combinatorial language, and then uses a general 'structure vs randomness' principle combined with an iterative argument to solve this combinatorial problem.

Many important consequences of the Riemann Hypothesis would remain true even if there were some zeros off the critical line, provided these exceptions to the Riemann Hypothesis are suitably rare. We can unconditionally prove some results on the...

Anisha Thomas is hosting the festival of Holi for the IAS community.

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...

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...

Logarithmic Gromov-Witten invariants generalize usual and relative Gromov-Witten invariants and were first suggested by Siebert and then recently introduced by Gross-Siebert and Abramovich-Chen. Applications include more general degeneration...

Following Katz-Nishinou, we will compute the number of lines on a quintic threefold in $\mathbb P^4$ by degenerating the quintic to the union of coordinate hyperplanes. This motivates degeneration formulae in Gromov-Witten theory that I will give...

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...

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...

I'll begin with a leisurely introduction to Fukaya A-infinity algebras and their bounding chains. Then I'll explain how to use bounding chains to define open Gromov-Witten invariants. The bounding chain invariants can be computed using an open...

I'll begin with a leisurely introduction to Fukaya A-infinity algebras and their bounding chains. Then I'll explain how to use bounding chains to define open Gromov-Witten invariants. The bounding chain invariants can be computed using an open...

I will give an introduction to the microlocal theory of sheaves after Kashiwara and Schapira, and some of its recent applications in symplectic topology. I'll start with the basics, but target applications for the 75 minutes are Tamarkin's proof of...

I will survey the coherent-constructible correspondence of Bondal, which embeds the derived category of coherent sheaves on a toric variety into the derived category of constructible sheaves on a compact torus. The tools of the first lecture turn...