Seminars Sorted by Series

During the last 10 years the results and ideas from my work on unipotent flows have been widely used and applied to various problems arising from number theory, spectral theory, ergodic theory, the theory of elliptic curves, moduli spaces, dynamics...

Although equivariant cohomology originated -- at this Institute -- nearly half a century ago, only much more recently has it become an active area of algebraic geometry. The equivariant cohomology rings of simple algebraic varieties such as...

Although equivariant cohomology originated -- at this Institute -- nearly half a century ago, only much more recently has it become an active area of algebraic geometry. The equivariant cohomology rings of simple algebraic varieties such as...

Although equivariant cohomology originated -- at this Institute -- nearly half a century ago, only much more recently has it become an active area of algebraic geometry. The equivariant cohomology rings of simple algebraic varieties such as...

In 2007, Zeev Dvir shocked experts by giving a one-page proof of the finite field Kakeya problem. The new idea in the proof was to introduce high degree polynomials into a problem about points and lines. This idea has led to progress on several...

Polynomials are a special class of functions. They are useful in many branches of mathematics, often in problems which don't mention polynomials. We discuss two examples: polynomials in error-correcting codes and polynomials in geometric...

Incidence geometry is a part of combinatorics that studies the intersection patterns of geometric objects. For example, suppose that we have a set of L lines in the plane. A point is called r-rich if it lies in r different lines from the set. For a...

One of the most studied objects in mathematics is the modular curve, which is the quotient of hyperbolic 2-space by the action of \(\mathrm{SL}_2(\mathbb Z)\). It is naturally the home of modular forms, but it also admits an algebraic structure. The...

One of the most studied objects in mathematics is the modular curve, which is the quotient of hyperbolic 2-space by the action of \(\mathrm{SL}_2(\mathbb Z)\). It is naturally the home of modular forms, but it also admits an algebraic structure. The...

One of the most studied objects in mathematics is the modular curve, which is the quotient of hyperbolic 2-space by the action of \(\mathrm{SL}_2(\mathbb Z)\). It is naturally the home of modular forms, but it also admits an algebraic structure. The...

An important theme in homogenous dynamics is that two parameter diagonalizable actions have much more rigidity than one parameter actions. One manifestation of this rigidity is rigidity of joinings of such actions. Joinings are an important concept...

An important theme in homogenous dynamics is that two parameter diagonalizable actions have much more rigidity than one parameter actions. One manifestation of this rigidity is rigidity of joinings of such actions. Joinings are an important concept...

In contrast to the two dimensional case, in dimension $d \geq 3$ averaging operators on the $d-1$-sphere using finitely many rotations, i.e. averaging operators of the form $Af(x)= |S|^{-1} \sum_{\theta \in S} f(s x)$ where $S$ is a finite subset of...

Understanding the structure of large graphs is a fundamental problem, as it can yield critical insights into topics ranging from the spread of diseases to how the brain works to patterns in the primes. Szemerédi's regularity lemma gives a rough...

A celebrated theorem of Roth from 1953 shows that every dense set of integers contains a three-term arithmetic progression. This has been the starting point for the development of an enormous amount of beautiful mathematics. In this talk, I will...

We describe a simple yet surprisingly powerful probabilistic technique that shows how to find, in a dense graph, a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently, this technique has had...

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it...

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it...

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it...

In this lecture we will review the notion of the holonomy group of a Riemannian manifold and the Berger classification. We will discuss special algebraic structures in dimensions 6, 7 and 8, emphasising exterior algebra, and then go on to...

We will discuss the constructions of compact manifolds with exceptional holonomy (in fact, holonomy $G_{2}$), due to Joyce and Kovalev. These both use “gluing constructions”. The first involves de-singularising quotient spaces and the second...