Oct 25 2016

### Arithmetic regularity, removal, and progressions

Speaker: Jacob Fox

4:00pm | S-101
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 discuss some shocking...

Oct 25 2016

### Dependent random choice

Speaker: Jacob Fox

4:00pm | S-101
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 several striking applications,...

Oct 24 2016

### Regularity methods in combinatorics, number theory, and computer science

Speaker: Jacob Fox

4:00pm | S-101
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 structural result for all...

Mar 06 2015

### On random walks in the group of Euclidean isometries

Speaker: Elon Lindenstrauss

2:00pm | S-101
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 $\mathrm{SO}(d)$, can...

Mar 04 2015

### Joint equidistribution of arithmetic orbits, joinings, and rigidity of higher rank diagonalizable actions II

Speaker: Elon Lindenstrauss

2:00pm | S-101
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 the study of dynamical...

Mar 02 2015

### Joint equidistribution of arithmetic orbits, joinings, and rigidity of higher rank diagonalizable actions I

Speaker: Elon Lindenstrauss

2:00pm | S-101
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 the study of dynamical...

Feb 14 2014

### Arithmetic hyperbolic 3-manifolds, perfectoid spaces, and Galois representations III

Speaker: Peter Scholze

3:30pm | S-101
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 interplay of these...

Feb 12 2014

### Arithmetic hyperbolic 3-manifolds, perfectoid spaces, and Galois representations II

Speaker: Peter Scholze

2:00pm | S-101
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 interplay of these...

Feb 10 2014

### Arithmetic hyperbolic 3-manifolds, perfectoid spaces, and Galois representations I

Speaker: Peter Scholze

2:00pm | S-101
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 interplay of these...

Mar 14 2013

### The Codimension Barrier in Incidence Geometry

Speaker: Larry Guth

2:00pm | S-101
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 given L and a given...