Seminars Sorted by Series

The Goncharov reading group is an informal seminar which will read the paper "Volumes of hyperbolic manifolds and mixed Tate motives" and related materials. We will meet on Wednesdays at 10 am in Simonyi 114.

The Goncharov reading group is an informal seminar which will read the paper "Volumes of hyperbolic manifolds and mixed Tate motives" and related materials. We will meet on Wednesdays at 10 am in Simonyi 114.

The Goncharov reading group is an informal seminar which will read the paper "Volumes of hyperbolic manifolds and mixed Tate motives" and related materials. We will meet on Wednesdays at 10 am in Simonyi 114.

The Goncharov reading group is an informal seminar which will read the paper "Volumes of hyperbolic manifolds and mixed Tate motives" and related materials. We will meet on Wednesdays at 10 am in Simonyi 114.

The Goncharov reading group is an informal seminar which will read the paper "Volumes of hyperbolic manifolds and mixed Tate motives" and related materials. We will meet on Wednesdays at 10 am in Simonyi 114.

The Goncharov reading group is an informal seminar which will read the paper "Volumes of hyperbolic manifolds and mixed Tate motives" and related materials. We will meet on Wednesdays at 10 am in Simonyi 114.

We consider the problem of finding complete conformal metrics determined by a symmetric function of Ricci tensor in a negative convex cone on compact manifolds. A consequence of our main results is that any smooth bounded domain in Euclidean space...

I will discuss how some questions in conformal geometry can be answered using twistor theory. One such application is to the classification of locally conformally flat Hermitian surfaces. Another application is to determining the conformal...

A well-known example by N. N. Ural'tseva suggests that for fixed p > 2 there is no unique $W^2_p$-solvability of elliptic equations under p > the condition that the leading coefficients are measurable in two spatial variables. We will present a...

It has been known for a long time that varieties of general type are the most complicated algebraic varieties. It is only recently, however, that the correct definition of the "simplest" algebraic varieties was established. These are the rationally...

Hermann Weyl Lecture

Lecture 4. The Ax conjecture and degenerations. Originating with his studies on the logic of finite fields, James Ax conjectured that every PAC field is $C_1$. The recent proof of this in characteristic 0 is connected with degenerations of...

Summary: These lectures are devoted to the interplay between cohomology and Chow groups of a complex algebraic variety, and also to the consequences, on the topology of a family of smooth projective varieties, of statements concerning Chow groups of...

Random graphs and expander graphs can be viewed as sparse approximations of complete graphs, with Ramanujan expanders providing the best possible approximations. We formalize this notion of approximation and ask how well an arbitrary graph can be...

We will explain our recent solution of the Kadison-Singer Problem and the equivalent Bourgain-Tzafriri and Paving Conjectures. We will begin by introducing the method of interlacing families of polynomials and use of barrier function arguments to...

We explain what Ramanujan graphs are, and prove that there exist infinite families of bipartite Ramanujan graphs of every degree. Our proof follows a plan suggested by Bilu and Linial, and exploits a proof of a conjecture of theirs about lifts of...

These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the first lecture, we will set up the enumerative problem and survey what we know and what we conjecture about it. In...

These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the first lecture, we will set up the enumerative problem and survey what we know and what we conjecture about it. In...

These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the first lecture, we will set up the enumerative problem and survey what we know and what we conjecture about it. In...

On the reality of black holes. I will give a quick introduction to the initial value problem in GR and overview of the problems of Rigidity, Stability and Collapse and how they fit with regard to the Final State Conjecture.The gravitational waves...

I will discuss in some detail the main difficulties of the problem of nonlinear stability of black holes and the recent advances on the related issue of linear stability.The gravitational waves detected recently by LIGO were produced in the final...

I will discuss a recent result in collaboration with J. Szeftel concerning the nonlinear stability of the Schwarzschild spacetime under axially symmetric, polarized perturbations.The gravitational waves detected recently by LIGO were produced in the...

This introductory lecture will describe results about counting rational points on certain non-algebraic sets and sketch how they can be used to attack certain problems in diophantine geometry and functional transcendence.

This lecture will describe the historical context and some key properties of o-minimality. It will then describe certain results in functional transcendence, generalizing the classical results on exponentiation due to Ax, and sketch how they can be...

The Zilber-Pink conjecture is a far reaching finiteness conjecture in diophantine geometry, unifying and extending Mordell-Lang and Andre-Oort. This lecture will state the conjecture, illustrate its varied faces, and indicate how the point-counting...