Seminars Sorted by Series

Let Q be a non-degenerate indefinite quadratic form in d variables. In the mid 80's, Margulis proved the Oppenheim conjecture, which states that if d ≥ 3 and Q is not proportional to a rational form then Q takes values arbitrarily close to zero at...

In this talk I will discuss some definitions of exponential mixing and other rates of mixing and discuss some of its consequences.

In classical or quantum systems with time scales widely separated by a small slowness parameter, the fast system is driven by the slow and reacts back on it. The asymptotics of the driven fast motion has been much studied, but understanding the...

I shall discuss two related local regularity results for asymptotically hyperbolic (or complex hyperbolic) Einstein metrics, near a point at infinity: local polyhomogeneity and unique continuation.

A three dimensional strongly pseudoconvex Cauchy Riemann manifold can be considered as a contact manifold with a conformal structure on the hyperplane distribution. In this talk, we will discuss CR structures near the standard one on S^3 , the...

Simple cell decompositions of surfaces are in one to one correspondence with certain conjugacy classes of subgroups of the modular group. Polycrystalline structures in 2 dimensional materials give rise to statistical simple cell decompositions of...

In 2007, Dvir proved the Kakeya conjecture over finite fields. His proof uses the polynomial method: we take a hypothetical strange set, find a polynomial that vanishes on the set, and use properties of polynomials to show that the set does not...

The k-dilation of a mapping F measures how much the mapping stretches k-dimensional areas. If a map F has k-dilation L , then it maps each k-dimensional surface of k-volume V to an image of k-volume at most LV. If the k-dilation of a map is very...

Let $H$ be any smooth function on $R^4$ and let $Y$ be any compact and regular level set. I'll explain a proof that $Y$ admits an infinite family of proper compact subsets that are invariant under the Hamiltonian flow, which moreover have dense...

In joint work with Barry Mazur, we obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields, giving evidence for a generalized Parity Conjecture. Heegner points can account for large Selmer groups in dihedral...

Since the proof of Iwasawa's main conjecture in the classical case (theorem of Mazur and Wiles), automorphic forms on GL(2) have played an essential role to understand Iwasawa theory for GL(1). In this lecture, Leopoldt 's conjecture for totally...

For the Rankin-Selberg L-function L(s, , ), there are central value formulas or derivative formulas depending on its root number. Using theta-lifting, Waldspurger showed an explicit formula relating the central value to certain period integral. We...

Let F be a local field of characteristic 0. We consider distributions on GL(n+1,F) which are invariant under the adjoint action of GL(n,F). We prove that such distributions are invariant under transposition. This implies that an irreducible...

In this talk, I will present a proof of a Poincaré--Birkhoff theorem for Hamiltonian maps on Liouville domains which are only continuous at the boundary. The motivation is finding periodic orbits in the circular, restricted three-body problem. Based...

The US political system is built on representatives chosen by geographically localized regions. This presents the government with the problem of designing these districts. Every ten years, the US census counts the population and new political...

In these two lectures, I will come back and develop the material outlined in the Monday Seminar. More precisely, I will explain with more details the notion of microsupport of sheaves and its behaviour with respect to the operations, in particular...

In these two lectures, I will come back and develop the material outlined in the Monday Seminar. More precisely, I will explain with more details the notion of microsupport of sheaves and its behaviour with respect to the operations, in particular...

Consider a group of measure preserving transformations acting on a probability space. The limiting behavior of the nonconventional ergodic averages associated with this action has been the subject of much attention since the work of Furstenberg on...

A number is said to be $y$-smooth if all of its prime factors are less than $y$. Such numbers appear in many places throughout analytic and combinatorial number theory, and much work has been done to investigate their distribution. I will try to...

Thanks to the work of Katz and Sarnak on L-functions over function fields, we know that the Frobenius classes associated to L-functions of hyperelliptic curves over a finite field with $q$ elements, $F_{q}$, becomes equidistributed in the unitary...

We review the well known microscopic correspondence between random zeros of the Riemann zeta-function and the eigenvalues of random matrices, and discuss evidence that this correspondence extends to larger mesoscopic collections of zeros or...

The logical questions concern algorithms for testing solvability of equations (and more generally truth of first-order sentences), and have positive answers for the real exponential and the Weierstrass functions (assuming respectively the Schanuel...

This talk will contain a more technical discussion of the material covered in the Princeton University Mathematics Colloquium the previous day.

We consider the ground state of the $XY$ model of an infinite spin chain at zero temperature. Following C. Bennett, H. Bernstein, S. Popescu, and B. Schumacher, we use the von Neumann entropy of a sub-system as a measure of entanglement. G. Vidal, J...

Loop calculus is a new theoretical tool which allows to express partition function of a statistical inference/physics problem on a graph in terms of a series. Each term of the series is associated with a loop on the graph. Utility of the loop...

We will briefly review the construction of the quantum sigma model with target a Torus adapting the work of Kapustin and Orlov (hep-th/0010293v2) to the Hamiltonian setup. This allows us to set up mirror-symmetry for tori entirely within the vertex...

The theory of Hitchin systems and their moduli spaces of solutions has important connections to N=2 gauge theory in four dimensions. Exploring this connection, we have conjectured the existence of certain integral invariants which encode the...

The NLSE is relevant for the explorations of Bose-Einstein Condensates and for Nonlinear Classical Optics. In presence of a random potential it can be used to study the competition between Anderson localization, that is characteristic of linear...

In this talk I will describe a real-variable method to extract long-time asymptotics for solutions of many nonlinear equations (including the Schrodinger and mKdV equations). The method has many resemblances to the classical stationary phase method...

The Coulomb Gas is a model of Statistical Mechanics with a special type of phase transition. In the first part of the talk I will review the expected features conjectured by physicists and the few mathematical results so far obtained. The second...

It is well known that spectral properties of quasiperiodic operators depend rather delicately on the arithmetics of the parameters involved. Consequently, obtaining results for all parameters often requires considerably more difficult arguments than...

The rigorous derivation of the Vlasov equation from Newtonian mechanics of $N$ Coulomb-interacting particles is still an open problem. In the talk I will present recent results, where an $N$-dependent cutoff is used to make the derivation possible...