Seminars Sorted by Series

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...

We explain how the Edge-reinforced random walk, introduced by Coppersmith and Diaconis in 1986, is related to several models in statistical physics, namely the supersymmetric hyperbolic sigma model studied by Disertori, Spencer and Zirnbauer (2010)...

Liouville Conformal Field Theory (LCFT) is an essential building block of Polyakov’s formulation of non critical string theory. Moreover, scaling limits of statistical mechanics models on random lattices (planar maps) are believed to be described by...

We prove that the Cauchy problem for the Benjamin-Ono-Burgers equation is uniformly globally well-posed in H^1 for all "\epsilon\in [0,1]". Moreover, we show that for any T>0 the solution converges in C([0,T]:H^1) to that of Benjamin-Ono equation as...

Manifolds with geometric structure carry large and useful families of non-standard “subharmonic” functions. For example, any almost complex manifold with hermitian metric carries plurisubharmonic functions. Moreover, it also carries “Lagrangian...

In three very interesting and suggestive papers, H. Carayol introduced new aspects of complex geometry and Hodge theory into the study of non-classical automorphic representations -- in particular, those involving the totally degenerate limits of...

The classical Pell equation $X^2-DY^2=1$, to be solved in integers $X,Y\neq 0$, has a variant for function fields (studied already by Abel), where now $D=D(t)$ is a complex polynomial of even degree and we seek solutions in nonzero complex...

Let \(N \geq 3\). In this talk, I will sketch a proof that the ring generated by Eisenstein series of weight \(1\) on the principal congruence subgroup \(\Gamma(N)\) contains all modular forms in weights \(2\) and above. This means that the only...