Seminars Sorted by Series

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...

I will discuss an approach to studying the limiting behavior of automorphic forms on quaternion algebras that succeeds admirably when the levels involved are large squares, and describe some new technical problems that arise in trying to relax this...

I will explain joint work with Kannan Soundararajan, where we find an "L-function analogue" of the Brun-Hooley sieve. Essentially, our method allows us to work analytically with long truncated Euler products inside the critical strip. As a...

We consider level sets of the Gaussian free field on the $d$-dimensional lattice, for $d>2$, above a given real-valued height $h$. This defines a percolation model with strong, algebraically decaying correlations. We prove a conjecture of Lebowitz...

We consider level sets of the Gaussian free field on the d-dimensional lattice, for d>2, above a given real-valued height h. This defines a percolation model with strong, algebraically decaying correlations. We prove a conjecture of Lebowitz...

Suppose you have a finite group G and you want to study certain related structures (e.g., random walks, Cayley graphs, word maps, etc.). In many cases, this might be done using sums over the characters of G. A serious obstacle in applying these...

Rank gives a natural filtration on representations of classical groups. The eta correspondence provides a clean description of a natural family of representations of a given rank, subject to certain bounds. There is evidence that this construction...

We present a deterministic algorithm for graph connectivity that uses the minimal amount of memory possible, up to a constant factor. Specifically, the algorithm's memory is comparable to that needed to store only a single node of the graph (i.e...

I will explain a very intriguing connection between low dimensional topology, knot invariants, and quantum computation: It turns out that in some well defined sense, quantum computation is _equivalent_ to certain approximations of the Jones...

Huygens' principle (in the narrow Hadamard's sense) for a second-order hyperbolic equation means that its fundamental solution is located on the characteristic conoid. Physically this implies that a localised disturbance will have an effect...

Very recently, J.Y. Welschinger introduced a set of invariants for real varieties that give lower bounds on the number of real algebraic curves satisfying certain incidence relations. After J. Solomon's homological interpretation, these invariants...

We study systems of linear ordinary differential equations dy/dz=A(z)y, where A is a matrix-valued rational function of z. By definition, such equation is rigid if it is uniquely determined by the type of its singularities. Our goal is to provide a...

The notion of Q-operator has been introduced by Baxter as a basic tool to solve quantum integrable systems. We develop Baxter Q-operator formalism for $\mathfrak{g}$-Toda chains for $\mathfrak{g}=\mathfrak{gl}(N,\mathbb{R})$. The constructed Q...

Drinfeld has initiated two geometric approaches to global Langlands conjectures over function fields: one by constructing automorphic sheaves and another one by realizing representations in cohomology of the moduli spaces of F-sheaves (also known as...