Seminars from until

The generalized exclusion system on Z models the dynamics of particles with strong local interaction induced by an exclusion rule in which at most K particles may occupy the same site. When the underlying random walks have symmetric transition rates and particle locations are initialized according to a (possibly non-homogeneous) product Binomial measure, the occupation variables of the system obey a strong form of negative association called the strong Rayleigh property. As shown by Liggett (2009), this property yields simply-stated (but abstract) conditions for the scaled number of particles in a set to converge to a Poisson distribution. This extends naturally to conditions for convergence of the point process of particle positions to a Poisson random measure (PRM) on the real line. A precise analysis of particle covariances gives explicit scaling limits to a PRM with exponential intensity in the context of translation invariance and a highly-nonequilibrium `step’ initial condition in which infinitely many particles lie below a maximal one. Moreover, these limit theorems can be extended to certain initial conditions outside the strong-Rayleigh context. This talk will discuss joint work with Adrian Gonzalez Casanova (Arizona State) and Sunder Sethuraman (Arizona).

We present our solutions to two long standing open problems, one from probability theory formulated by Malyshev in 1970 and another one from a crossroad of geometry and dynamics, going back to Darboux in 1879. The Malyshev problem is of finding effective, explicit necessary and sufficient conditions in the closed form to characterize all random walks in the quarter plane with a finite group of the random walk of order 2n, for all n ≥ 2. Previously known results covered the cases n = 2, 3, and 4. We also describe all n-periodic Darboux transformations for four-bar link problems for all n ≥ 2, thus completely solving the Darboux problem, that he solved for n = 2, and which was recently extended to n = 3. The talk is based on a joint work with Milena Radnovic (arXiv:2512.21976).

In this talk we examine some aspects of the classical-quantum correspondence induced by symplectic maps and metaplectic operators. We first recall the notion of the metaplectic group, the double covering of the symplectic group.

We then extend this construction to the complex setting and define the metaplectic semigroup associated with the semigroup of positive complex symplectic linear maps. In this context, we review the various definitions appearing in the literature, notably those due to M. Brunet and P. Kramer, L. Hörmander, and R. Howe.

We finally establish several properties of the metaplectic semigroup, with particular emphasis on applications to time-frequency analysis and to evolution equations with complex quadratic Hamiltonians.

This talk is based on joint work with G. Giacchi, M. Malagutti, A. Parmeggiani and L. Rodino.

Since the groundbreaking work of M. Gromov in the 1980s many tools have been developed for distinguishing open symplectic domains. However, until recently, similar questions in the contact geometric setup were largely open. For instance, it was not known whether there are open domains in the standard contact vector space of dimension $>3$ which are diffeomorphic but not contactomorphic to it (in dimension $3$ it is known that all of them are). In my lecture I will discuss Floer theoretic tools for answering this type of questions. As one application I will construct a continuous family of pairwise non-contactomorphic open balls in the standard contact ${\mathbb R}^5$. The lecture is based on a joint work in progress with K. Ajij, Mahan Mj, Dishant Pancholi and L. Polterovich.

Let us consider two notions of concentration for homogeneous polynomials in $d$ complex variables on the unit sphere: a local notion measuring the fraction of the $L^2$-norm supported on a measurable subset and a global notion given by the generalized Wehrl entropy. Lieb and Solovej proved that the extremizers in both cases are monomials up to a unitary rotation. Their result generalizes the one by Lieb in 1978 on the Wehrl entropy conjecture for coherent states in representations of the Heisenberg group to symmetric representations of the groups $\operatorname{SU}(d)$.

In this talk, we will focus on the stability of the previous inequalities. Namely, if the concentration is close to the optimal one, we will quantify how close the polynomial is to the extremizers. This is obtained in full generality in the case $d=2$, while in the case of higher dimensions restrictions on the size of the subset or on the degree of the polynomials arise. We will finally recover analogous stability results in the Bargmann–Fock space.

This is a joint work with Joaquim Ortega-Cerdà (UB-CRM).

The Zakharov-Kuznetsov equation (ZK) is a model for the propagation of waves in the context of plasma physics and can be viewed as a two-dimensional analogue of the celebrated Korteweg-de Vries equation (KdV). In this talk, we study the Cauchy problem associated with the $k$-generalized Zakharov-Kuznetsov equation (gZK) posed on $\mathbb{R} \times \mathbb{T}$, where $k \geq 2$ is an integer. We establish several new Strichartz-type estimates in the framework of Jean Bourgain's $X_{s,b}$ spaces, with the main contributions being an almost optimal linear $L^4$-estimate and a family of bilinear refinements of this bound. As a direct application, we prove multilinear $X_{s,b}$-estimates that lead to improved local well-posedness thresholds for gZK via a fixed-point iteration.