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14 seminars found


, Thursday

Probability in Mathematical Physics

Room P3.10, Mathematics Building, Instituto Superior TécnicoInstituto Superior Técnico


, INRIA Lyon.

Abstract

In this talk, I am going to present a generalization of the Porous Media Model (PMM) analogue of the Bernstein polynomial basis, in the context of gradient models. The PMM is a symmetric nearest-neighbour process associated with the Porous Media Equation, and the corresponding dynamics are kinetically constrained, in the sense that particles diffuse in the lattice under a set of conditions on local configurations. While in the PMM, the occupation values of two neighbouring sites are exchanged only if there are "enough" groups of particles around them, our generalized model describes a system where, at very low densities, there is no interaction, while at high densities, there is no space for movement. I am going to present the construction of the model and its main properties, and, if time permits, discuss its extension in a long-range interaction context.


, Friday

Lisbon young researchers

Room P3.10, Mathematics Building, Instituto Superior TécnicoInstituto Superior Técnico


Simone Gallivanone, Università degli Studi di Milano Bicocca.

Abstract

Since their introduction, generalized Toeplitz structures (in the sense of L. Boutet de Monvel and V. Guillemin) over contact manifolds have found numerous applications in fields such as CR geometry, analysis, and quantization. More recently, S. Zelditch introduced the concept of dynamical Toeplitz operators to study the dynamics of quantized contact transformations. These operators, closely tied to the geometry of the underlying manifold, have demonstrated significant applications in both geometry and analysis.

The aim of this talk is to provide a simple introduction to the geometric and analytical context of these operators on Grauert tube boundaries and to present, as an application, their connection to the complexification of Laplacian eigenfunctions.



, Tuesday

Geometria em Lisboa

Room P3.10, Mathematics Building, Instituto Superior TécnicoInstituto Superior Técnico


Francisco Nascimento, Instituto Superior Técnico.

Abstract

We present a systematic study of kinematic formulas in convex geometry. We first give a classical presentation of kinematic formulas for integration with respect to the rotation group $SO(n)$, where Steiner's Formula, the intrinsic volumes and Hadwiger's Characterization Theorem play a crucial role. Then we will show a new extension to integration along the general linear group $GL(n)$. Using the bijection of matrix polar decomposition and a Gaussian measure to integrate along positive definite matrices, a new formula is obtained, for which the classical $SO(n)$ formula is a particular case. We also reference the unitary group $U(n)$ case and its corresponding extension to the symplectic group $Sp(2n,\mathbb{R})$.


, Thursday

Probability in Mathematical Physics

Room P3.10, Mathematics Building, Instituto Superior TécnicoInstituto Superior Técnico


, Imperial College.

Abstract

We present a random interface model on the one-dimensional torus of size $N$ with a weak perturbation, i.e. an asymmetry $\sim N^{-\gamma}$ of the direction of growth that switches from up to down based on the sign of the area underneath. The evolution of the interface can be studied in terms of the density field of an underlying, non-Markovian exclusion process. We compute the order of the correlation functions of this process for the invariant measure of the interface model, and investigate the stationary fluctuations of the density field: we establish the convergence to an Ornstein-Uhlenbeck equation for $\gamma>\frac{8}{9}$, and discuss the limit for $\frac{1}{2}\leq \gamma<\frac{8}{9}$. Based on joint work with Martin Hairer and Patrícia Gonçalves.


, Friday

Probability in Mathematical Physics

Unusual schedule
Room P3.10, Mathematics Building, Instituto Superior TécnicoInstituto Superior Técnico


, Universidade do Minho.

Abstract

Reaction-diffusion equations arise naturally when modelling multi-component systems of interacting populations. These equations are widely employed to describe pattern formation phenomena across various biological, chemical and physical processes. The kinetic theory of statical mechanics provides a powerful framework to describe different types of interactions at multiple spatial or temporal scales. Through appropriate hydrodynamic limits of the kinetic systems, macroscopic equations can be derived, describing observable quantities and explaining how macroscopic phenomena emerge from the underlying microscopic dynamics. In this talk, I will apply these tools to study the evolution and interactions of competing bacterial populations on a leaf surface. Specifically, I will consider self and cross diffusion effects and investigate Turing instability properties leading to the formation and persistence of stationary spatial patterns.

This work is a collaboration with D. Cusseddu (University of Minho), M. Bisi and R. Travaglini (University of Parma, Italy).


, Tuesday

Geometria em Lisboa

Room P3.10, Mathematics Building, Instituto Superior TécnicoInstituto Superior Técnico


, The Chinese University of Hong Kong.

Abstract

3d mirror symmetry is a mysterious duality for certain pairs of hyperkähler manifolds, or more generally complex symplectic manifolds/stacks. In this talk, we will describe its relationships with 2d mirror symmetry. This could be regarded as a 3d analog of the paper Mirror Symmetry is T-Duality by Strominger, Yau and Zaslow which described 2d mirror symmetry via 1d dualities.


, Thursday

Lisbon WADE — Webinar in Analysis and Differential Equations

Room P3.10, Mathematics Building, Instituto Superior TécnicoInstituto Superior Técnico


, Institute for Theoretical Studies, ETH Zürich.

Abstract

I will discuss some recent results obtained in collaboration with A. Figalli, S. Kim and H. Shahgholian. We consider minimizers of the Dirichlet energy among maps constrained to take values outside a smooth domain $O$ in $\mathbb{R}^m$. These minimizers can be thought of either as solutions of a vectorial obstacle problem, or as harmonic maps into the manifold-with-boundary given by the complement of $O$. I will discuss results concerning the regularity of the minimizers, the location of their singularities, and the structure of the free boundary.




Instituto Superior Técnico
Av. Rovisco Pais, Lisboa, PT