14:00h – 14:40h

Free boundary regularity for the obstacle problem

14:50h – 15:30h

Controlled Latent Diffusion Models for 3D Porous Media Reconstruction

Inverse problems are pivotal in porous media analysis, demanding the reconstruction of subsurface microstructures from limited imaging data—critical for applications such as energy exploration, hydrocarbon recovery, and underground storage. While traditional approaches often rely on statistical or physics-based models, recent breakthroughs in deep generative methods—particular­ly diffusion-based approaches—present new avenues for enhanced accuracy and computational efficiency.

  14:00h – 14:40h

Approximate controllability of a nonlocal hyperbolic coupled system

14:50h – 15:30h

Some properties of Steklov eigenfunctions

 14:00h – 14:40h

Computational homogenization for the estimation of overall properties in linear viscoelastic composites

14:50h – 15:30h

Quantum Uncertainty, the Heisenberg Group,
and the Sub-Laplacian Operator:
A Mathematical Bridge

The interplay between partial differential equations (PDEs) and quantum
physics has long been a source of profound mathematical insights. In this talk, we explore the deep connections between quantum uncertainty, the Heisenberg group, and the sub-Laplacian operator, revealing a fascinating mathematical bridge between these areas. We begin with an overview of the uncertainty prin-
ciple in quantum mechanics, highlighting its foundational role in understanding the limits of measurement and its mathematical formulation in terms of com- mutators. From there, we introduce the Heisenberg group Hn, a nilpotent Lie group that arises naturally in the study of quantum systems and sub-Riemannian ge-
ometry. We discuss its group structure, Lie algebra, and the canonical commutation relations that mirror the uncertainty principle. The Heisenberg group serves as a prototype for hypoelliptic operators, and we focus on the sub-Laplacian operator, a second-order differential operator that is central to the analysis of PDEs on Hn. We examine its spectral properties, eigenfunctions, and its role in

bridging the gap between classical PDE theory and quantum mechanics. Additionally, we introduce some challenging open problems that arise in this context. Through this exploration, we demonstrate how the Heisenberg group and the sub-Laplacian operator provide a unifying framework for understanding both physical phenomena and mathematical structures.

14:00h – 14:40h

General double phase functionals: recent results and applications

14:50h – 15:30h

Normalized solutions, ground state solutions and beyond

Abstract. I shall discuss some basic classes of solutions of nonlinear PDEs, such as“normalized solutions” and “ground state solutions”. The content of my talk is based on the recent papers [1], [2]