## Description

Back to topLaplacian growth models describe the evolution of a surface separating two domains, filled with different materials or different phases of the same material. The evolution of the interface is governed by the energy imbalance along the interface, whereas the evolution of the energy is governed by a heat-like equation. There exist many versions of such models, including the Stefan and Hele-Shaw problems, and they serve as building blocks in various models of fundamental physical and biological processes: e.g., melting and solidification, condensation, crystal growth, aging of alloys, interaction of fluids with different viscosities, dynamics of membrane potentials in a network of neurons, tumor growth, etc. In addition to the applications in natural sciences, certain Laplacian growth models are also used in mathematical finance for systemic risk modeling. Due to the (typical) singularities in the solutions, to date, there exists no general well-posedness theory for Laplacian growth models. This question has received a lot of attention in the recent years, with novel probabilistic methods being combined with the more classical analytical ones to yield new existence and uniqueness results.

The meeting will bring together both reseachers who are primarily interested in the theoretical advancement of Laplacian growth models and those who approach this topic from an applied point of view. We believe that this combination will generate synergy effects for both sides: on the one hand, many challenging questions arising in Physics, Biology and Finance can be addressed by Laplacian growth models, on the other hand, in order to use these models one needs appropriate theoretical foundation, in particular, the well-posedness of solutions and convergence of numerical schemes. Another goal of the organizers is to create a bridge between the researchers who use mainly PDE and geometric analysis methods and those who primarily employ probabilistic techniques.

## Organizers

Back to top## Speakers

Back to top## Schedule

Back to top**Speaker: **Allan Sly (Princeton University)

**Speaker: **Amanda Turner (University of Leeds)

**Speaker: **Lionel Levine (Cornell University)

**Speaker: **Harald Garcke (University Regensburg)

**Speaker: **Inwon Kim (University of California, Los Angeles (UCLA))

**Speaker: **Rami Atar (Technion – Israel Institute of Technology)

**Speaker: **Sara Svaluto-Ferro (University of Verona)

**Speaker: **Scander Mustapha (Princeton University)

**Speaker: **Andreas Søjmark (The London School of Economics)

**Speaker: **Christoph Reisinger (University of Oxford)

**Speaker: **Kevin Yang (Harvard University)

**Speaker: **Irene Fonseca (Carnegie-Mellon University)

**Speaker: **Riccarda Rossi (University of Brescia)

**Speaker: **Mahir Hadzic (University College London)

**Speaker: **Mihaela Ignatova (Temple University)

**Speaker: **Etienne Tanré (Institut National de Recherche en Informatique et Automatique (INRIA))

**Speaker: **Eviatar Procaccia (Technion- Israel Institute of Technology)

**Speaker: **Yucheng Guo (Princeton University)

**Speaker: **Mete Soner (Princeton University)

## Videos

Back to topWell-posedness of the supercooled Stefan problem with oscillatory initial conditions

Scander Mustapha

June 27, 2023

Singular and smoothed models for systemic risk with endogenous contagion

Christoph Reisinger

June 27, 2023

Visco-Energetic solutions to a rate-independent system for crack propagation

Riccarda Rossi

June 29, 2023

Probabilistic Solutions to 3D Stefan-Gibbs-Thomson Problems under Radial Symmetry: Regularity and Uniqueness

Yucheng Guo

June 30, 2023