Description

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Laplacian 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

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C C
Christa Cuchiero University of Vienna
S N
Sergey Nadtochiy Illinois Institute of Technology
M S
Mykhaylo Shkolnikov Princeton University

Speakers

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R A
Rami Atar Technion – Israel Institute of Technology
I F
Irene Fonseca Carnegie Mellon University
H G
Harald Garcke Universität Regensburg
Y G
Yucheng Guo Princeton University
M H
Mahir Hadzic University College London
M I
Mihaela Ignatova Temple University
I K
Inwon Kim University of California, Los Angeles (UCLA)
L L
Lionel Levine Cornell University
S M
Scander Mustapha Princeton University
E P
Eviatar Procaccia Technion – Israel Institute of Technology
C R
Christoph Reisinger University of Oxford
R R
Riccarda Rossi University of Brescia
A S
Allan Sly Princeton University
A S
Andreas Søjmark London School of Economics
M S
Mete Soner Princeton University
S S
Sara Svaluto-Ferro Università degli studi di Verona
E T
Etienne Tanré Inria
A T
Amanda Turner University of Leeds
K Y
Kevin Yang Stanford University

Schedule

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Monday, June 26, 2023
9:00-9:45 CDT
Spread of infections in random walkers

Speaker: Allan Sly (Princeton University)

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
Growth of Stationary Hasting-Levitov

Speaker: Amanda Turner (University of Leeds)

11:35-12:20 CDT
Universality Conjectures for Activated Random Walk

Speaker: Lionel Levine (Cornell University)

12:35-14:00 CDT
Lunch
14:00-14:45 CDT
Multi-phase Laplacian growth models: Analysis and Numerics

Speaker: Harald Garcke (University Regensburg)

15:00-15:15 CDT
Coffee Break
15:15-16:00 CDT
Optimal Transport with Stopping time and the Stefan problem

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

Tuesday, June 27, 2023
9:00-9:45 CDT
Boundary-free free boundary problems and particle systems with selection

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

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
Propagation of minimality in the supercooled Stefan problem

Speaker: Sara Svaluto-Ferro (University of Verona)

11:35-12:20 CDT
Well-posedness of the supercooled Stefan problem with oscillatory initial conditions

Speaker: Scander Mustapha (Princeton University)

12:35-14:00 CDT
Lunch
14:00-14:45 CDT
The supercooled Stefan problem with noise: blow-ups and systemic risk

Speaker: Andreas Søjmark (The London School of Economics)

15:00-15:15 CDT
Coffee Break
15:15-16:00 CDT
Singular and smoothed models for systemic risk with endogenous contagion

Speaker: Christoph Reisinger (University of Oxford)

Wednesday, June 28, 2023
9:00-9:45 CDT
Scaling limits for growth driven by reflecting Brownian motion

Speaker: Kevin Yang (Harvard University)

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
Phase Separation in Heterogeneous Media

Speaker: Irene Fonseca (Carnegie-Mellon University)

12:35-14:00 CDT
Lunch & Social Hour
Thursday, June 29, 2023
9:00-9:45 CDT
Visco-Energetic solutions to a rate-independent system for crack propagation

Speaker: Riccarda Rossi (University of Brescia)

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
Type II melting rates for the Stefan problem

Speaker: Mahir Hadzic (University College London)

11:35-12:20 CDT
On Voigt Boussinesq Equations

Speaker: Mihaela Ignatova (Temple University)

12:35-14:00 CDT
Lunch
14:00-14:45 CDT
Spontaneous oscillations in purely excitatory network of IF type neurons

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

15:00-15:15 CDT
Coffee Break
15:15-16:00 CDT
Extremal points of the harmonic measure.

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

Friday, June 30, 2023
9:00-9:45 CDT
Probabilistic Solutions to 3D Stefan-Gibbs-Thomson Problems under Radial Symmetry: Regularity and Uniqueness

Speaker: Yucheng Guo (Princeton University)

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
Computing free boundaries by neural networks and simulations

Speaker: Mete Soner (Princeton University)


Videos

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Spread of infections in random walkers

Allan Sly
June 26, 2023

Growth of Stationary Hasting-Levitov

Amanda Turner
June 26, 2023

Universality Conjectures for Activated Random Walk

Lionel Levine
June 26, 2023

Multi-phase Laplacian growth models: Analysis and Numerics

Harald Garcke
June 26, 2023

Optimal Transport with Stopping time and the Stefan problem

Inwon Kim
June 26, 2023

Boundary-free free boundary problems and particle systems with selection

Rami Atar
June 27, 2023

Propagation of minimality in the supercooled Stefan problem

Sara Svaluto-Ferro
June 27, 2023

Well-posedness of the supercooled Stefan problem with oscillatory initial conditions

Scander Mustapha
June 27, 2023

The supercooled Stefan problem with noise: blow-ups and systemic risk

Andreas Søjmark
June 27, 2023

Singular and smoothed models for systemic risk with endogenous contagion

Christoph Reisinger
June 27, 2023

Scaling limits for growth driven by reflecting Brownian motion

Kevin Yang
June 28, 2023

Phase Separation in Heterogeneous Media

Irene Fonseca
June 28, 2023

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

Riccarda Rossi
June 29, 2023

On Voigt Boussinesq Equations

Mihaela Ignatova
June 29, 2023

Spontaneous oscillations in purely excitatory network of IF type neurons

Etienne Tanré
June 29, 2023

Extremal points of the harmonic measure.

Eviatar Procaccia
June 29, 2023

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

Yucheng Guo
June 30, 2023

Computing free boundaries by neural networks and simulations

Mete Soner
June 30, 2023