Recent Advances on Elliptic and Parabolic Equations

Program Website

http://ias.ust.hk/events/202505epe/

Overview

Elliptic and parabolic partial differential equations (PDEs) are fundamental in mathematical analysis and have profound applications in various scientific and engineering disciplines, including physics, finance, and biology. These equations describe phenomena such as heat conduction, fluid flow, and the pricing of financial derivatives. Over the past decades, significant progress has been made in the theoretical understanding and numerical methods of these equations, leading to new insights and innovative applications.

Recent years have witnessed remarkable advances in the study of elliptic and parabolic equations. Notable developments include:

• Optimal regularity and classification of singularity for free boundary problems

• Regularity and dynamics for fast diffusion equations and porous medium equations

• Theory for integro-differential equations

• Minimal surfaces and their nonlocal counter-parts

• Nonconvex Hamiltonian-Jacobi equations

The important recent advances in elliptic and parabolic PDEs make this an ideal time to gather all contributors to exchange ideas, foster collaborations, and further advance the field. Recent theoretical advancements can greatly benefit from collaborative efforts to tackle open problems and explore new theoretical frameworks.

The focused program aims to:

• Showcase recent advances in elliptic and parabolic equations.

• Provide a platform for researchers from diverse fields to exchange ideas and form interdisciplinary collaborations.

• Discuss and identify future research directions and open problems in the field.

• Engage with young researchers and provide them with exposure to cutting-edge research and potential career pathways.

Organizers

• Henri BERESTYCKI, EHESS (IAS Senior Visiting Fellow)

• Tianling JIN, HKUST

• Yannick SIRE, Johns Hopkins University

• Jingang XIONG, Beijing Normal University

• Hui YU, National University of Singapore

Enquiries

For further enquiries, please contact the program secretariat at ias2025epe@ust.hk.