Department of Mathematics and Statistics

Mini-Course: Nonlocal Problems in PDEs and Geometry

May 20-24, 2019

Prof. Eleonora Cinti (Università di Bologna, Italy) will teach a 5-day mini-course aimed at graduate students and junior researchers at the intersection of Analysis and Geometry. Here is the poster of the event.

Dr. Cinti earned her Ph.D in 2010 and since then has worked at the Max Planck Institute in Leipzig, the Weierstrass Institute in Berlin, and various Italian universities (Pavia, Bologna, Torino). Eleonora Cinti's research focuses on nonlocal partial differential equations, geometric measure theory, and calculus of variations.

Schedule

The mini-course will be structured as follows:

• Lecture 1 (Monday, May 20): Preliminaries: basic facts about the Laplacian and harmonic functions.
• Lecture 2 (Tuesday, May 21): The fractional Laplacians: motivations and properties.
• Problem Session (Wednesday, May 22).
• Lecture 3 (Thursday, May 23): $s$-Harmonic functions and the Caffarelli-Silvestre extension theorem.
• Lecture 4 (Friday, May 24): Geometry meets PDEs, a nonlocal phase transition model and nonlocal minimal surfaces.

All lectures will be in Jeffery Hall. Monday May 20th is a holiday (Victoria Day) and lunch will be provided. Due to constructions on the second floor of Jeffery Hall, some of the lectures may be moved to other rooms to minimize noise.

Preliminaries and Bibliography

Problem Session

Here are the exercises for the problem session on Wednesday morning: Problems

Wednesday Seminar

On Wednesday afternoon, Ikemefuna Agbanusi (Colgate University / Colorado College) will give a seminar related to the topics of the mini-course. The seminar will be at 1:30 pm in Room 101.

Title: Non-Local Operators Everywhere

Abstract: My goal in this talk is to give another approach---along with examples, characterizations and refinements of local and non-local operators. Very loosely speaking, non-local operators are necessary if one wishes to "albegraically complete" the local ones and my goal in this talk is to explain why and show also that pretty much all the "interesting" operators are non-local.

Registered participants

• Daniel Adu (Queen's)
• Ikemefuna Agbanusi (Colgate University / Colorado College)
• Mohammad Akbari Varnousfaderani (Queen's)
• Iris Arenas (Queen's)
• Thomas Barthelmé (Queen's)
• Becca Bonham-Carter (Queen's)
• Himesh Bhatia (Queen's)
• Robert Burklund (M.I.T.)
• Juan Diego Cardenas Cartagena (Queen's)
• Fernando Camacho Cadena (Queen's)
• Francesco Cellarosi (Queen's)
• Chengjie Diao (Queen's)
• Kasun Fernando (University of Toronto)
• Nicolas Garica (Queen's)
• Bahman Gharesifard (Queen's)
• Meysam Ghomi (Queen's)
• Ali Kara (Queen's)
• Henry Kavle (Queen's)
• Xinyi Ke (Queen's)
• Andrew Lewis (Queen's)
• Na Li (Queen's)
• Siqi Li (Queen's)
• Ankai Liu (Queen's)
• Molly Liu (Queen's)
• Giusy Mazzone (Queen's)
• Neil MacVicar (Queen's)
• Adama Ndoye (Technische Universität of Chemnitz) 
• Daniel Offin (Queen's)
• Tariq Osman (Queen's)
• Yuyang Peng (Queen's)
• Alessandro Portaluri (Università di Torino)
• Sonja Ruzic (Queen's)
• Sina Sanjari (Queen's)
• Somya Singh (Queen's)
• Matthew Spragge (Queen's)
• Pei-Lun Tseng (Queen's)
• Jian-Jia Weng (Queen's)
• James Xie (Queen's)
• Mohammad Yaali Jahromi (Queen's)
• Serdar Yüksel (Queen's)
• Bora Yongacoglu (Queen's)

Registration

If you want to attend the mini-course, please email nonlocal19@queensu.ca.

Sponsors

The event is sponsored by the Principal’s Development Fund for Visiting Scholars and by the Department of Mathematics and Statistics.