Bridging PDE and Geometric Flows - An LMS-HIMR Research School JS
July 22nd - 26th, 2024 at Cardiff University in Wales

          Venue           Info           About           Lecturers           Programme           Fees and financial support           Apply           Organisers


Abacws Building, Seminar room 302
Senghennydd Road
Cardiff CF24 4AG
Location Guide

Practical information during the school

Accommodation: The very most of you are accommodated at
Senghennydd Court
Cardiff University
Salisbury Road
Cardiff CF24 4DS

Breakfast is served from 7:30 to 9:00 at Trevithick Restaurant, Trevithick Building 5, Off The Parade, Newport Rd, Cardiff CF24 3AA. On the first day (Monday), Prachi will be around at the accommodation reception on Monday morning to show you the way. Departure 7:45 on the nose.

Conference dinner Tuesday 23rd, 7pm at Henry's Cafe Bar, Park Pl, Cardiff. Either be there at 7pm, or walk with Prachi from the accommodation reception at 18:30.

For every other dinner, you will be reimbursed max. 10 GBP after the conference, provided you collect receipts of your expenses.

Excursion: On Wednesday afternoon, there will be an excursion in form of a guided city tour through Cardiff, which lasts roughly 2 hours, starting at 3pm. Participation is of course optional. We depart from Abacws building at 14:30.

About the Research School (Poster)

The field of geometric flows is a highly active research area located in the intersection of partial differential equations (PDE), differential geometry and convex geometry. The most prominent prototype equations are the mean curvature flow and the Ricci flow, the latter being the main key to the so far only solution of a Millennium problem listed by the Clay institute, the so-called Poincaré conjecture, which was solved by Perelman building upon ideas of Hamilton.

These geometric equations are fully nonlinear systems and the PDE theory required to rigorously understand their details is in the most cases much deeper than what is taught in undergraduate PDE courses. They comprise results from regularity theory for fully nonlinear (elliptic and parabolic) PDE, advanced results from functional analysis and operators on manifolds.

Contrary to what is usually covered in research schools on geometric flows, this school is supposed to focus on the PDE aspects of geometric flows, which is often considered as technical and therefore neglected. Our PDE expert lecturer Dr. Ben Lambert aims to make this material as accessible as possible and the theory will be accompanied by their application to the curvature flow equations, delivered by Prof. Alessandra Pluda. Additional guest lectures with further applications to geometry will be held by Prof. Mohammad N. Ivaki.

This research school is well-suited for research students roughly at PhD level and for early career researchers working in one or both of the fields of PDE and Differential Geometry. In particular, anyone working with PDE is encouraged to apply, even if their work is not related to geometric flows.



Here is a tentative programme outline, which might still undergo few adjustments.

Some recommended literature

For those who want to read a bit in advance of the school, the following texts might be helpful, especially for those with little or no PDE background. None of this is mandatory, but it might help you to have a smooth start into the school.

Fees and financial support

The following registration fees apply.

How to apply

The selection criteria upon which participants will be selected are

In order to apply, please provide the following documents no later than the application deadline: April 7th, 2024 to

Important: In the application form you have the chance to indicate whether you would like to apply for financial support. After the selection of participants and in case you are selected, you will be asked to provide details demonstrating your need for financial support.

For international applicants, please find out about your visa requirements to enter the UK and make sure that you apply for your visa as early as possible, if applicable. Upon request, we can provide supporting statements.

The organisers

Prachi Sahjwani                  GU-Logo
Prachi Sahjwani                  Julian Scheuer