Schedule for: 19w5130 - Convex Integration in PDEs, Geometry, and Variational Calculus

Arriving in Banff, Alberta on Sunday, August 11 and departing Friday August 16, 2019
Sunday, August 11
16:00 - 17:30 Check-in begins at 16:00 on Sunday and is open 24 hours (Front Desk - Professional Development Centre)
17:30 - 19:30 Dinner
A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
20:00 - 22:00 Informal gathering (Corbett Hall Lounge (CH 2110))
Monday, August 12
07:00 - 08:45 Breakfast
Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
08:45 - 09:00 Introduction and Welcome by BIRS Staff
A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.
(TCPL 201)
09:00 - 10:00 Angkana Rüland: Convex Integration in Materials Science (TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 11:30 Baisheng Yan: Convex Integration for the Gradient Flow of Polyconvex Functionals (TCPL 201)
11:30 - 13:00 Lunch
Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
13:00 - 14:00 Guided Tour of The Banff Centre
Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.
(Corbett Hall Lounge (CH 2110))
14:00 - 14:20 Group Photo
Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!
(TCPL 201)
14:20 - 15:00 Seonghak Kim: Fine Phase Mixtures in 1D Hyperbolic-Elliptic Problem (TCPL 201)
15:00 - 15:30 Coffee Break (TCPL Foyer)
15:30 - 16:30 Dominik Inauen: Rigidity and Flexibility of Isometric Embeddings (TCPL 201)
16:30 - 17:30 Sam Krupa: Uniqueness of Solutions Versus Convex Integration for Conservation Laws in One Space Dimension (TCPL 201)
17:30 - 19:30 Dinner
A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
Tuesday, August 13
07:00 - 09:00 Breakfast (Vistas Dining Room)
09:00 - 10:00 Eduard Feireisl: Convex Integration and Compressible Euler System (TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 11:30 Ondřej Kreml: Wild Solutions to Isentropic Euler Equations Starting from Smooth Initial Data (TCPL 201)
11:30 - 13:30 Lunch (Vistas Dining Room)
14:00 - 15:00 Simon Markfelder: On some non-uniqueness results for the compressible Euler equations based on convex integration
We consider the compressible Euler equations in multiple space dimensions. These equations describe the time evolution of a compressible inviscid fluid. We give an overview over some results showing existence of infinitely many solutions. All these results are based on the convex integration method, which was used by De Lellis and Szekelyhidi in the context of the incompressible Euler equations. After considering general initial data, we focus on a special type of two-dimensional initial data, namely those which are constant in each of the two half spaces (Riemann data).
(TCPL 201)
15:00 - 15:30 Coffee Break (TCPL Foyer)
15:30 - 16:30 Alexey Cheskidov: Wild Solutions to the 3D Navier-Stokes Equations (TCPL 201)
16:30 - 17:30 Mimi Dai: Flexibility & Rigidity for Incompressible Flows (TCPL 201)
17:30 - 19:30 Dinner (Vistas Dining Room)
Wednesday, August 14
07:00 - 09:00 Breakfast (Vistas Dining Room)
09:00 - 10:00 Piotr Gwiazda: Onsager's Conjecture for General Conservation Laws (TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 11:30 Agnieszka Świerczewska-Gwiazda: Measure-Valued-Strong Uniqueness for General Conservation Laws and Convex Integration for a Nonlocal Euler System (TCPL 201)
11:30 - 13:30 Lunch (Vistas Dining Room)
13:30 - 17:30 Free Afternoon (Banff National Park)
17:30 - 19:30 Dinner (Vistas Dining Room)
Thursday, August 15
07:00 - 09:00 Breakfast (Vistas Dining Room)
09:00 - 10:00 Roman Shvydkoy: Mechanisms for Energy Balance Restoration in the Onsager (Super)Critical Flows (TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 11:30 Sara Daneri: Non-uniqueness for the incompressible Euler equations up to Onsager's critical exponent (TCPL 201)
11:30 - 13:30 Lunch (Vistas Dining Room)
14:00 - 15:00 Young-Heon Kim: The Monge problem in Brownian stopping optimal transport
We discuss a recent progress in an optimal Brownian stopping problem, called the optimal Skorokhod embedding problem, which is an active research area especially in relation to mathematical finance. Given two probability measures with appropriate order, the problem considers the stopping time under which the Brownian motion carries one probability measure to the other, while minimizing the transportation cost. We focus on the cost given by the distance between the initial and the final point. A strong duality result of this optimization problem is obtained, which enables us to prove that the optimal stopping time is given by the first hitting time to a barrier determined by the optimal dual solutions. The main part of this talk is based on joint work with Nassif Ghoussoub (UBC) and Aaron Palmer (UBC).
(TCPL 201)
15:00 - 15:30 Coffee Break (TCPL Foyer)
15:30 - 16:30 Christian Zillinger: Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Scaling and Numerical Implementations
We study convex integration solutions in the context of the modelling of shape-memory alloys. In a first part we relate the maximal regularity of convex integration solutions to the presence of lower bounds in variational models with surface energy. Hence, variational models with surface energy could be viewed as a selection mechanism allowing for or excluding convex integration solutions. Secondly, we present the first numerical implementations of convex integration schemes for the model problem of the geometrically linearised two-dimensional hexagonal-to-rhombic phase transformation. This is based on joint work with Angkana Rüland and Jamie Taylor.
(TCPL 201)
16:30 - 17:30 Marta Lewicka: Convex Integration Solutions to the Monge-Ampère Equation (TCPL 201)
17:30 - 19:30 Dinner (Vistas Dining Room)
Friday, August 16
07:00 - 09:00 Breakfast (Vistas Dining Room)
09:00 - 10:00 Emil Wiedemann: Convex Integration vs. the Chain Rule
We provide counterexamples to the chain rule for divergence-free vectorfields, based on a Gromov-type convex integration scheme. Joint work with G. Crippa, N. Gusev, and S. Spirito.
(TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 11:30 Martina Hofmanova: Convex Integration in Stochastic Setting (TCPL 201)
11:30 - 12:00 Checkout by Noon
5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.
(Front Desk - Professional Development Centre)
12:00 - 13:30 Lunch from 11:30 to 13:30 (Vistas Dining Room)