MIT 2020 — Calculus of Variations, Homogenization and Disorder

August 31, 2020 — Calculus of Variations

10:00 — 10:50 CDT: 'Regularity of the free boundary for the two-phase Bernoulli problem and eigenvalues partitions' — Guido De Philippis (Courant Institute of Mathematical Sciences - NYU) — Moderated by David Jerison

10:50 — 11:10 CDT: Q&A/Break

11:10 — 12:00 CDT: ‘A capillarity model for soap films’ — Francesco Maggi (University of Texas) — Moderated by Guy David

12:00 — 12:45 CDT: Short Q&A / LUNCH BREAK

12:45 — 13:35 CDT: 'Optimal Shapes of Level Sets' — David Jerison (Massachusetts Institute of Technology) — Moderated by Guy David

13:35 — 13:55 CDT: Q&A /Break

14:00: Discussion Topic 1: 'Formation of Materials' with Professor Craig Carter (Massachusetts Institute of Technology) — Moderated by Li Chen

15:00: Discussion Topic 2: 'Soap Film Capillary Model' with Francesco Maggi (University of Texas) — Moderated by Guy David

September 1, 2020 — Homogenization

10:00 — 10:50 CDT: ‘Blackhole waves at corners of negative material’ — Anne-Sophie Bonnet-Ben Dhia (Centre national de la recherche scientifique) — Moderated by Guy David

10:50 — 11:10 CDT: Q&A/Break

11:10 — 12:00 CDT:  ‘On Einstein’s effective viscosity formula’  Antoine Gloria (Sorbonne Université) — Moderated by Svitlana Mayboroda

12:00 — 12:45 CDT: Short Q&A / LUNCH BREAK

12:45 — 13:35 CDT: 'Quantitative Stochastic Homogenization and Large-Scale Regularity' — Tuomo Kuusi (University of Helsinki) — Moderated by Guy David

13:35 — 13:55 CDT: Q&A /Break

14:00: Discussion Topic 1: Informal Q&A and Coffee Break — Moderated by Li Chen

15:00: Discussion Topic 2 with Antoine Gloria — Moderated by Li Chen

September 2, 2020 — Disordered Environments

10:00 — 10:50 CDT: ‘Quantum Brownian motion conjecture' — László Erdös (Institute of Science and Technology, Austria) — Moderated by Guy David

10:50 — 11:10 CDT: Q&A/Break

11:10 — 12:00 CDT: ‘Bogoliubov theory for trapped Bose-Einstein condensates’ — Benjamin Schlein (University of Zürich) — Moderated by Guy David

12:00 — 12:45 CDT: Short Q&A / LUNCH BREAK

12:45 — 13:35 CDT: ‘Delocalization of random band matrices’ — H.T. Yau (Harvard University) — Moderated by David Jerison

13:35 — 13:55 CDT: Q&A /Break

14:00: Discussion Topic 1: ‘Quantum Brownian motion as a scaling limit' with László Erdös (Institute of Science and Technology, Austria) — Moderated by Li Chen

15:00: Discussion Topic 2 with Benjamin Schlein (University of Zürich) — Moderated by Li Chen

September 3, 2020 — Large Group Collaboration Discussion

• 11:00 — 13:00 CDT: PI Meeting (closed Zoom meeting)
• 13:00 — 13:30 CDT: Break
• 13:30 — 14:30 CDT: 'Excitons and related topics' with Moungi Bawendi (MIT) Zoom room link
• 14:30pm — 16:00 CDT: Collaboration Working Meeting — List of possible topics:
• WAVE Alpha (Zoom room link) — Regularity of free boundary
• How smooth is the boundary separating two phases in a free boundary problem (e.g. ice melting)?
• WAVE Beta (Zoom room link) — Formation and growth of nitrite in semiconductor materials
• What are suitable formation and growth mechanisms for GaN and InGaN in semiconductors? In each model, how can one do simulation and numerical analysis?
• WAVE Delta (Zoom room link) — Stochastic homogenization
• A heterogeneous media exhibiting random behavior on a microscopic scale can have a deterministic effective behavior on a macroscopic scale after the randomness is averaged out. How can one isolate the effective behaviors in various disordered/random microscopic systems?
• WAVE Gamma (Zoom room link) — Justification for the mesoscopic Poisson-Schrodinger equations
• In which regime can one rigorously justify the use of band off-set $\delta E_c$ and $\delta E_v$ in the Poisson-Schrodinger equation, instead of solving the full equation before homogenizing the background crystal structure?
• WAVE Echo (Zoom room link) — Band structure in non-periodic semiconductors
• What are suitable notions of band structure in non-periodic semiconductors? When are they valid? (e.g. what if the disorder in the semiconductor is on the scale of the lattice constant?)
• WAVE Zeta (Zoom room link) — Phonon coupling in semiconductor and their effective 1-body theory
• How to include phonon coupling in semiconductor equations? Phonons can be coupled to the electrons Hamiltonian on the level of 2nd quantization. It might be hopeful to use a self-consistent method to derive an effective 1-body equation with phonon coupling. One way to do this is through quasi-free reduction. What are suitable quasi-free/Gaussian states for the phonon coupled Hamiltonian?
• WAVE Lamba (Zoom room link) — Evolution of BEC under disorder
• In a disordered median, what is the behavior of an initially trapped BEC after the trap is removed? To what extent does localization persist?
• WAVE Pi (Zoom room link) — Validity of smoothed out point like dopant charge
• In a semiconductor, one smooths out point-like doped charge distributions to have some scale length $\sigma$. How should this choice of $\sigma$ be made?
• WAVE Omega (Zoom room link) — Many-body landscape to 1-body landscape
• Starting from an N-body Hamiltonian H (with 2 body interaction terms), we can define the landscape function in the usual way: Hu = 1. In this case $u \in R^{3N}$ is extremely difficult to study. Is there an effective 1-body theory for u under a suitable regime?
• WAVE Admin (Zoom room link) — PI Topic: Disorder, localization/delocalization, random matrices
• WAVE Lounge (Zoom room link)
• No Topic, general virtual coffeebreak room