# MIT 2020 — Calculus of Variations, Homogenization and Disorder

## View abstracts and presentation slides here

**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 — View recorded presentation**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

- WAVE Alpha (Zoom room link) —