Svitlana Mayboroda, University of Minnesota
The 2022 Simons Collaboration on Localization of Waves Annual Meeting will bring together world leading mathematicians and physicists whose work illuminates profound connections between disorder, geometric complexity, and the behavior of waves. The meeting will highlight how recent advances in mathematics yield important applications in physics involving wave localization. In particular, speakers will unveil groundbreaking results relating harmonic analysis and geometrical measure theory to cold atoms, nitride-based LEDs, and perovskites.
The meeting will be a place of exchange and discussion, and will also offer an opportunity to present new perspectives for the Localization of Waves project.
Thursday, February 17
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Svitlana Mayboroda | Localization of Waves: Director's Overview 10:30 AM BREAK 11:00 AM James S. Speck | Unraveling the Inner Working of GaN-Based Light-Emitting Diodes 12:00 PM LUNCH 1:00 PM William D. Phillips | The Coldest Stuff in the Universe: From Quantum Clocks to Quantum Simulators 2:00 PM BREAK 2:30 PM Guy David | Estimates on Eigenfunctions and Eigenvalues Using the Landscape Function 3:30 PM BREAK 4:00 PM Richard Friend | Static and Dynamic Disorder in Organic and Perovskite Semiconductors 5:00 PM DAY ONE CONCLUDES
Friday, February 18
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Camillo De Lellis | The Mumford–Shah Functional and Its Challenges 10:30 AM BREAK 11:00 AM Marcel Filoche | The Wigner–Weyl Approach to Wave Localization 12:00 PM LUNCH 1:00 PM Hugo Duminil-Copin | On the Geometry of Nodal Lines of Random Waves 2:00 PM MEETING CONCLUDES
University of Minnesota
Localization of Waves: Director’s Overview
This talk is an overview of the progress and future plans of the Simons Collaboration on Localization of Waves.
James S. Speck
University of California, Santa Barbara
Unraveling the Inner Working of Gan-Based Light-Emitting Diodes
Solid state lighting has been a disruptive technology for artificial light sources due to the remarkable efficiency, compact size, wide functionality, and accessibility. The technology is based on nitride-based semiconductors, particularly GaN and the alloy InxGa1-xN. In comparison to much more established group IV semiconductors (Si, Ge) and compound semiconductors (e.g., GaAs), the nitrides offer new physics due to their polar wurtzite crystal structure. InxGa1-xN alloys show strong natural compositional disorder that cannot be described the virtual crystal approximation. The alloy disorder directly impacts electron and hole transport and carrier recombination. In this talk, Speck will describe the emerging story of the internal physical processes in nitride alloys and devices, and the essential role of alloy disorder in the behavior of nitride alloys and nitride devices.
William D. Phillips
University of Maryland
The Coldest Stuff in the Universe: From Quantum Clocks to Quantum Simulators
Cold atom (and cold molecule) physics has given us a new experimental platform with a variety of applications. Nanokelvin temperatures are now routine and are many orders of magnitude colder than any naturally occurring temperatures. Already, cold atoms have revolutionized atomic clocks, providing the basis for international timekeeping and providing unprecedented tests of fundamental theories. Cold atoms also provide a quantum system that is more easily controlled and measured than, for example, electrons in solids, offering the opportunity to better understand these complex systems. Some unsolved problems of many-body physics are being illuminated by these methods, as are phenomena such as Anderson localization.
Estimates on Eigenfunctions and Eigenvalues Using the Landscape Function
The landscape function (a solution of Lu=1 for the operator L at hand) has been used with success to get valuable information on the eigenfunctions, their localization and eigenvalues, for instance of Schrödinger operators. In this talk, David will describe different mathematical results that use that function and try to explain some of the features of the proofs and challenges for further estimates.
University of Cambridge
Static and Dynamic Disorder in Organic and Perovskite Semiconductors
Organic, molecular semiconductors are now successfully used in semiconductor devices such as LEDs for OLED displays and solar cells. Electronic overlap between adjacent molecules is relatively poor, so that disorder can readily cause spatial localization of electronic states and thus limit transport. Friend and collaborators have been exploring the different roles of static disorder and of dynamic disorder due to thermal populations of phonons. Where dynamic disorder is dominant, coupling of vibrational excitations to electronic excitations can allow novel regimes for high mobility transport, and they have investigated this in molecular systems that show long range exciton diffusion. Separately, they have been exploring static and dynamic disorder in the family of lead halide perovskites that are now used in efficient thin-film solar cells. These materials show unexpectedly clean semiconductor behavior despite high levels of structural disorder. Friend and collaborators have modeled static disorder in bromide/iodide alloy systems and have used the landscape formalism to explore compositional disorder on a wide range of length scales.
Camillo De Lellis
Institute for Advanced Study
The Mumford–Shah Functional and Its Challenges
The Mumford–Shah functional poses a very elegant and simple variational problem, which combines two of the most studied energies in the calculus of variations, the area functional and the Dirichlet energy. In spite of its simplicity, the regularity of minima is still a widely open field. De Lellis will review what is known about the simplest situation of two-dimensional minimizers, where a conjectural list of all possible local pictures is well-known and a complete epsilon-regularity theory is available.
The Wigner–Weyl Approach to Wave Localization
One of the most recent discoveries of the localization landscape theory relates to the structure of the landscape in phase space. We will present a new approach to localization combining the landscape approach with the Wigner–Weyl formalism, based on a new decomposition of phase space adapted to localized features. This approach allows us to predict extremely efficiently all energy-dependent quantities. It will be exemplified in two examples. In systems of cold atoms, it yields the first analytic prediction of spectral functions across the classical and quantum regime without adjustable parameters. In inorganic semiconductors, the incorporation of the landscape scheme in a drift-diffusion computation enables to speed up by a factor of 1,000 the computation of light absorption for three-dimensional random InGaN alloys in samples of side length 100nm, a computation otherwise beyond the reach of usual quantum computations. In this talk, Filoche will show how this approach will allow us in the future to investigate the delicate formation of excitons (electron-hole pairs) and bi-excitons, and how it will be tested experimentally in cold atom platforms.
Université de Genève
On the Geometry of Nodal Lines of Random Waves
In this talk, Duminil-Copin will review recent progress in the understanding of nodal lines of random waves and related models. In particular, Duminil-Copin will discuss the possible emergence of giant nodal lines with complicated topological properties, thus partially answering a conjecture of Peter Sarnak. He will also discuss future research directions and possible connections between percolation theory and waves’ localization.
Participation & Funding
Participation in the meeting falls into the following four categories. An individual’s participation category is communicated via their letter of invitation.
Group A – PIs and Speakers
The foundation will arrange and pay for all air and train travel to the conference as well as hotel accommodations and reimbursement of local expenses. Business-class or premium economy airfare will be booked for all flights over five hours.
Group B – Out-of-town Participants
The foundation will arrange and pay for all air and train travel to the conference as well as hotel accommodations and reimbursement of local expenses. Economy-class airfare will be booked for all flights.
Group C – Local Participants
Individuals in Group C will not receive financial support, but are encouraged to enjoy all conference-hosted meals.
Group D – Remote Participants
Individuals in Group D will participate in the meeting remotely. Please register at the link above and a remote participation link will be sent to you approximately two weeks prior to the meeting.
Travel & Hotel
Air and Train
The foundation will arrange and pay for all air and train travel to the conference for those in Groups A and B. Please provide your travel specifications by clicking the registration link above. If you are unsure of your group, please refer to your invitation sent via email.
For participants in Groups A & B driving to Manhattan, The James NoMad Hotel offers valet parking. Please note there are no in-and-out privileges when using the hotel’s garage, therefore it is encouraged that participants walk or take public transportation to the Simons Foundation.
Participants in Groups A & B who require accommodations are hosted by the foundation for a maximum of three nights at The James NoMad Hotel. Any additional nights are at the attendee’s own expense. To arrange accommodations, please register at the link above.
The James NoMad Hotel
22 E 29th St
New York, NY 10016
(between 28th and 29th Streets)
For driving directions to The James NoMad, please click here.
ALL in-person meeting attendees must be vaccinated against the COVID-19 virus with a World Health Organization approved vaccine, be beyond the 14-day inoculation period of their final dose, and provide proof of vaccination upon arrival to the conference. Acceptable vaccines can be found at the bottom of this page on WHO’s site.
Individuals in Groups A & B will be reimbursed for meals not hosted by the Simons Foundation as well as local expenses, including ground transportation. Additional information in this regard will be emailed on the final day of the meeting.