2026 Simons Collaboration on the Localization of Waves Annual Meeting

Jaume de Dios Pont
New York University

Some Extreme Regimes of the Laplace Operator

The Laplace operator plays a central role in the mathematical description of many physical phenomena, such as quantum mechanics, wave propagation, or diffusion processes. This lets us, in many classical settings, use physical intuition to interpret the spectral properties of the Laplace operator on a fixed domain by considering a constant coefficient version of the physical phenomenon at hand.
This talk takes a complementary point of view. We study the behavior of the first few eigenfunctions of the Laplace operator in extreme geometric or asymptotic regimes. In the limit, the operator itself undergoes a qualitative change, recovering variable coefficient physical equations. Depending on the regime, the limiting behavior may be described by an effective Schrödinger operator, a drift–diffusion equation, or a heat equation with an emergent time variable. Such effects arise, for instance, in high dimensional domains, highly perforated or sieve-type domains, as well as in situations where geometric constraints enforce strong localization.
Several classical problems will serve as guiding examples, including questions related to the hot spots and KLS conjectures, homogenization for perforated domains, and rigidity phenomena for eigenfunctions of convex sets. Although these topics are not governed by a single unifying mechanism, they share a common feature: informative spectral behavior becomes visible only in limiting regimes where an effective operator emerges. The goal is to illustrate how pushing the Laplacian into such extreme settings sheds light on localization, geometry, and the structure of low-energy eigenfunctions.
 

Marcel Filoche
ESPCI Paris – PSL University

Water Waves in Hyperuniform and Fractal Structures

Surface water waves provide a unique experimental platform for probing wave transport in two-dimensional structures by offering the rare capability of direct, spatially, and time-resolved measurements of the full complex wavefield, both in amplitude and phase. Moreover, surface waves allow exploration across a broad wavelength range, enabling the investigation of complex geometries and scattering processes and direct access to the underlying structure of energy transport. In this talk, we present an experimental setup using water waves to test various types of disorder, from hyperuniform to fractal. We report the first experimental observation of a transition from a scattering to a non-scattering regime for water waves propagating through a stealthy hyperuniform (SHU) disorder. One key feature of this platform is that water acts as an absorbing background medium, introducing dissipation that competes with correlation-induced transparency. This dissipation is also enhanced by the introduction of pre-fractal structures, enabling us to probe not only the ideal theoretical predictions for several types of disorder, but also their robustness in realistic, lossy environments.
 

Thierry Giamarchi
University of Geneva

Waves, Disorder, and Interactions

As discovered in the seminal paper of P. W. Anderson in 1958 when an equation such as the Schrödinger equation (and other related wave equations) is subjected to a random potential, the nature of the solutions changes drastically going from plane waves to localizes states. An important question is what happens to this phenomenon when instead of looking at the properties of one single particle one wants to deal with a large number of interacting quantum particles, as is relevant for several experimental realizations, both in cold atomic gases and in condensed matter.
This talk provides an overview of this class of phenomena, with questions ranging from the phases that can be reached in such interacting disordered systems to the consequences for the transport properties of such systems, and finally the delicate question of the role of the temperature, in presence or absence of a thermal bath. I will also discuss what happens for other classes of potentials than the plain disorder, such as quasiperiodic potentials, or colored noise, both from a theoretical perspective but also in contact with recent experiments in cold atomic gases. I will point to the challenges in the field.
Disclaimer: Since it is a talk given by a physicist, there will unfortunately be no theorems but a set of “unproven” results, some of which could perhaps be called “conjectures,” and which hopefully will stimulate the curiosity of a more rigorously inclined audience.
 

Javier Gómez-Serrano
Brown University

“Modern Mathematics” in the Age of AI

In this talk, I will explain several recent and ongoing results combining machine-learning techniques and more traditional mathematics. The overarching theme is the interplay between AI and human expertise in order to discover new solutions of certain mathematical problems, leading sometimes to mathematics at scale and even automated, end-to-end rigorous mathematical proofs.
 

Svitlana Mayboroda
University of Minnesota

Overview of the Collaboration Progress and Future Directions

The talk will be devoted to an overview of the progress of the Collaboration to date, along with a discussion of open problems and future directions.
 

Jill Pipher
Brown University

Regularity of Solutions to Elliptic and Parabolic Operators

This lecture will trace some of the historical milestones, up through recent developments, for this field at the interface of harmonic analysis, geometric measure theory, and PDE. Between 1957 and 1961, several seemingly unrelated mathematical discoveries appeared: Carleson measures in analytic interpolation, De Giorgi-Nash regularity of solutions to elliptic and parabolic divergence form equations with bounded measurable coefficients, and the John-Nirenberg space of bounded mean oscillation (BMO) functions. (Published simultaneously, Moser used BMO in his approach to regularity of solutions.) In 1971, C. Fefferman illuminated the profound connections between harmonic functions and Carleson measures and BMO. This opened up a theory of boundary value problems aimed at quantifying the connections between the geometry of domains, the regularity of coefficients of elliptic/parabolic operators, and the behavior of solutions. Evolving over a half century, this theory has found new direction and significance in the work of the Localization of Waves Collaboration.
 

Jim Speck
University of California Santa Barbara

Electron Emission from Active Semiconductor Devices: Imaging Hot Electrons and Their Origins

Semiconductor materials and devices serve as the foundation of nearly all electronic systems that power our daily lives. While the physics in these semiconductor systems is well described by theory, little has been done to experimentally study the carrier physics in active devices.
This talk will focus on our recent progress on electron emission microscopy (EEM) and spectroscopy (EES) of III-N semiconductor devices. EEM images the internally generated electrons emitted from active devices, allowing us directly “see” the electrons in these semiconductor devices in-operando. EES measurements yield the energies of these emitted electrons, giving us insights into their physical origins.
Studies of current spreading on p-n diodes and carrier injection in LEDs show phenomenal agreement with theory and simulations. On the other hand, studies of the recombination mechanisms in p-n diodes disagree with conventionally employed defect-assisted recombination models.
 

Douglas Stone
Yale University

Controlling and Functionalizing Multiple Scattering in Complex Geometries

Harnessing interference to control wave propagation in multiple scattering geometries is a fundamental challenge in both classical and quantum physics. With the advent of new tools for wavefront shaping, it has become possible to optimize target functions over a space of possible coherent input fields, but there was little mathematical understanding of the achievable performance, leading to a reliance on black-box optimization techniques. We have shown that it is possible to formulate a large class of useful scattering target functions as non-Hermitian eigenvalue problems, a first example being coherent perfect absorption, or time-reversed lasing. This implies that a class of optimal solutions exist as spectra in the complex frequency plane and can lead to physical steady-state solutions by tuning system parameters to move one such eigenfrequency to the real axis. More highly constrained solutions, e.g., demultiplexing of a multi-frequency input, are achieved by generating coincidences of these eigenfrequencies. We show in simulations and experiments that a “chaotic cavity” containing tunable scattering elements is a robust platform for realizing this scenario. The general mathematical framework presented applies to all the linear classical and quantum wave equations of physics.

Participation in the meeting falls into the following four categories. An individual’s participation category is communicated via their letter of invitation.

The Simons Foundation will never ask for credit card information or require payment for registration to our events.

Group A – Speakers & Organizers

Individuals in Group A receive travel and hotel coordination within the following parameters:

Travel
Economy Class: For flights that are three hours or less to your destination, the maximum allowable class of service is Economy class.
Premium Economy Class: For flights where the total air travel time (excluding connection time) is more than three hours and less than seven hours per segment to your destination, the maximum allowable class of service is premium economy.
Business Class: When traveling internationally (or to Hawaii/Alaska) travelers are permitted to travel in Business Class on those segments that are seven hours or more. If the routing is over budget, a premium economy or mixed-class ticket will be booked.

Hotel
Up to 3 nights at the conference hotel, arriving on Wednesday, February 18, 2026 and departing on Saturday, February 21, 2026.

Group B – Funded Participants

Individuals in Group B receive travel and hotel coordination within the following parameters:

Travel
Economy class travel will be booked regardless of flight length.

Hotel
Up to 3 nights at the conference hotel, arriving on Wednesday, February 18, 2026 and departing on Saturday, February 21, 2026.

Group C – Unfunded 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.

Air and Rail

For funded individuals, the foundation will arrange and pay for round-trip travel from their home city to the conference city. All travel and hotel arrangements must be booked through the Simons Foundation’s preferred travel agency.

Travel Deviations

The following travel specifications are considered deviations and will only be accommodated if the cost is less than or equal to the amount the Simons Foundation would pay for a standard round-trip ticket from your home city to the conference city:

• Preferred airline
• Preferred travel class
• Specific flights/flight times
• Travel dates outside those associated with the conference
• Arriving or departing from an airport other than your home city or conference city airports, i.e. multi-segment or triangle trips.

All deviations must be reviewed and approved by the Simons Foundation and, if the cost is more than what would normally be paid, a reimbursement quote must be obtained through the foundation’s travel agency before proceeding to booking and paying for travel out of pocket. All reimbursements for travel booked directly will be paid after the conclusion of the meeting.

Changes After Ticketing

All costs related to changes made to ticketed travel are to be paid for by the participant and are not reimbursable. Please contact the foundation’s travel agency for further assistance.

Personal & Rental Cars

Personal car and rental trips over 250 miles each way require prior approval from the Simons Foundation via email.

Rental cars must be pre-approved by the Simons Foundation.

The Royalton Park Avenue 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.

Hotel

Funded individuals who require hotel accommodations are hosted by the foundation for a maximum of 3 nights at the conference hotel, arriving on Wednesday, February 18, 2026 and departing on Saturday, February 21, 2025.

Any additional nights are at the attendee’s own expense. To arrange accommodations, please register at the link included in your invitation.

Royalton Park Avenue
420 Park Ave S.
New York, NY 10016
https://www.royaltonparkavenue.com/

For driving directions to the Royalton Park Avenue, please click here.

Overview

In-person participants will be reimbursed for meals and local expenses including ground transportation. Expenses should be submitted through the foundation’s online expense reimbursement platform after the meeting’s conclusion.

Expenses accrued because of meetings not directly related to the Simons Foundation-hosted meeting (a satellite meeting or meeting held at another institution, for example) will not be reimbursed by the Simons Foundation and should be paid by other sources.

Below are key reimbursement takeaways; a full policy will be provided with the final logistics email circulated approximately 2 weeks prior to the meeting’s start.

Meals

The daily meal limit is $125; itemized receipts are required for expenses over $24 USD. The foundation DOES NOT provide a meal per diem and only reimburses actual meal expenses up the following amounts.

• Breakfast $20
• Lunch $30
• Dinner $75

Allowable Meal Expenses

• Meals taken on travel days (when you traveled by air or train).
• Meals not provided on a meeting day, dinner on Friday for example.
• Group dinners consisting of fellow meeting participants paid by a single person will be reimbursed up to $75 per person and the amount will count towards the $125 daily meal limit.

Unallowable Meal Expenses

• Meals taken outside those provided by the foundation (breakfast, lunch, breaks and/or dinner).
• Meals taken on days not associated with Simons Foundation-coordinated events.
• Minibar expenses.
• Meal expenses for a non-foundation guest.

• Ubers, Lyfts, taxis, etc., taken to and from restaurants in Manhattan.

  • Accommodations will be made for those with mobility restrictions.

Ground Transportation

Expenses for ground transportation will be reimbursed for travel days (i.e. traveling to/from the airport or train station) as well as subway and bus fares while in Manhattan are reimbursable.

Transportation to/from satellite meetings are not reimbursable.

Attendance

In-person participants and speakers are expected to attend all meeting days. Participants receiving hotel and travel support wishing to arrive on meeting days which conclude at 2:00 PM will be asked to attend remotely.

Entry & Building Access

Upon arrival, guests will be required to show their photo ID to enter the Simons Foundation and Flatiron Institute buildings. After checking-in at the meeting reception desk, guests will be able to show their meeting name badge to re-enter the building. If you forget your name badge, you will need to provide your photo ID.

The Simons Foundation and Flatiron Institute buildings are not considered “open campuses” and meeting participants will only have access to the spaces in which the meeting will take place. All other areas are off limits without prior approval.

If you require a private space to conduct a phone call or remote meeting, please contact your meeting manager at least 48-hours ahead of time so that they may book a space for you within the foundation’s room reservation system.

Guests & Children

Meeting participants are required to give 24-hour advance notice of any guests meeting them at the Simons Foundation either before or after the meeting. Outside guests are discouraged from joining meeting activities, including meals.

With the exception of Simons Foundation and Flatiron Institute staff, ad hoc meeting participants who did not receive a meeting invitation directly from the Simons Foundation are not permitted.

Children under the age of 18 are not permitted to attend meetings at the Simons Foundation. Furthermore, the Simons Foundation does not provide childcare facilities or support of any kind. Special accommodations will be made for nursing parents.

Meeting & Policy Questions

Christina Darras
Events Manager
[email protected]

Travel & Hotel Support

FCM Travel Meetings & Events
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