2026 Simons Collaboration on Probabilistic Paths to Quantum Field Theory Annual Meeting

Sourav Chatterjee
Stanford University

What Is a Probabilistically Defined Quantum Field Theory?

Sourav Chatterjee will give a broad overview of what it means to rigorously define and construct a quantum field theory, what progress has been made so far, and what remains to be done. Since the subject is vast, Chatterjee will be highly selective, but they will try to present some actual mathematics and emphasize a few concrete examples and frameworks that make the basic ideas feel less mysterious. The talk will end with a brief discussion of the Clay Millennium problem of Yang–Mills existence and the mass gap, and how it fits into the broader quest to build interacting quantum field theories.
 

Martin Hairer
École Polytechnique Fédérale de Lausanne (EPFL)

Stochastic Quantisation of Gauge Theories

Martin Hairer will review Parisi and Wu’s original motivation for introducing the ’stochastic quantisation’ procedure for QFT’s. 40 years after their insight, this approach is finally bearing fruit in a way that they predicted at the time.
 

Igor Klebanov
Princeton University

Strings from Local Field Theory: QCD and Some Simpler Models

The talk will begin with a brief review of quantum chromodynamics (QCD) and the confinement problem. Lattice gauge theory (LGT) provides a non-perturbative formulation of QCD, which has led to good numerical results for the low-lying hadron spectra. The confinement is related to formation of QCD strings. Numerical studies of the excitation spectra of long strings in SU(N) gauge theory show agreement with the Nambu–Goto action plus corrections. In the large N limit, the string breaking is suppressed. Igor Klebanov will then discuss other large N theories where strings are emergent. One of them is based on the gauge/gravity duality and is described by the warped deformed conifold background of type IIB string theory. This theory exhibits confinement, and the quark-antiquark potential is similar to that found in LGT. In the 2D model for large N QCD, the spectrum of mesons is obtained by solving the integral equation obtained by ‘t Hooft in 1974. A similar equation called the Marchesini–Onofri equation describes the adjoint states in the SU(N) symmetric quantum mechanics of a Hermitian matrix. Recent solution of this equation leads to spectra that may be related to oscillating strings.
 

Antti Kupiainen
University of Helsinki

Conformal Field Theory and Path Integrals

Conformal field theory (CFT) describes universality classes of statistical mechanics systems at the critical temperature of a second order phase transition as well as Quantum field theories of fundamental physics in the limits of small and large length scales. CFTs have special symmetries leading to a rich mathematical structure which has inspired representation theory and geometry. However, a rigorous mathematical foundation for CFT is still lacking. Two major approaches in physics to CFT are the path integral approach and the conformal bootstrap approach. In this talk, Antti Kupiainen will discuss a path integral approach to two dimensional CFT based on probabilistic tools such as the Gaussian multiplicative chaos. Kupiainen will explain how the conformal bootstrap can be approached in the probabilistic setup leading to a complete solution of Liouville CFT, which plays a central role in the theory of random surfaces and how these constructions could be extended to other CFTs, such as sigma models, which have interesting connections to geometry. In particular, the probabilistic construction allows us to prove a surprising correspondence between Liouville CFT and a Wess–Zumino–Witten sigma model originally conjectured by Ribault, Teschner, Hikida, and Schomerus and argued by Teschner and Gaiotto to define a “quantum” deformation of the analytic Langlands correspondence of Etingof, Frenkel, and Kazhdan.
 

Nathan Seiberg
Institute for Advanced Study

What Is Quantum Field Theory?

Seiberg will share his views on the subject.
 

Scott Sheffield
Massachusetts Institute of Technology (MIT)

Yang–Mills Gauge Theory and Random Geometry in 2 and 4 Dimensions

Many of the basic objects of 2D mathematical physics (such as bond percolation, uniform spanning trees, loop-erased random walks, Ising and other sigma models, Gaussian free fields, etc.) have very natural one-form-level-higher analogs in 4D (plaquette percolation, uniform spanning 2-trees, cycle-spanning branches, Ising and other lattice gauge theories, 1-form Gaussian free fields, etc.). Scott Sheffield will discuss the direct and indirect role that two-dimensional random surfaces play in our understanding of four dimensional models, along with many open problems involved in the rigorous construction of off-critical continuum limits.
 

Xin Sun
Peking University

CFT Perspectives on 2D Percolation and Brownian Motion

Conformal field theory (CFT) has proven to be a powerful framework for studying two-dimensional (2D) Bernoulli percolation at criticality. Classic applications include the derivation of certain critical exponents and crossing probabilities. Yet, the precise nature of the underlying CFT remains elusive and is a subject of active investigation in both the mathematics and physics communities. In this talk, Xin Sun will first provide an overview of this topic and then present recent progress on another fundamental planar fractal “Brownian motion,” revealing that its percolative properties may be governed by an equally rich, and perhaps more enigmatic, CFT.
 

Yilin Wang
Eidgenössische Technische Hochschule (ETH) Zürich

Holography from a Geometric Perspective

The holographic principle looks to encode geometric quantities by conformally invariant quantities on its boundary of one lower dimension, or vice versa. This philosophy has been very successful in relating gravity theory in the bulk to the conformal field theory on the boundary.

From a geometric perspective, a classical construction using Epstein’s truncation, relates the hyperbolic geometry in the bulk to the conformal geometry on its boundary. Yilin Wang will survey how this geometric construction can be applied to give exact holographic expressions for several actions in QFT, including Liouville action, Loewner energy, and Schwarzian action.

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 three nights at the conference hotel, arriving on Wednesday, April 20 and departing on Saturday, May 2.

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 three nights at the conference hotel, arriving on Wednesday, April 20 and departing on Saturday, May 2.

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 Hotel AKA NoMad 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 three nights, arriving on Wednesday, April 20 and departing on Saturday, May 2.

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

Hotel AKA NoMad
131 Madison Ave
New York, NY 10016
(between 30th and 31st Streets)
https://www.stayaka.com/

For driving directions to the Hotel AKA NoMad 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

Meghan Fazzi
Senior Manager, Events & Administration, MPS
[email protected]

Travel & Hotel Support

FCM Travel Meetings & Events
[email protected]
Hours: M-F, 8:30 AM-5:00 PM ET
+1-888-789-6639