All speakers have been asked to give broadly accessible review-style talks.
| Monday | Tuesday | Wednesday | |
|---|---|---|---|
| 9:00-9:30 | Welcome | Welcome | Welcome |
| 9:30-10:30 | Armstrong | Ferrari | Gorbenko |
| 11:00-12:00 | Jacobsen | Curien | Mastropietro |
| 12:00-14:00 | Lunch | Lunch | Lunch |
| 14:00-15:00 | Mazac | Weber | Nahmod |
| 15:10-16:10 | Berestycki | Garban | Kozlowski |
All talks will take place on the 12th floor of the Courant Institute in Warren Weaver Hall. Lunch will be served on the 13th floor of the Courant Institute. NYU building registration and government ID is required to enter.
Scott Armstrong (CNRS)
Stochastic homogenization as a method for RG
Jesper Jacobsen (ENS)
Correlation functions in two-dimensional critical loop models.
Using a combination of lattice algebra and conformal bootstrap methods we determine correlation functions of critical loop models in various geometries. Examples include the probability that three given points are on the same loop in the sphere geometry, the probability that the loop passing through one given point is non-trivial in the torus geometry, or the probability that two given points are not separated by any loop in the disc geometry with free or wired boundary conditions. We discuss the perspectives of going beyond such specific examples and setting up the principles for determining all geometric correlation functions in critical loop models.
Dalimil Mazac (CEA-Saclay)
Conformal bootstrap for probabilistic models
The conformal bootstrap has proven very powerful for analyzing reflection-positive conformal models. In my talk, I will review this method and suggest a way to generalize it beyond the reflection-positive case, drawing inspiration from the spectral theory of automorphic forms.
Nathanael Berestycki (Vienna)
Massive SLE and near-critical field theory
Frank Ferrari (Brussels)
Review of probabilistic and discrete models for JT gravity
In the first part of the talk, I review the standard approach to Jackiw-Teitelboim quantum gravity (JTQG) with conformally compact hyperbolic boundary conditions for the metric. In particular, I carefully explain how the Schwarzian field theory can be derived in this framework. Some key applications will be briefly discussed.
In the second part of the talk, I focus on very recent developments aimed at defining JTQG on finite-size geometries, using free boundary conditions for the metric. The theory can be formulated by discretizing. This yields a new combinatorial model for self-overlapping polygons counted with an appropriate multiplicity. The theory can also be formulated directly in the continuum, revealing a deep and perhaps surprising relationship between JTQG and Liouville quantum gravity (LQG) techniques. I present the path integral, probabilistic, formulation of the problem, and also write down the associated JT CFT. This is a conformal field theory that plays the same role for JTQG as Liouville CFT does for LQG.
A fundamental conjecture is that the the continuum description is equivalent to the scaling limit of the discrete model, paralleling the expected equivalence between triangulation-based and continuum formulations of Liouville quantum gravity. Another conjecture is that negative curvature JT on finite size geometries converges to the Schwarzian field theory in an appropriate large size limit. If established, this provides a concrete mechanism for the emergence of time.
Nicolas Curien (Orsay)
Survey about random hyperbolic surfaces
I will survey recent developments concerning the geometric properties of random hyperbolic surfaces. While in low genus a clear connection with random planar maps has recently emerged, the geometry of random hyperbolic surfaces in large genus remains largely mysterious, despite significant progress on the spectral side. Starting from the breakthrough work of Maryam Mirzakhani on Weil–Petersson random surfaces, I will discuss what is known about typical geometric features such as the distribution of lengths of closed geodesics, the behavior of the systole, and diameter estimates.
Christophe Garban (Lyon 1)
Spin Systems with Continuous Symmetry: Overview and Small Perturbations
In this talk, I will start with a review on spin systems defined on a lattice Z^d and with values in a target space with continuous symmetry — such as spheres S^{N-1} with N\geq 2. The case N=2 has Abelian continuous symmetry and is called the XY model while N=3 has non-Abelian continuous symmetry and is called the classical Heisenberg model. I will emphasise key contributions and viewpoints from both physics and mathematics.
In the second part of this talk, I will focus on more recent results and in particular on the following question: what happens to Polyakov’s prediction from 1975 when the target space S^2 is slightly perturbed ? The second part is based on a joint work with Nathan de Montgolfier.
Hendrik Weber (Münster)
Global Dynamics for Stochastic Quantisation
Stochastic quantisation, introduced by Parisi and Wu, realises Euclidean quantum field theories as invariant measures of stochastic evolution equations. Over the last decade, the theory of singular stochastic PDEs—initiated by Hairer’s regularity structures—has transformed this idea into a mathematically robust framework for the construction of interacting field theories.
The theory of regularity structures provides a powerful general local solution theory, but extending solutions to global times presents a major challenge. Recent work shows that this can be achieved by combining the small-scale regularity theory with a large-scale damping mechanism. In this talk I will survey progress in this direction, leading to global well-posedness results for stochastic quantisation equations for $\phi^4$ theories and new quantitative control of the associated Gibbs measures.
As applications, I will highlight how these methods have enabled the full construction of Euclidean field theories satisfying the Osterwalder–Schrader axioms, yield precise pathwise comparison with Gaussian reference measures, and lead to new results on perturbative expansions and phase transitions. I will conclude by discussing current efforts to extend these ideas to models with weaker damping mechanisms.
Victor Gorbenko (EPFL)
Confinement at Negative Curvature
Confining flux tubes are objects that underlie the phenomenon of confinement in gauge theories like Yang-Mills. While there is a plenty of numerical evidence that they form in known confining QFTs, the mechanism of their formation and detailed dynamical structure is still unknown. After reviewing analytic and numerical results in flat space, I will suggest a new approach in which we place a gauge theory on hyperbolic space to regulate IR divergences. At large curvature radius we recover flat space. At small radius gauge theory is perturbative, however, flux is still confined to a line due to the gravitational potential induced by curvature. By changing the radius we can interpolate between the two regimes. I will then present results of calculations of the energy spectra of flux tubes in 3D YM and show some evidence that perturbative expansions around small and large radii may match in the middle. The method is applicable to other observables in gauge theories as well.
Vieri Mastropietro (Rome La Sapienza)
Critical review of constructive QFT
The talk is organized in three parts.
In the first part, the basic concepts of renormalization and the Renormalization Group are reviewed, with a brief discussion of the challenges involved in constructing the Standard Model in a non-perturbative framework.
In the second part, we revisit some classical results in constructive quantum field theory, focusing on the analysis of some renormalizable models through the rigorous Renormalization Group.
In the third part, we present recent progress toward more realistic models, including the study of the non-renormalization properties of chiral anomalies in two and four dimensions, the implementation of Ward identities within the Renormalization Group framework, and the computation of the gyromagnetic factor in certain sectors via convergent series.
Andrea Nahmod (Amherst)
Invariant Gibbs measures and propagation of randomness for nonlinear dispersive PDE.
The study of propagation of randomness in the context of dispersive PDEs can be traced back to work by Lebowitz–Rose–Speer (1988, 1989) and Bourgain (1994, 1996) concerning the Gibbs measure for nonlinear Schrodinger equations. Since then there have been substantial developments of their ideas by many different researchers, extending them in different directions (geometric, infinite volume, other dispersive relations). In the last few years, this field has seen significant progress and many new ideas and methods have been introduced. The aim of this talk is to briefly review these recent developments (random averaging operators and random tensor theories) and describe some of the foundations upon which these recent developments have built upon, in particular Bourgain’s seminal work in the subject.
Karol Kozlowski (ENS Lyon)
The S-matrix bootstrap program in 1+1 dimensions: an overview.
The S-matrix bootstrap program was devised in the late 70s and mid 80s as a possible path for a fully explicit construction of numerous massive integrable quantum field theories in 1+1 dimensions. On technical grounds, the bootstrap program refers to a coupled system of Riemann–Hilbert problems whose solution allows one to explicitly realise the quantum fields of the theory as generalised integral operators on suitable spaces of functions. Among other things, this construction allows one to produce explicit expressions for the correlation functions, i.e. the central objects in those theories. These are given in terms of series of multiple integrals and allow to establish the compatibility of the bootstrap construction with the Wightman axiomatic formulation of a quantum field theory.
This talk, will review the various developments of the theory up to discussing the most recent results and the numerous open questions. For illustrative purposes, I shall focus on the simplest non-trivial massive integrable quantum field theory in 1+1 dimensions: the Sinh-Gordon model.
Participants
Abdelmalek Abdesselam, University of Virginia
Maria Stella Adamo, Kyoto University
Anshul Adve, Princeton University
Jeonghyun Ahn, mit
Michael Aizenman, Princeton University
Jie Jun Ang, University of California San Diego
Scott Armstrong, CNRS/Sorbonne University & Courant/NYU
Juhan Aru, EPFL
Nikolay Barashkov, Max Planck Institute for Mathematics in the Sciences
Roland Bauerschmidt, New York University
Nathanael Berestycki, University of Vienna
Denis BERNARD, Laboratoire de Physique de l’Ecole Normale Superieure (LPENS)
Manan Bhatia, MIT
Thierry Bodineau, CNRS, Institut des Hautes Études Scientifiques
Bjoern Bringmann, Princeton University
Federico Camia, New York University Abu Dhabi
Sky Cao, Massachusetts Institute of Technology
Baptiste Cerclé, CNRS – Sorbonne University
Ajay Chandra, Purdue University
Dmitry Chelkak, University of Michigan, Ann Arbor
Ilya Chevyrev, SISSA (International School for Advanced Studies)
Kyuhyeon Choi, Massachusetts Institute of Technology
Nicolas Curien, Université Paris-Saclay
Nguyen-Viet Dang, Université de Strasbourg
Yu Deng, University of Chicago
Paweł Duch, École polytechnique fédérale de Lausanne
Bertrand Duplantier, Paris-Saclay University
Nikolay Ebel, Institut des Hautes Études Scientifiques
Frank Ferrari, Université Libre de Bruxelles (ULB) and International Solvay Institutes
Victor Gorbenko, Ecole Polytechnique Federale de Lausanne
Maria (Masha) Gordina, University of Connecticut/University of Rochester
Colin Guillarmou, Université Paris-Saclay
Trishen Gunaratnam, Tata Institute of Fundamental Research
Martin Hairer, EPF Lausanne
Tyler Helmuth, Durham University
Michael Hofstetter, Weizmann Institute
Nina Holden, New York University
Yulai HUANG, Institut de Mathématiques de Marseille
Nathan Huguenin, Aix-Marseille Uinversity
Jesper Jacobsen, École Normale Supérieure
Younghun Jo, Massachusetts Institute of Technology
Janne Junnila, KTH Royal Institute of Technology
Konstantinos Kavvadias, Massachusetts Institute of Technology
Tom Kennedy, University of Arizona
Richard Kenyon, Yale University
Karol Kozlowski, Ecole Normale Supérieure de Lyon
Antti Kupiainen, University of Helsinki
Tuomo Kuusi, University of Helsinki
Gregory Lawler, University of Chicago
Andre LeClair, Cornell University
Thierry Lévy, Sorbonne Université
Tianyue Liu, Beijing international center for mathematical research
Amélie Loher, Oxford
Nikolai Makarov, Caltech
Vieri Mastropietro, Universita’ di Roma La Sapienza
Dalimil Mazac, Institut de Physique Theorique, CEA-Saclay
Grégory Miermont, Ecole Normale Supérieure de Lyon
Deven Mithal, University of Chicago
Andrea Nahmod, University of Massachusetts, Amherst
Charles Newman, New York University
Nikita Nekrasov, Simons Center for Geometry and Physics
Ron Nissim, Massachusetts Institute of Technology
Jiwoon Park, Republic of Korea Air Force Academy
Martin Peev, Martin Peev
Jaka Pelaic, University of Oxford
Colin Piernot, École Polytechnique Fédérale de Lausanne
Wei Qian, The University of Hong Kong
Rémi Rhodes, Aix-Marseille University
Pierre-François Rodriguez, University of Cambridge
Vyacheslav Rychkov, Institut des Hautes Etudes Scientifiques
Eero Saksman, University of Helsinki
Kihoon Seong, École Polytechnique Fédérale de Lausanne
Sylvia Serfaty, Sorbonne Université
Scott Sheffield, Massachusetts Institute of Technology (MIT)
PHILIPPE SOSOE, Cornell University
Thomas Spencer, Thomas Spencer
Rhys Steele, Max Planck Institute for Mathematics in the Sciences
Xin Sun, Peking University
Jörg Teschner, Universität Hamburg and DESY
Fredrik Viklund, KTH Royal Institute of Technology
Yilin Wang, Eidgnössische Technische Hochschule Zürich
Yuanzheng Wang, Massachusetts Institute of Technology
Hendrik Weber, University of Münster
Pavel Wiegmann, University of Chicago
Kay Wiese, ENS Paris
Peter Wildemann, University of Geneva
Yang Xiao, Aix Marseille Universite
Shengjing Xu, University of Pennsylvania
Oren Yakir, Massachusetts Institute of Technology
Masahito Yamazaki, University of Tokyo
Jaeyun Yi, Korea Institute for Advanced Study
Wenhao Zhao, Ecole Polytechnique Federale de Lausanne
Xiangchan Zhu, Chinese Academy of Sciences
Rongchan Zhu, Beijing Institute of Technology
ZIJIE ZHUANG, University of Pennsylvania
Omar Abdelghani, New York University
Yuri Bakhtin, Courant Institute
Paul Bourgade, New York University
Ivan Corwin, Columbia University
Christophe Garban, New York University and University Lyon 1
Chokri Manai, New York University
Yifan Wang, New York University
Pu Yu, New York University
Edward Zeng, New York University
Matt Kleban, New York University
Jasper Shogren-Knaak, New York University
Zhenfeng Tu, New York University
Louis-Pierre Arguin, CUNY
Julien Dubedat, Columbia
Enrique Rivera Ferraiuoli, New York University
Vismay Sharan, New York University
Kexin Zhang, New York University
Yuchen Fan, New York University
Yu Gu, Maryland
Sung Chul Park, Michigan
Yu Feng, Michigan
Justin Kulp, Simons Center for Geometry and Physics
Michael Douglas, Harvard
Ansh Saxena, Princeton University
