Collaborators

Scott Sheffield

Director, MIT Boston

Scott Sheffield is a probabilist and mathematical physicist. He has authored several of the foundational mathematical works on random fractal curves and loop ensembles (SLE/CLE), random distributions (Gaussian and fractional Gaussian fields), and random surfaces (both discrete random planar maps and continuum Liouville quantum gravity surfaces). He has more recently written about surface expansions of Wilson loop observables in the context of Yang-Mills theory.

Roland Bauerschmidt

NYU, New York

Roland Bauerschmidt is a probabilist and mathematical physicist, with background in rigorous renormalization group analysis. His work most related to this collaboration concerns the probabilistic implementation of Bosonization, the connection of the probabilistic Bakry-Emery theory and renormalization , and analysis of some non-linear sigma models.

Denis Bernard

CNRS & ENS, Paris

Denis Bernard is a theoretical and mathematical physicist. He pioneered the study of the WZW models on Riemann surfaces, writing the now-called KZB equations. With M. Bauer, they pioneered the SLE/CFT correspondence, and defined the multiple SLE. With A. LeClair, they developed the use of quantum group symmetries in integrable field theories. With collaborators, they transfer SLE techniques to turbulence to reveal traces of conformal invariance in the 2D inverse turbulent cascade. Together with K. Gawedzki and A. Kupiainen, they contributed to solve the up-to-now unique solvable model of turbulent transport.

Sourav Chatterjee

Sourav Chatterjee is a probabilist who has made contributions to the rigorous study of lattice gauge theories, including a proof of gauge-string duality in large N lattice gauge theories, exact asymptotics for Wilson loop expectations in Ising lattice gauge theory in the weak coupling limit, and a proof that mass gap plus unbroken center symmetry implies quark confinement.

Massimilliano Gubinelli

University of Oxford

Massimiliano Gubinelli is a probabilist and analyst with a background in theoretical physics. He introduced tools to resolve the small-scale singularities of SPDE and developed PDE techniques to address the large field problem in the stochastic quantisation of Φ⁴₃ models also in relation with a nonperturbative implementation of Polchinski’s continuous RG approach. He  studied  probabilistically the Euclidean fermions and   supersymmetric localization in the context of stochastic quantisation.

Colin Guillarmou

CNRS, Paris-Saclay

Colin Guillarmou is a geometric analyst, who worked on PDE in geometric settings, spectral theory, chaotic dynamical systems, and on conformal field theory. With other PIs, he has contributed to the mathematical construction and resolution of Liouville CFT, the H3 WZW model  and Imaginary Liouville CFT.

Martin Hairer

EPFL, Lausanne

Martin Hairer is a probabilist and analyst who mainly works in the area of SPDE. He developed the theory of regularity structures, which provides a toolbox for interpreting and solving the type of singular SPDE that arise in the context of stochastic quantisation. This allowed, in particular, to gain new mathematical insights into the Φ⁴₃ model and the Yang-Mills theories and to demonstrate their universality under approximations.

Nina Holden

NYU, New York

Nina Holden is a probabilist who works on SLE and LQG. She established (with PI X. Sun) the first convergence result for uniform random planar maps to LQG under conformal embedding. In numerous works she has developed and applied the theory of conformal welding of LQG surfaces, building on fundamental papers of PI S. Sheffield and collaborators.

Antti Kupiainen

University of Helsinki

Antti Kupiainen is a mathematical physicist who has  pioneered  the rigorous theory of the renormalisation group and QFT approach to turbulence. He has also pioneered the path integral approach to WZW CFT, the mathematical theory of stochastic quantisation and most recently  the conformal bootstrap for Liouville CFT  and the probabilistic construction of the H3 model.

Nikita Nekrasov

SCGP, Stony Brook

Nikita Nekrasov is a theoretical and mathematical physicist. He led the non-perturbative QFT analysis by performing all-instanton resummation of the low-energy effective action of many N=2 super-Yang-Mills theories, with various matter multiplets, proving the celebrated Seiberg-Witten conjecture. His partition function connects in a subtle way the 2d CFT, 3d hyperbolic geometry, 4d manifold invariants, and topological strings on local Calabi-Yau threefolds.  He proposed the BPS/CFT correspondence, which provides an enumerative expression for conformal blocks of various CFT in two dimensions/their q-analogues.  The AGT conjecture is  a particular case.

Rémi Rhodes

I2M, Aix-Marseille université

Rémi Rhodes is a probabilist. He has worked on homogenization theory and then pioneered the renewal of Gaussian Multiplicative Chaos theory with V. Vargas  with applications to fully developed turbulence and 2D quantum gravity. His main achievements are the construction of non critical bosonic strings, the probabilistic construction of some major CFTs, e.g. the Liouville CFT or the H3-WZW model, and the conformal bootstrap for the Liouville theory.

Slava Rychkov

IHÉS, Bures-sur-Yvette

Slava Rychkov is a theoretical and mathematical physicist. He pioneered the conformal bootstrap studies of conformal field theories above two dimensions, leading to accurate prediction of the critical exponents of the 3D Ising model. He also pioneered (jointly with T. Kennedy) the mathematically rigorous theory of tensor network renormalization group for lattice models.

Xin Sun

PKU, Beijing

Xin Sun is a probabilist. His  work with PI N. Holden established a strong relation between uniform random planar maps and LQG.  With various collaborators, he pioneered the synergy between the SLE/LQG coupling theory and Liouville CFT, and use it to obtain exact results in 2D statistical physics,  culminating in the derivation of backbone exponent for planar percolation  and the imaginary DOZZ formula for loop models.

Fredrik Viklund

KTH, Stockholm

Fredrik Viklund is a probabilist and complex analyst who has made contributions to the geometric and multifractal analysis of SLE. His work has established new links between SLEs, critical lattice models, and CFT, and the Loewner energy in collaboration with PI Wang. He has recently helped develop the probabilistic approach to lattice Yang-Mills theories.

Yilin Wang

ETH, Zurich

Yilin Wang is a probabilist, complex analyst, and geometric analyst who pioneered the semiclassical analysis of SLE curves with PI Viklund and discovered their relation to Teichmüller theory. She established the path-integral formulation of SLE loops and their Virasoro representations, and related the action of SLE to the renormalized volume of hyperbolic 3-manifolds.