# Seminars (SRQ)

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Event When Speaker Title Presentation Material
SRQW01 3rd September 2018
10:00 to 11:00
Antti Kupiainen Introduction to the Renormalisation Group - 1
Lecture notes for the course are at: https://courses.helsinki.fi/sites/default/files/course-material/4594153/MathPhys2018final.pdf We discuss parts of sections 4,6,7,8,9 which are self contained
SRQW01 3rd September 2018
11:30 to 12:30
Antti Kupiainen Introduction to the Renormalisation Group - 2
SRQW01 3rd September 2018
13:30 to 14:30
Martin Hairer Stochastic quantisation of Yang-Mills
Co-authors: Ajay Chandra (Imperial College London), Hao Shen (Columbia University)
SRQW01 3rd September 2018
14:30 to 15:30
Lorenzo Zambotti Renormalisation in regularity structures - part 1
This should be a mini-course on the algebraic side of the theory of regularity structures.
SRQW01 3rd September 2018
16:00 to 17:00
Felix Otto Regularity structures: Reconstruction and Integration - part 1
This minicourse is coordinated with the one of Lorenzo Zambotti. The joint goal is to treat the dynamical phi-4-3 model. This minicourse will provide the basic notions in regularity structures and discuss reconstruction and integration. It will mostly follow Martin Hairer's 2015 notes "Regularity structures and the dynamical phi-4-3 model''.
SRQW01 4th September 2018
09:00 to 10:00
Felix Otto Regularity structures: Reconstruction and Integration - part 2
This minicourse is coordinated with the one of Lorenzo Zambotti. The joint goal is to treat the dynamical phi-4-3 model. This minicourse will provide the basic notions in regularity structures and discuss reconstruction and integration. It will mostly follow Martin Hairer's 2015 notes "Regularity structures and the dynamical phi-4-3 model''.
SRQW01 4th September 2018
10:00 to 11:00
Lorenzo Zambotti Renormalisation in regularity structures - part 2
This should be a mini-course on the algebraic side of the theory of regularity structures.
SRQW01 4th September 2018
11:30 to 12:30
Antti Kupiainen Introduction to the Renormalisation Group - 3
SRQW01 4th September 2018
13:30 to 14:30
Vieri Mastropietro Universality in solid state physics and Constructive Renormalization Group
I will review some universality results in graphene and Hall insulators obtained by Renormalization Group methods.
SRQW01 4th September 2018
14:30 to 15:30
Antti Kupiainen Introduction to the Renormalisation Group - 4
SRQW01 4th September 2018
16:00 to 17:00
Slava Rychkov CFT and the bootstrap
SRQW01 5th September 2018
09:00 to 10:00
Felix Otto Regularity structures: Reconstruction and Integration - part 3
This minicourse is coordinated with the one of Lorenzo Zambotti. The joint goal is to treat the dynamical phi-4-3 model. This minicourse will provide the basic notions in regularity structures and discuss reconstruction and integration. It will mostly follow Martin Hairer's 2015 notes "Regularity structures and the dynamical phi-4-3 model''.
SRQW01 5th September 2018
10:00 to 11:00
Lorenzo Zambotti Renormalisation in regularity structures - part 3
This should be a mini-course on the algebraic side of the theory of regularity structures.
SRQW01 5th September 2018
11:30 to 12:30
Horst Knoerrer Symmetry breaking in a gas of bosons - an approach using constructive field theory
T.Balaban, J.Feldman, E.Trubowitz and the speaker have the long term goal to rigorously demonstrate symmetry breaking in a gas of weakly interaction bosons hopping on a three-dimensional lattice. Technically, to show that the correlation functions decay at a nonintegrable rate when the chemical potential is sufficiently positive, the nonintegrability reflecting the presence of a long range Goldstone boson mediating the inteaction between quasiparticles in the superfluid condensate. In addition to a report on the status of this program, I will try to describe in more detail the method of block spin transformations that we use to define and control a renormalization group flow.
SRQW01 6th September 2018
09:00 to 10:00
Gordon Slade Renormalisation group and critical phenomena - 1
The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly self-avoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for long-range models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt.
SRQW01 6th September 2018
10:00 to 11:00
Nicolas Perkowski Infinite-dimensional paracontrolled distributions: the Burgers generator
Regularity structures, paracontrolled distributions and all that provide pathwise, deterministic tools to solve and study singular stochastic PDEs over finite-dimensional spaces. From a probabilistic point of view we would also like to understand the associated Kolmogorov backward equations, which can be interpreted as infinite-dimensional singular SPDEs. I will discuss on the example of the conservative stochastic Burgers equation how to construct a space of (para-) paracontrolled distributions in which the backward equation is well posed. As an application we obtain a martingale formulation and an alternative proof for the well-posedness of "energy solutions", without using the Cole-Hopf transform. The approach extends to some other singular SPDEs with Gaussian invariant measures and quadratic nonlinearities. This is joint work with Massimiliano Gubinelli.
SRQW01 6th September 2018
11:30 to 12:30
Gordon Slade Renormalisation group and critical phenomena - 2
The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly self-avoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for long-range models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt.
SRQW01 6th September 2018
13:30 to 14:30
Felix Otto Regularity structures: Reconstruction and Integration - part 4
This minicourse is coordinated with the one of Lorenzo Zambotti. The joint goal is to treat the dynamical phi-4-3 model. This minicourse will provide the basic notions in regularity structures and discuss reconstruction and integration. It will mostly follow Martin Hairer's 2015 notes "Regularity structures and the dynamical phi-4-3 model''.
SRQW01 6th September 2018
14:30 to 15:30
Lorenzo Zambotti Renormalisation in regularity structures - part 4
This should be a mini-course on the algebraic side of the theory of regularity structures.
SRQW01 6th September 2018
16:00 to 17:00
Christoph Kopper The Flow equations of the renormalization group
The Flow equations in Polchinski's setting allow for a simple and transparent proof of perturbative renormalizability, cirumventing auxiliary combinatoric structures. They also permit to prove properties of perturbative Schwinger functions which are out of reach in other settings. The main problem for a nonperturbative analysis of those equations lies in their combinatoric instability, which is present already at the mean field level.
SRQW01 6th September 2018
17:15 to 18:15
Antti Kupiainen Wilsonian RG for SPDEs (Informal discussion)
SRQW01 7th September 2018
09:00 to 10:00
Roland Bauerschmidt Spectral gap critical exponent for Glauber dynamics of hierarchical spin models
We develop a renormalisation group approach to deriving the asymptotics of the spectral gap of the generator of Glauber type dynamics of spin systems at and near a critical point. In our approach, we derive a spectral gap inequality, or more generally a Brascamp--Lieb inequality, for the measure recursively in terms of spectral gap or Brascamp--Lieb inequalities for a sequence of renormalised measures. We apply our method to hierarchical versions of the $4$-dimensional $n$-component $|\varphi|^4$ model at the critical point and its approach from the high temperature side, and the $2$-dimensional Sine--Gordon and the Discrete Gaussian models in the rough phase (Kosterlitz--Thouless phase). For these models, we show that the spectral gap decays polynomially like the spectral gap of the dynamics of a free field (with a logarithmic correction for the $|\varphi|^4$ model), the scaling limit of these models in equilibrium. Co-author: Thierry Bodineau
SRQW01 7th September 2018
10:00 to 11:00
Gordon Slade Renormalisation group and critical phenomena - 4
The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly self-avoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for long-range models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt.
SRQW01 7th September 2018
11:30 to 12:30
Gordon Slade Renormalisation group and critical phenomena - 3
The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly self-avoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for long-range models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt.
SRQW01 7th September 2018
13:30 to 14:30
Massimiliano Gubinelli A stochastic approach to constructive QFT
Co-author: Nikolay Barashkov (University of Bonn)We propose a new existence proof of the Phi^4_{2,3} Euclidean quantum fields in a periodic domain using tools from stochastic analysis, in particular a stochastic control interpretation of Wilson's continuous RG.
SRQ 10th September 2018
11:00 to 12:30
David Brydges Reflection Positivity which plays an important role in QFT and statistical mechanics.
SRQ 12th September 2018
15:00 to 16:30
Margherita Disertori Why fermions?
Fermions appear naturally in representations of stochastic processes. I will discuss one or two examples.
SRQ 14th September 2018
11:00 to 12:30
Hendrik Weber, David Brydges Chessboard estimates and their role in the 1976
Froehlich-Simon-Spencer proof of existence of phase transitions followed by Hendrik Weber on scaling and function spaces for rough paths.
SRQ 17th September 2018
11:00 to 12:30
Hendrik Weber Renormalisation in QFT, statistical mechanics and stochastic PDE's
Hendrik Weber introducing scaling and function spaces for rough paths
SRQ 19th September 2018
15:30 to 16:30
Margherita Disertori Why Fermions, part II
Fermions appear naturally in representations of stochastic processes. I will discuss one or two examples.
SRQ 21st September 2018
11:00 to 12:30
Hendrik Weber Renormalisation in QFT, statistical mechanics and stochastic PDE's
Hendrik Weber introducing scaling and function spaces for rough paths
SRQ 27th September 2018
11:00 to 12:00
Peter Friz Rough paths
I will survey Lyons' rough path theory and some of its connections to Hairer's regularity structures.
SRQ 28th September 2018
11:00 to 12:30
Takashi Hara Why Yang-Mills: a review of no-go results for phi^4_4
SRQ 28th September 2018
16:00 to 17:00
Martin Hairer Rothschild Lecture: Random rubber bands
A "rubber band" constrained to remain on a manifold evolves by trying to shorten its length, eventually settling on a closed geodesic, or collapsing entirely. It is natural to try to consider a noisy version of such a model where each segment of the band gets pulled in random directions. Trying to build such a model turns out to be surprisingly difficult and generates a number of nice insights, as well as some beautiful algebraic and analytical objects. We will survey some of the main results obtained on the way to this construction.
SRQ 1st October 2018
11:00 to 12:30
Thierry Levy 2-dimensional Yang-Mills theory and the Makeenko-Migdal equations (I)
SRQ 3rd October 2018
15:30 to 16:30
Thierry Levy 2-dimensional Yang-Mills theory and the Makeenko-Migdal equations (II)
SRQ 5th October 2018
11:00 to 12:30
Hendrik Weber Local estimates for reaction diffusion equations with applications to $\Phi^4_3$
SRQ 8th October 2018
11:00 to 12:30
Fabio Toninelli Lecture 1 - The interacting dimer model
The aim of this minicourse is to present recent results, obtained together with Vieri Mastropietro (arXiv:1406.7710 and arXiv:1612.01274), on non-integrable perturbations of the classical dimer model on the square lattice. In the integrable situation, the model is free-fermionic and the large-scale fluctuations of its height function tend to a two-dimensional massless Gaussian field (GFF). We prove that convergence to GFF holds also for sufficiently small non-integrable perturbations. At the same time, we show that the dimer-dimer correlations exhibit non-trivial critical exponents, continuously depending upon the strength of the interaction: the model belongs, in a suitable sense, to the Luttinger liquid' universality class. The proofs are based on constructive Renormalization Group for interacting fermions in two dimensions.   Contents:   1. Basics: the model, height function, interacting dimer model. The main results for the interacting model: GFF fluctuations and    Haldane relation.   2. The non-interacting dimer model: Kasteleyn theory, thermodynamiclimit, long-distance asymptotics of correlations, GFF fluctuations. Fermionic representation of the non-interacting and of the interacting dimer model.   3. Multi-scale analysis of the free propagator, Feynman diagrams and dimensional estimates. Determinant expansion.   Non-renormalized multiscale expansion.   4. Renormalized multiscale expansion. Running coupling constants. Beta function.   5. The reference continuum model (the infrared fixed point'): the Luttinger model. Exact solvability of the Luttinger model. Bosonization.   6. Ward identities and anomalies. Schwinger-Dyson equation. Closed equation for the correlation functions. Comparison of the lattice model with the reference one.
SRQ 10th October 2018
15:30 to 17:00
Fabio Toninelli Lecture 2 - The interacting dimer model
The aim of this minicourse is to present recent results, obtained together with Vieri Mastropietro (arXiv:1406.7710 and arXiv:1612.01274), on non-integrable perturbations of the classical dimer model on the square lattice. In the integrable situation, the model is free-fermionic and the large-scale fluctuations of its height function tend to a two-dimensional massless Gaussian field (GFF). We prove that convergence to GFF holds also for sufficiently small non-integrable perturbations. At the same time, we show that the dimer-dimer correlations exhibit non-trivial critical exponents, continuously depending upon the strength of the interaction: the model belongs, in a suitable sense, to the Luttinger liquid' universality class. The proofs are based on constructive Renormalization Group for interacting fermions in two dimensions.   Contents:   1. Basics: the model, height function, interacting dimer model. The main results for the interacting model: GFF fluctuations and    Haldane relation.   2. The non-interacting dimer model: Kasteleyn theory, thermodynamiclimit, long-distance asymptotics of correlations, GFF fluctuations. Fermionic representation of the non-interacting and of the interacting dimer model.   3. Multi-scale analysis of the free propagator, Feynman diagrams and dimensional estimates. Determinant expansion.   Non-renormalized multiscale expansion.   4. Renormalized multiscale expansion. Running coupling constants. Beta function.   5. The reference continuum model (the infrared fixed point'): the Luttinger model. Exact solvability of the Luttinger model. Bosonization.   6. Ward identities and anomalies. Schwinger-Dyson equation. Closed equation for the correlation functions. Comparison of the lattice model with the reference one.
SRQ 12th October 2018
11:00 to 12:30
Fabio Toninelli Lecture 3 - The interacting dimer model (copy)
The aim of this minicourse is to present recent results, obtained together with Vieri Mastropietro (arXiv:1406.7710 and arXiv:1612.01274), on non-integrable perturbations of the classical dimer model on the square lattice. In the integrable situation, the model is free-fermionic and the large-scale fluctuations of its height function tend to a two-dimensional massless Gaussian field (GFF). We prove that convergence to GFF holds also for sufficiently small non-integrable perturbations. At the same time, we show that the dimer-dimer correlations exhibit non-trivial critical exponents, continuously depending upon the strength of the interaction: the model belongs, in a suitable sense, to the Luttinger liquid' universality class. The proofs are based on constructive Renormalization Group for interacting fermions in two dimensions.   Contents:   1. Basics: the model, height function, interacting dimer model. The main results for the interacting model: GFF fluctuations and    Haldane relation.   2. The non-interacting dimer model: Kasteleyn theory, thermodynamiclimit, long-distance asymptotics of correlations, GFF fluctuations. Fermionic representation of the non-interacting and of the interacting dimer model.   3. Multi-scale analysis of the free propagator, Feynman diagrams and dimensional estimates. Determinant expansion.   Non-renormalized multiscale expansion.   4. Renormalized multiscale expansion. Running coupling constants. Beta function.   5. The reference continuum model (the infrared fixed point'): the Luttinger model. Exact solvability of the Luttinger model. Bosonization.   6. Ward identities and anomalies. Schwinger-Dyson equation. Closed equation for the correlation functions. Comparison of the lattice model with the reference one.
SRQ 15th October 2018
11:00 to 12:30
Alessandro Giuliani Lecture 4 - The interacting dimer model
The aim of this minicourse is to present recent results, obtained together with Vieri Mastropietro (arXiv:1406.7710 and arXiv:1612.01274), on non-integrable perturbations of the classical dimer model on the square lattice. In the integrable situation, the model is free-fermionic and the large-scale fluctuations of its height function tend to a two-dimensional massless Gaussian field (GFF). We prove that convergence to GFF holds also for sufficiently small non-integrable perturbations. At the same time, we show that the dimer-dimer correlations exhibit non-trivial critical exponents, continuously depending upon the strength of the interaction: the model belongs, in a suitable sense, to the Luttinger liquid' universality class. The proofs are based on constructive Renormalization Group for interacting fermions in two dimensions.   Contents:   1. Basics: the model, height function, interacting dimer model. The main results for the interacting model: GFF fluctuations and    Haldane relation.   2. The non-interacting dimer model: Kasteleyn theory, thermodynamiclimit, long-distance asymptotics of correlations, GFF fluctuations. Fermionic representation of the non-interacting and of the interacting dimer model.   3. Multi-scale analysis of the free propagator, Feynman diagrams and dimensional estimates. Determinant expansion.   Non-renormalized multiscale expansion.   4. Renormalized multiscale expansion. Running coupling constants. Beta function.   5. The reference continuum model (the infrared fixed point'): the Luttinger model. Exact solvability of the Luttinger model. Bosonization.   6. Ward identities and anomalies. Schwinger-Dyson equation. Closed equation for the correlation functions. Comparison of the lattice model with the reference one.
SRQ 17th October 2018
15:00 to 16:30
Alessandro Giuliani Lecture 5 - The interacting dimer model
The aim of this minicourse is to present recent results, obtained together with Vieri Mastropietro (arXiv:1406.7710 and arXiv:1612.01274), on non-integrable perturbations of the classical dimer model on the square lattice. In the integrable situation, the model is free-fermionic and the large-scale fluctuations of its height function tend to a two-dimensional massless Gaussian field (GFF). We prove that convergence to GFF holds also for sufficiently small non-integrable perturbations. At the same time, we show that the dimer-dimer correlations exhibit non-trivial critical exponents, continuously depending upon the strength of the interaction: the model belongs, in a suitable sense, to the Luttinger liquid' universality class. The proofs are based on constructive Renormalization Group for interacting fermions in two dimensions.   Contents:   1. Basics: the model, height function, interacting dimer model. The main results for the interacting model: GFF fluctuations and    Haldane relation.   2. The non-interacting dimer model: Kasteleyn theory, thermodynamiclimit, long-distance asymptotics of correlations, GFF fluctuations. Fermionic representation of the non-interacting and of the interacting dimer model.   3. Multi-scale analysis of the free propagator, Feynman diagrams and dimensional estimates. Determinant expansion.   Non-renormalized multiscale expansion.   4. Renormalized multiscale expansion. Running coupling constants. Beta function.   5. The reference continuum model (the infrared fixed point'): the Luttinger model. Exact solvability of the Luttinger model. Bosonization.   6. Ward identities and anomalies. Schwinger-Dyson equation. Closed equation for the correlation functions. Comparison of the lattice model with the reference one.
SRQ 19th October 2018
11:00 to 12:30
Alessandro Giuliani Lecture 6 - The interacting dimer model
The aim of this minicourse is to present recent results, obtained together with Vieri Mastropietro (arXiv:1406.7710 and arXiv:1612.01274), on non-integrable perturbations of the classical dimer model on the square lattice. In the integrable situation, the model is free-fermionic and the large-scale fluctuations of its height function tend to a two-dimensional massless Gaussian field (GFF). We prove that convergence to GFF holds also for sufficiently small non-integrable perturbations. At the same time, we show that the dimer-dimer correlations exhibit non-trivial critical exponents, continuously depending upon the strength of the interaction: the model belongs, in a suitable sense, to the Luttinger liquid' universality class. The proofs are based on constructive Renormalization Group for interacting fermions in two dimensions.   Contents:   1. Basics: the model, height function, interacting dimer model. The main results for the interacting model: GFF fluctuations and    Haldane relation.   2. The non-interacting dimer model: Kasteleyn theory, thermodynamiclimit, long-distance asymptotics of correlations, GFF fluctuations. Fermionic representation of the non-interacting and of the interacting dimer model.   3. Multi-scale analysis of the free propagator, Feynman diagrams and dimensional estimates. Determinant expansion.   Non-renormalized multiscale expansion.   4. Renormalized multiscale expansion. Running coupling constants. Beta function.   5. The reference continuum model (the infrared fixed point'): the Luttinger model. Exact solvability of the Luttinger model. Bosonization.   6. Ward identities and anomalies. Schwinger-Dyson equation. Closed equation for the correlation functions. Comparison of the lattice model with the reference one.
SRQW02 22nd October 2018
09:30 to 10:30
Giovanni Jona-Lasinio Some questions and remarks on the theory of singular stochastic PDEs
In the last decade there has been important progress in understanding singular stochastic PDEs (SSPDEs). In this talk I will briefly discuss the following points. 1. There are singular stochastic PDEs successfully used by physicists which are still beyond the reach of the present approaches and deserve mathematical investigation. 2. The present theory should be further developed by viewing SSPDEs as infinite dimensional dynamical systems. 3. Certain methods developed long ago for euclidean field theories in infinite volume may be useful in the study of the large time behavior of SSPDEs.
SRQW02 22nd October 2018
11:00 to 12:00
Volker Bach Beyond the van Hove time scale
Given an arbitrarily large, but fixed, time t >0, we derive approximations for the time evolution of the spin-boson model in terms of the propagator generated by a free effective Hamiltonian. Our construction rests on the renormalization group induced by the isospectral Feshbach-Schur ap. This is joint work with Jacob Schach Möller and Matthias Westrich.
SRQW02 22nd October 2018
13:30 to 14:30
Abdelmalek Abdesselam Pointwise multiplication of random Schwartz distributions with Wilson's operator product expansion
I will present a general theorem for the multiplication of random distributions which is similar in spirit to the construction of local Wick powers of a Gaussian field. However, this theorem is much more general in scope and applies to non-Gaussian measures, even without translation invariance and in the presence of anomalous scaling, provided the random fields involved are less singular than white noise. Conjecturally, the construction of the energy field of the 3D Ising scaling limit as a square of the spin field should fall within the purview of the theorem. Our construction involves multiplying mollified distributions followed by suitable additive and multiplicative renormalizations before a proof of almost-sure convergence when the mollification is removed. The main tools for the proof are combinatorial estimates on moments. The main hypothesis for the theorem is Wilson's OPE with precise quantitative bounds for pointwise correlations at noncoinciding points. I will also explain how the theorem works on the example of a simple conformal field theory of mean field type, namely, the fractional Gaussian field.
SRQW02 22nd October 2018
14:30 to 15:30
Patricia Gonçalves Non-equilibrium fluctuations for the slow boundary symmetric exclusion
In this talk, I will present the symmetric simple exclusion process in contact with slow stochastic reservoirs which are regulated by a factor $n^{-\theta}$, $\theta\geq 0$. I will review the hydrodynamic limit and the goal of my talk is to present the non-equilibrium fluctuations for this model. Depending on the range of the parameter $\theta$ we obtain processes with various boundary conditions. As a consequence of the previous result together with an application of the matrix ansatz method - which gives us information on the stationary measure for the model - we deduce the non-equilibrium stationary fluctuations. The main ingredient to prove these results is the derivation of precise bounds on the two-point space-time correlation functions.
SRQW02 22nd October 2018
16:00 to 17:00
Manfred Salmhofer Functional Integrals for Bose-Fermi Systems
SRQW02 23rd October 2018
09:00 to 10:00
Giuseppe Da Prato BV functions in separable Hilbert spaces
A probabily m non necessarily Gaussian is given in a separable Hilbert space. We present necessary and sufficient conditions for a function u has a finite total variation with respect to m. Several examples of set of finite perimeters are presented.
SRQW02 23rd October 2018
10:00 to 11:00
Marcello Porta Edge universality in interacting topological insulators
In the last few years there has been important progress on the rigorous understanding of the stability of gapped topological phases for interacting condensed matter systems. Most of the available results deal with bulk transport, for systems with no boundaries. In this talk, I will consider interacting 2d topological insulators on the cylinder. According to the bulk-edge duality, one expects robust gapless edge modes to appear. By now, this has been rigorously understood for a wide class of noninteracting topological insulators; the main limitation of all existing proofs is that they do not extend to interacting systems. In this talk I will discuss the bulk-edge duality for a class of interacting 2d topological insulators, including the Haldane-Hubbard model and the Kane-Mele-Hubbard model. Our theorems give a precise characterization of edge transport: besides the bulk-edge duality, the interacting edge modes satisfy the Haldane relations, connecting the velocities of the edge currents, the edge Drude weights and the edge susceptibilities. The proofs are based on rigorous renormalization group, with key nonperturbative inputs coming from the combination of lattice and emergent Ward identities. Based on joint works with G. Antinucci (Zurich) and V. Mastropietro (Milan).
SRQW02 23rd October 2018
11:30 to 12:30
Slava Rychkov Walking, Weakly First-Order Phase Transitions, and Complex CFTs
Teaser: Most people have heard that the 2d Potts model with Q=5 states has a first order phase transition, but not everyone knows that the correlation length at this phase transition is 2500 lattice spacings. This is going to be a nonrigorous physics talk. We will give an introduction to "walking RG" behavior in gauge theories and connect it to Type II weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two phenomena both imply approximate scale invariance in a range of energies and have the same RG interpretation: a flow passing between pairs of fixed point at complex coupling, dubbed "complex CFTs". Observables of the real walking theory are approximately computable by perturbing the complex CFTs. The general mechanism will be illustrated by a specific and computable example: the two-dimensional Q-state Potts model with Q > 4. Based on http://arxiv.org/abs/1807.11512 and http://arxiv.org/abs/1808.04380
SRQW02 23rd October 2018
14:00 to 15:00
Seiichiro Kusuoka Invariant measure and flow associated to the Phi4-quantum field model on the three-dimensional torus
We consider the invariant measure and flow of the Phi4-model on the three-dimensional torus, which appears in the quantum field theory. By virtue of Hairer's breakthrough, such a nonlinear stochastic partial differential equation became solvable and is studied as a hot topic. In the talk, we apply the paracontrolled calculus and directly construct the global solution and the invariant measure by using the invariant measures of approximation equations and showing the tightness of associated processes. This is a joint work with Sergio Albeverio.
SRQW02 23rd October 2018
15:00 to 16:00
Martin Lohmann The critical behavior of $\phi^4_4$
We discuss the approach to the critical point of the $\phi^4$ model in 4 dimensions. One of the major successes of the renormalization group technique has been to explain why this model features logarithmic corrections to the scaling predictions for the blow up of thermodynamic quantities. We review the strategy of the proof in the "symmetric regime" with zero external magnetic field, in which case this is a classic result. We then present the proof of logarithmic corrections to the magnetization as the magnetic field tends to zero. Despite being a central aspect of the model, these have been an open problem until now, probably because technical complications where expected due to the broken symmetry. We have found these concerns to be unfounded, and our proof only needs a single cluster expansion on top of the classic RG construction for the critical point.
SRQW02 24th October 2018
09:00 to 10:00
Stefan Hollands Perturbative QFT in D = 4
Non-abelian Yang-Mills theories are the key building blocks of the standard model of particle physics. Their renormalization, even at the perturbative level, is a difficult problem because it must be shown that -- and in precisely what sense -- there exists a renormalization scheme preserving local gauge invariance.In this talk, I outline solutions to this problem (a) in the context of curved Lorentzian spacetimes and (b) within the context of flat Euclidean space. The methods presented are rather different, in that the first is based on a generalization of the Epstein-Glaser method -- also called "causal perturbation theory", while the second is based on the so called "flow equation method".The talk will be introductory in nature.
SRQW02 24th October 2018
10:00 to 11:00
Kasia Rejzner Renormalized quantum BV operator and observables in gauge theories and gravity
In this talk I will give an overview of the BV quantization, which is a universal framework for constructing models in perturbative QFT (including gauge theories and effective quantum gravity). Using the version of this framework developed by Fredenhagen and myself, one can construct local nets of observable algebras satisfying Haag-Kastler axioms, in the sense of formal power series in h-bar. The crucial role is played by the renormalized quantum BV operator, which is defined abstractly, without the explicit use of the BRST charge.
SRQW02 24th October 2018
11:30 to 12:30
Martin Hairer The RG landscape in 1+1 dimensions
This is joint work with Giuseppe Cannizzaro.
SRQW02 25th October 2018
09:00 to 10:00
Ajay Chandra Renormalisation in Regularity Structures: Part I
The inception of regularity structures provided a robust deterministic theory that generalized the notion of “Taylor expansion" and classical notions of regularity in a way flexible enough to encode renormalisation - this led to rapid development in the local existence theory for singular stochastic SPDE. In the years that followed the framework for implementing renormalisation in regularity structures has become much more robust. I will describe these developments with an emphasis on how the stochastic estimates needed in regularity structures can be obtained by using methods from multiscale perturbation theory with a twist.
SRQW02 25th October 2018
10:00 to 11:00
Jeremie Unterberger The scaling limit of the KPZ equation in space dimension 3 and higher
We study in the present article the Kardar-Parisi-Zhang (KPZ) equation $$\partial_t h(t,x)=\nu\Del h(t,x)+\lambda |\nabla h(t,x)|^2 +\sqrt{D}\, \eta(t,x), \qquad (t,x)\in{\mathbb{R}}_+\times{\mathbb{R}}^d$$ in $d\ge 3$ dimensions in the perturbative regime, i.e. for $\lambda>0$ small enough and a smooth, bounded, integrable initial condition $h_0=h(t=0,\cdot)$. The forcing term $\eta$ in the right-hand side is a regularized space-time white noise. The exponential of $h$ -- its so-called Cole-Hopf transform -- is known to satisfy a linear PDE with multiplicative noise. We prove a large-scale diffusive limit for the solution, in particular a time-integrated heat-kernel behavior for the covariance in a parabolic scaling. The proof is based on a rigorous implementation of K. Wilson's renormalization group scheme. A double cluster/momentum-decoupling expansion allows for perturbative estimates of the bare resolvent of the Cole-Hopf linear PDE in the small-field region where the noise is not too large, following the broad lines of Iagolnitzer-Magnen. Standard large deviation estimates for $\eta$ make it possible to extend the above estimates to the large-field region. Finally, we show, by resumming all the by-products of the expansion, that the solution $h$ may be written in the large-scale limit (after a suitable Galilei transformation) as a small perturbation of the solution of the underlying linear Edwards-Wilkinson model ($\lambda=0$) with renormalized coefficients $\nu_{eff}=\nu+O(\lambda^2),D_{eff}=D+O(\lambda^2)$. This is joint work with J. Magnen.
SRQW02 25th October 2018
11:30 to 12:30
Franco Flandoli A scaling limit from Euler to Navier-Stokes equations with random perturbation
In the past years there has been intense research on Euler equations with multiplicative transport type noise and Navier-Stokes equations with additive noise. Each model has its own motivations but apparently there is no link between them. We show that a special scaling limit of the stochastic Euler equations leads to the stochastic Navier-Stokes equations. Remarkable is the difference of the noises. And the inversion with respect to usual paradigms which consider Euler equations as limit of Navier-Stokes equations in special regimes. This is a joint work with Dejun Luo, Academy of Sciences, Beijing.
SRQW02 25th October 2018
14:00 to 15:00
Martina Hofmanova A PDE construction of the Euclidean $\Phi^4_3$ quantum field theory
We present a self-contained construction of the Euclidean $\Phi^4$ quantum field theory on $\mathbb{R}^3$ based on PDE arguments. More precisely, we consider an approximation of the stochastic quantization equation on $\mathbb{R}^3$ defined on a periodic lattice of mesh size $\varepsilon$ and side length $M$. We introduce an energy method and prove tightness of the corresponding Gibbs measures as $\varepsilon \rightarrow 0$, $M \rightarrow \infty$. We show that every limit point satisfies reflection positivity, translation invariance and nontriviality (i.e. non-Gaussianity). Our argument applies to arbitrary positive coupling constant and also to multicomponent models with $O(N)$ symmetry. Joint work with Massimiliano Gubinelli.
SRQW02 25th October 2018
15:00 to 16:00
Bertrand Duplantier CLE Nesting and Liouville Quantum Gravity
We describe recent advances in the study of Schramm-Loewner Evolution (SLE), a canonical model of non-crossing random paths in the plane, and of Liouville Quantum Gravity (LQG), a canonical model of random surfaces in 2D quantum gravity. The latter is expected to be the universal, conformally invariant, continuum limit of random planar maps, as weighted by critical statistical models. SLE multifractal spectra have natural analogues on random planar maps and in LQG. An example is extreme nesting in the Conformal Loop Ensemble (CLE), as derived by Miller, Watson and Wilson, and nesting in the O(n) loop model on a random planar map, as derived recently via combinatorial methods. Their respective large deviations functions are shown to be conjugate of each other, via a continuous KPZ transform inherent to LQG. Joint work with Gaetan Borot and Jérémie Bouttier.
SRQW02 26th October 2018
09:00 to 10:00
Thierry Bodineau Spectral gap for Glauber dynamics of hierarchical spin models
We will present a renormalisation group approach to estimate the decay of the spectral gap of hierarchical models. In particular, we will consider a hierarchical version of the 4-dimensional $\Phi_4$ model at the critical point and its approach from the high temperature side, as well as a hierarchical 2-dimensional Sine-Gordon model. For these models, we show that the spectral gap decays polynomially like the spectral gap of the dynamics of a free field. This is a joint work with Roland Bauerschmidt.
SRQW02 26th October 2018
10:00 to 11:00
Fabien Vignes-Tourneret Constructive Tensor Field Theory through an example
In the last ten years, a new approach to quantum gravity has emerged. Called Tensor Field Theory, it generalizes random matrix models in a straightforward way. This talk will be the occasion of recalling the main motivations for such field theories and to present the state-of-the-art of their constructive study. This is joint work with Vincent Rivasseau.
SRQW02 26th October 2018
11:30 to 12:30
Yvain Bruned Renormalisation in Regularity Structures: Part 2
The amount of computation for solving some singular SPDEs via Regularity Structures is huge and requires a good algebraic framework. In this talk, we will present the main ideas which allow us to automatize the renormalisation of these singular SPDEs and to get some symmetry properties of the solution.
SRQW02 26th October 2018
13:30 to 14:30
Margherita Disertori Supersymmetry and Ward identities: an alternative approach to renormalization.
joint work with T.Spencer and M.Zirnbauer
SRQW02 26th October 2018
14:30 to 15:30
John Imbrie Feshbach-Schur RG for the Anderson Model
Consider the localization problem for the Anderson model of a quantum particle moving in a random potential. We develop a renormalization-group framework based on a sequence of Feshbach-Schur maps. Each map produces an effective Hamiltonian on a lower-dimensional space by localizing modes in space and in energy. Randomness in ever-larger neighborhoods produces nontrivial eigenvalue movement and separates eigenvalues, making the next step of the RG possible. We discuss a particularly challenging case where the disorder has a discrete distribution.
SRQ 29th October 2018
11:00 to 12:30
Milton Jara Non-equilibrium fluctuations of interacting particle systems, lecture 1
I will present new entropy methods developed in   collaboration with Patrícia Gonçalves and Otávio Menezes (IST, Lisbon)   in order to study the large-scale behaviour of interacting particle   systems. The first lecture will introduce Yau's relative entropy   method and a new variational formula for exponential moments of   observables in the context of general Markov processes, and it could   be of independent interest. In the second and third lectures I will   explain how to derive large-scale limits of non-equilibrium   interacting particle systems out of these ideas.
SRQ 31st October 2018
15:00 to 16:30
Milton Jara Non-equilibrium fluctuations of interacting particle systems, lecture 1
I will present new entropy methods developed in   collaboration with Patrícia Gonçalves and Otávio Menezes (IST, Lisbon)   in order to study the large-scale behaviour of interacting particle   systems. The first lecture will introduce Yau's relative entropy   method and a new variational formula for exponential moments of   observables in the context of general Markov processes, and it could   be of independent interest. In the second and third lectures I will   explain how to derive large-scale limits of non-equilibrium   interacting particle systems out of these ideas.
SRQ 1st November 2018
11:00 to 12:30
Milton Jara Non-equilibrium fluctuations of interacting particle systems, lecture 3
I will present new entropy methods developed in   collaboration with Patrícia Gonçalves and Otávio Menezes (IST, Lisbon)   in order to study the large-scale behaviour of interacting particle   systems. The first lecture will introduce Yau's relative entropy   method and a new variational formula for exponential moments of   observables in the context of general Markov processes, and it could   be of independent interest. In the second and third lectures I will   explain how to derive large-scale limits of non-equilibrium   interacting particle systems out of these ideas.
SRQ 2nd November 2018
11:00 to 12:30
Giovanni Jona-Lasinio Towards a non-equilibrium thermodynamics: the role of large fluctuations
In non-equilibrium there is an enormous variety of phenomena so we cannot  hope to formulate a unique theory having a generality comparable to  classical thermodynamics. We have to restrict to subclasses of problems. Diffusion is a phenomenon almost ubiquitous and in recent years  considerable progress in its understanding has been obtained. One  difficulty is to define suitable thermodynamic functionals in far from  equilibrium situations. Large fluctuations have offered a way out as large  deviation rates provide genuine thermodynamic functionals whose singularities describe new phase transitions some of which can take place  only out of equilibrium.
SRQ 5th November 2018
10:00 to 11:30
Giovanni Jona-Lasinio Towards a non-equilibrium thermodynamics: the role of large fluctuations
In non-equilibrium there is an enormous variety of phenomena so we cannot hope to formulate a unique theory having a generality comparable to classical thermodynamics. We have to restrict to subclasses of problems. Diffusion is a phenomenon almost ubiquitous and in recent years considerable progress in its understanding has been obtained. One  difficulty is to define suitable thermodynamic functionals in far from equilibrium situations. Large fluctuations have offered a way out as large deviation rates provide genuine thermodynamic functionals whose singularities describe new phase transitions some of which can take place only out of equilibrium.
SRQ 7th November 2018
15:00 to 15:30
Augustin Moinat Local bounds for the dynamic $\Phi^4_3$ model
We prove an a priori bound for solutions of the dynamic $\Phi^4_3$ equation.  This bound provides a control on solutions on a compact space-time set only in terms of the realisation of the noise on an enlargement of this set, and it does not depend on any choice of space-time boundary conditions. We treat the  large and small scale behaviour of solutions with completely different arguments. For small scales we use bounds very much akin to those presented in Hairer's theory of regularity structures. For large scales we use a PDE argument based on the maximum principle. Both regimes are connected by a solution-dependent regularisation procedure. The fact that our bounds do not depend on space-time boundary conditions makes them useful for the analysis of large scale properties of solutions. They can for example  be used  in a compactness argument to construct solutions on the full space and their invariant measures.
SRQ 7th November 2018
15:30 to 16:00
Susanne Hilger Renormalisation Group Analysis of a gradient model with nonconvex interaction
We study the finite volume Gibbs measure of a continuous Ising model on an integer lattice with non-convex interaction. S. Adams, R. Kotecky and S. Müller performed a Renormalisation Group Analysis to prove the strict convexity of the free energy. We extend their result to prove decay of covariances.
SRQ 7th November 2018
16:00 to 16:30
Henri Elad Altman Bessel S(P)DEs : a story of renormalization
Bessel processes are a very well-known family of diffusions, the dynamics of which involves a subtle renormalization procedure. More recently a family of SPDEs related to Bessel processes has been introduced, the dynamics of which involve similar, albeit more acute renormalizations. In my talk I shall introduce these processes and explain the nice structure underlying these renormalizations. This is based on joint work with Lorenzo Zambotti.
SRQ 9th November 2018
11:00 to 12:30
David Brydges The Higgs Mechanism
After recalling definitions for lattice gauge theory I will specialise to abelian theories and give a review  of  equivalences between different models and some of the simpler results that together are called "the Higgs Mechanism".
SRQ 12th November 2018
11:00 to 12:30
Pronob Mitter Introduction to the Renormalisation Group
In  these lectures I will introduce  and explore properties  of the Renormalisation  Group (RG) both in its discrete and continuous forms. Topics  to be discussed include  multi scale  expansions, the RG, Gaussian fixed points, Wick products from the RG point of view, ultraviolet cutoff removal, flow equations and perturbative flows, trivial and non-trivial fixed points, and  critical field theories. Time  permitting, I will discuss a rigorous application. These lectures are supposed to be elementary.
SRQ 14th November 2018
15:00 to 16:30
Pronob Mitter Introduction to the Renormalisation Group
In  these lectures I will introduce  and explore properties  of the Renormalisation  Group (RG) both in its discrete and continuous forms. Topics  to be discussed include  multi scale  expansions, the RG, Gaussian fixed points, Wick products from the RG point of view, ultraviolet cutoff removal, flow equations and perturbative flows, trivial and non-trivial fixed points, and  critical field theories. Time  permitting, I will discuss a rigorous application. These lectures are supposed to be elementary.
SRQ 16th November 2018
11:00 to 12:30
Pronob Mitter Introduction to the Renormalisation Group
In  these lectures I will introduce  and explore properties  of the Renormalisation  Group (RG) both in its discrete and continuous forms. Topics  to be discussed include  multi scale  expansions, the RG, Gaussian fixed points, Wick products from the RG point of view, ultraviolet cutoff removal, flow equations and perturbative flows, trivial and non-trivial fixed points, and  critical field theories. Time  permitting, I will discuss a rigorous application. These lectures are supposed to be elementary.
SRQ 19th November 2018
11:00 to 12:30
Massimiliano Gubinelli A variational approach to Phi^4_3
I will introduce a variational description of perturbations of Gaussian measures. In the case of the $\Phi^4_3$ measure I will explain how to use the variational formula to prove ultraviolet stability in finite volume and discuss the possibility of an explicit formula for the Laplace transform of the measure after UV cutoff removal. I will describe how the control problem is (heuristically, at the moment) linked with Wilson’s flow equation for the effective potential. This talk is based on joint work with N. Barashkov (Bonn).
SRQ 21st November 2018
15:00 to 16:30
Thierry Levy The partition function of the 2-dimensional Yang—Mills model
The partition function of the 2d Yang—Mills model is the natural mass of the Yang—Mills measure, and there is at least one reasonable way of defining it. For each oriented compact surface, it is a function on the set of all possible boundary conditions for the Yang—Mills field, which in the 2d case is finite-dimensional. This function plays for the 2d Yang—Mills field the role usually played by the transition kernel of a Markov process. The case of the sphere is unique among closed oriented surfaces in that, in the large N limit, the U(N) Yang—Mills model exhibits a third order phase transition, the Douglas—Kazakov phase transition, with respect to the total area of the sphere. This transition can be understood in terms of non-intersecting Brownian motions on a circle, as Karl Liechty and Dong Wang did, or in terms of a discrete Coulomb gas, as we did with Mylène Maïda.
SRQ 23rd November 2018
11:00 to 12:30
Ilya Chevyrev Yang-Mills measure on the two-dimensional torus as a random distribution
The Yang-Mills measure on a two-dimensional compact manifold has been completely constructed as a stochastic process indexed by loops. In this talk, I will present a construction of the Yang-Mills measure on the two-dimensional torus as a random distribution. More specifically, I will introduce a space of distributional one-forms for which holonomies (i.e. Wilson loop observables) along axis paths are well-defined, and show that there exists a random variable in this space which induces the Yang-Mills holonomies. An important feature of this space of one-forms is its embedding into Hölder-Besov spaces, which commonly appear in the analysis of stochastic PDEs, with the small scale regularity expected from perturbation theory. The construction is based on a Landau-type gauge applied to lattice approximations.
SRQ 26th November 2018
11:00 to 12:30
Mircea Petrache Large-N asymptotics of energy-minimizing measures on N-point configurations
If N points interact by Coulomb 2-point repulsion and under a "confining" potential V(x)=|x|^2, as N goes to infinity they spread uniformly in a ball. This is a typical problem about "energy-minimizing configurations".  What is the simplest problem that we get if we move from variational problems on N-point configurations, to variational problems on measures on N-point configurations? In that case there is a more natural replacement of the "confinement", previously played by V(x): it is to just "fix the 1-point marginal" of our measure on configurations. We obtain a generalization of optimal transport, for N-marginals instead of the usual 2-marginals case.   In my talk I'll describe the above two types of large-N asymptotics problems in more detail, I'll overview the techniques that we know, and I'll mention some parts of this subject that we currently don't understand.
SRQ 28th November 2018
15:00 to 16:00
Benjamin Gess Generation of random dynamical systems for SPDE with nonlinear noise.
In this talk we will revisit the problem of generation of random dynamical systems by
solutions to SPDE. Despite being at the heart of a dynamical system approach to
stochastic dynamics in infinite dimensions, most known results are restricted
to SPDE driven by affine linear noise, which can be treated via transformation
arguments. In contrast, in this talk we will address instances of SPDE with
nonlinear noise, with particular emphasis on porous media equations driven by
conservative noise.
SRQ 28th November 2018
16:00 to 16:30
Trishen Gunaratnam Quasi-invariant Gaussian Measures for the 3D Nonlinear Wave Equation
We show that a class of Gaussian measures, supported on
Sobolev spaces

of high regularity, are quasi-invariant under the dynamics
of the

cubic defocusing wave equation in 3 dimensions. This is
joint work

with Tadahiro Oh, Nikolay Tzvetkov and Hendrik
Weber.
SRQ 30th November 2018
11:00 to 12:30
Sandra Cerrai Large time behavior of infinite dimensional systems under the Smoluchowski-Kramers approximation
I will discuss the validity of the so-called Smoluchowski-Kramers approximation for systems with an infinite number of degrees of freedom in a finite time. Then, I will investigate the validity of such approximation for large time. In particular, I will address the problem of the convergence, in the small mass limit, of statistically invariant states for a class of semi-linear damped wave equations, perturbed by an additive Gaussian noise, with quite general nonlinearities. More precisely, I will show how the first marginals of any sequence of invariant measures for the stochastic wave equation converge in a suitable Wasserstein metric to the unique invariant measure of the limiting stochastic semi-linear parabolic equation obtained in the Smoluchowski-Kramers approximation.
SRQ 3rd December 2018
11:00 to 12:30
Tyler Helmuth Isomorphism theorems, random walks, and spin systems.
The celebrated BFS-Dynkin isomorphism theorem relates the local time of a random walk to the square of the Gaussian free field. I will discuss one way to see this connection, and also a similar relation between the local time of the vertex-reinforced jump process and hyperbolic spin models. If time permits I will also discuss an application: proving that the vertex-reinforced jump process is always recurrent in two dimensions.

SRQ 5th December 2018
15:00 to 16:30
Ajay Chandra Stochastic quantization of Yang Mills
I will discuss joint work in preparation with Martin Hairer and Hao Shen on the construction of gauge covariant dynamics on non-abelian gauge fields.

SRQ 7th December 2018
11:00 to 12:30
Roman Kotecky An abstract framework for a non-perturbative renormalisation
I will discuss a possibility of formulating a renormalisation theory without relying on a perturbative input.

SRQW03 10th December 2018
10:00 to 11:00
Martin Hairer tba
SRQW03 10th December 2018
11:30 to 12:30
Benjamin Schlein Bogoliubov Excitations of dilute Bose-Einstein Condensates
We consider systems of N bosons confined in a box with volume one and interacting through a potential with
short scattering length of the order 1/N (Gross-Pitaevskii regime). We determine the low-energy spectrum, i.e. the
ground state energy and low-lying excitations, up to errors that vanishes in the limit of large N, confirming
the validity of Bogoliubov’s predictions. This talk is based on joint work with C. Boccato, C. Brennecke, S. Cenatiempo.
SRQW03 10th December 2018
13:30 to 14:30
Panagiotis Souganidis New regularity results and long time behavior of pathwise (stochastic) Hamilton-Jacobi equations
I will discuss two new regularity results (regularizing effect and propagation of regularity) for viscosity solutions of uniformly convex Hamilton-Jacobi equations. In turn, the new estimates yield new intermittent stochastic regularization for pathwise (stochastic) viscosity solutions of Hamilton-Jacobi equations with uniformly convex Hamiltonians and rough multiplicative time dependence. The intermittent regularity estimates are then used to study the long time behavior of the pathwise (stochastic) viscosity solutions of convex Hamilton-Jacobi equations. This is joint work with P. L. Lions.

--
SRQW03 10th December 2018
14:30 to 15:30
Christophe Garban Quantum field theory and SPDEs under the light of near-criticality and noise sensitivity
Based on a joint work with Martin Hairer and Antti Kupiainen.
SRQW03 10th December 2018
16:00 to 17:00
Ivan Corwin Dynamic ASEP
The long-time behavior of the standard ASEP height function relates to the KPZ fixed point and the KPZ equation. In this talk we consider "dynamic" variants of ASEP in which the rates of increase / decrease for the height function depend on the height in such a way as to have height reversion to a preferred level. Very little is known about the long-time behavior of this type of process. We prove an SPDE limit of the model under very weakly asymmetric scaling. Along the way, we also touch on dynamic ASEP's Markov duality and relation to orthogonal polynomials.

This talk relates to a joint work with Alexei Borodin from last year (on the duality) and a new joint work with Konstantin Matetski and Promit Ghosal (on the SPDE limit).
SRQW03 11th December 2018
09:00 to 10:00
Jeremy Quastel The KPZ fixed point - 1
A determinantal formula for the transition probabilities of TASEP with right finite initial data allows us to pass to the limit and obtain the invariant Markov process at the centre of  the KPZ universality class.
SRQW03 11th December 2018
10:00 to 11:00
Pierre Le Doussal Large devations for the KPZ equation
SRQW03 11th December 2018
11:30 to 12:30
Yan Fyodorov Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities
We study one-dimensional decaying Burgers turbulence with the covariance of initial profile
of Gaussian-distributed velocities decaying as inverse square of the distance. Combining the
heuristic replica trick of statistical mechanics with insights from the random matrix theory we
reveal a freezing phase transition with decreasing viscosity. In the low-viscosity phase the
one-point probability density of velocities becomes non-Gaussian reflecting a spontaneous
one step replica symmetry breaking in the associated statistical mechanics problem. We
obtain the low orders velocity cumulants analytically which favourably agree with numerical
simulation. The presentation will be based on a joint work with P. Le Doussal and A. Rosso.
SRQW03 11th December 2018
13:30 to 14:30
Eveliina Peltola Crossing Probabilities of Multiple Ising Interfaces
In this talk, I discuss crossing probabilities of multiple interfaces in the critical Ising model with alternating boundary conditions. In the scaling limit, they are conformally invariant expressions given by so-called pure partition functions of multiple SLE(kappa) with kappa=3. I also describe analogous results for critical percolation and the Gaussian free field. Joint work with Hao Wu (Yau Mathematical Sciences Center, Tsinghua University)
SRQW03 11th December 2018
14:30 to 15:30
Remi Rhodes Sine-Gordon model revisited (again)
In this talk, I will discuss the Sine-Gordon model and its relation with the 2D neutral Coulomb gas. This is a model of electric charges with positive/negative signs interacting through the Coulomb potential. In the case when particles are confined to the boundary of a 2D domain (called boundary Sine-Gordon model) I will present a short proof that allows us to completely solve the ultraviolet renormalization of this model, including correlation functions. The method is purely probabilistic and relies on concentration methods for martingales.
SRQW03 12th December 2018
09:00 to 10:00
Hugh Osborn Seeking fixed points
Fixed points are crucial in understanding the RG flow of quantum field theories. The conformal bootstrap has proved a wonderful tool in determining the properties of CFTs at fixed points but tends to require guidance in terms of what symmetries to impose and what is the spectrum of relevant operators. Here I review what can be said in general by using the time honoured epsilon expansion. Although qualitatively this is not nowadays the most efficient method it provides qualitative information about possible fixed points. Finding fixed points which cannot be linked to the epsilon expansion could provide a clue to non Lagrangian theories.
SRQW03 12th December 2018
10:00 to 11:00
Alessandro Giuliani Scaling limit and universal finite size corrections in 2D interacting Ising models
In the last few years, the methods of constructive fermionic Renormalization Group have successfully been applied to the study of the scaling limit of several 2D statistical mechanics models at the critical point, including the 2D Ising with finite range interactions. Different instances of universality have been proved in these context, including the facts that the scaling limit of the bulk energy-energy correlations and the central charge (computed from the leading sub-leading contribution to the critical free energy) are independent of the interaction. More recently, we extended our constructive RG method to the study of more subtle finite size observables: I will report ongoing progress on the scaling limit of the energy correlations in finite domains, and on the computation of the modular-invariant function associated with the sub-leading contribution to the critical free energy. Our methods may be relevant in a more general context for the study of the flow of the effective boundary conditions in critical models in a finite domain.
Based on joint work with V. Mastropietro, R. Greenblatt and G. Antinucci.
SRQW03 12th December 2018
11:30 to 12:30
Jeremy Quastel The KPZ fixed point - 2
A determinantal formula for the transition probabilities of TASEP with right finite initial data allows us to pass to the limit and obtain the invariant Markov process at the centre of the KPZ universality class.
SRQW03 13th December 2018
09:00 to 10:00
Hendrik Weber Space-time localisation for the dynamic $\Phi^4_3$ model
We prove an a priori bound for solutions of the dynamic $\Phi^4_3$ equation. This bound provides a control on solutions on a compact space-time set only in terms of the realisation of the noise on an enlargement of this set, and it does not depend on any choice of space-time boundary conditions.
We treat the  large and small scale behaviour of solutions with completely different arguments.
For small scales we use bounds akin to those presented in Hairer's theory of regularity structures. For large scales we use a PDE argument based on the maximum principle. Both regimes are connected by a solution-dependent regularisation procedure.
The fact that our bounds do not depend on space-time boundary conditions makes them useful for the analysis of large scale properties of solutions. They can for example be used  in a compactness argument to construct solutions on the full space and their invariant measures.

Joint work with A. Moinat.
SRQW03 13th December 2018
10:00 to 11:00
Cedric Bernardin Hydrodynamic limit for a disordered harmonic chain
We consider a one-dimensional unpinned chain of harmonic oscillators with random masses. We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum and energy converge to the solution of the Euler equations. Anderson localization decouples the mechanical modes from the thermal modes, allowing the closure of the energy conservation equation even out of thermal equilibrium. This example shows that the derivation of Euler equations rests primarily on scales separation and not on ergodicity.

Joint with F. Huveneers and S. Olla
SRQW03 13th December 2018
11:30 to 12:30
Weijun Xu On mass-critical stochastic nonlinear Schrodinger equation
We report some recent joint works with Chenjie Fan on construction of global solutions to defocusing mass-critical stochastic nonlinear Schrodinger equation.
SRQW03 13th December 2018
13:30 to 14:30
Franco Flandoli Remarks on 2D inverse cascade turbulence
Recently the interest in certain invariant measures of 2D Euler equations was renewed, motivated for instance by questions of existence for almost every initial condition, similarly to the case of dispersive equations where probability on initial conditions allowed very succesful progresses.
Obviusly invariant measures of 2D Euler equations are primarily of interest for turbulence but those known are not realistic from several viewpoints, beside some element of great interest.
We discuss this issue and show modifications, unfortunately mostly heuristic, that would give much better results for turbulence.
SRQW03 13th December 2018
14:30 to 15:30
Hao Shen SPDE limits of six-vertex model
The theme of the talk is deriving stochastic PDE limits as description of large-scale fluctuations of the six-vertex (6V) model in various regimes.
We will consider two types of 6V model: stochastic 6V and symmetric 6V.
For stochastic 6V in a weakly asymmetric regime, under parabolic scaling the height function fluctuation converges to solution of KPZ equation after suitable re-centering and tilting. For symmetric 6V, in a regime where parameters are tuned into the ferroelectric/disordered phase critical point, under parabolic scaling the line density fluctuations in a one-parameter family of Gibbs states converge to solution of stationary stochastic Burgers.
Again for stochastic 6V, in a regime where the corner-shape vertex weights are tuned to zero, under hyperbolic scaling, the height fluctuation converges to the solution of stochastic telegraph equation.
We will discuss challenges and new techniques in the proofs.
Based on a joint work with Ivan Corwin, Promit Ghosal and Li-Cheng Tsai, and a joint work with Li-Cheng Tsai.
SRQW03 14th December 2018
09:00 to 10:00
Herbert Spohn Generalized hydrodynamics and the classical Toda chain
In the context of integrable quantum many-body systems, much progress has been achieved in
deriving and analysing the infinite set of coupled local conservation laws constituting
"generalized hydrodynamics". In my presentation I will outline the scheme for the
classical Toda chain exploring unexpected connections to random matrix theory.

SRQW03 14th December 2018
10:00 to 11:00
Claudio Landim Potential theory for nonreversible dynamics and corrections to the hydrodynamical limit
We present in this talk two results. First, variational formulas for the capacity of non-reversible Markovian
dynamics and some applications. Then we derive the viscous Burger's equation from an interacting particle system
as a correction to the hydrodynamic limit.
SRQW03 14th December 2018
11:30 to 12:30
Makiko Sasada Some generalization of Pitman’s transform and invariant measures for discrete integrable systems
In this talk, I will introduce some generalization of Pitman’s transform and show that the dynamics of several discrete integrable systems, such as the discrete Korteweg-de Vries equation, the ultra-discrete Korteweg-de Vries equation, the ultra-discrete Toda equation, the box-ball system, are given by them. We apply this observation to define infinite space versions of these models and study their invariant measures using the generalized Pitman’s transform. This talk is based on a joint work with David Croydon, Tsuyoshi Kato and Satoshi Tsujimoto.
SRQW03 14th December 2018
13:30 to 14:30
Ian Melbourne Deterministic homogenization with Levy process limits
We consider homogenization of deterministic fast-slow systems in the situation where the limiting SDE is driven by a stable Levy process. This is joint work with Chevyrev, Friz and Korepanov.
SRQW03 14th December 2018
14:30 to 15:30
Gianbattista Giacomin Two dimensional Ising model with columnar disorder and continuum limit of random matrix products
I will present results taken from a recent work with R. L. Greenblatt and F. Comets on the continuum limit of random matrix products. The focus will be on one of the applications: two dimensional Ising model with columnar disorder. 50 years ago McCoy and Wu pointed out that the free energy density of the two dimensional Ising model (on the square lattice, with nearest neighbor interactions) can be written in terms of the Lyapunov exponent of products of suitable random two by two matrices. Moreover they extracted from this remarkable formula a number of (even more remarkable) conclusions. I will present their approach and explain how some of the steps can be made mathematically rigorous. I will also explain what is missing to get to the McCoy and Wu conclusions.
SRQ 17th December 2018
11:00 to 12:30
Massimiliano Gubinelli Elliptic stochastic quantisation
I will describe the relation between elliptic SPDEs and Gibbs measures given by the dimensional reduction mechanism discovered by Parisi and Sourlas in ’79. In collaboration with S. Albeverio and F. C. De Vecchi we recently gave a rigorous proof of this relation in some particular (low dimensional) case. The proof goes via a supersymmetric representation of the law of the SPDE.