Videos and presentation materials from other INI events are also available.
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/coursematerial/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 YangMills
Coauthors: 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 minicourse 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 phi43 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 phi43 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 phi43 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 phi43 model''.


SRQW01 
4th September 2018 10:00 to 11:00 
Lorenzo Zambotti 
Renormalisation in regularity structures  part 2
This should be a minicourse 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 phi43 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 phi43 model''.


SRQW01 
5th September 2018 10:00 to 11:00 
Lorenzo Zambotti 
Renormalisation in regularity structures  part 3
This should be a minicourse 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 threedimensional 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 selfavoiding 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 longrange models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt.


SRQW01 
6th September 2018 10:00 to 11:00 
Nicolas Perkowski 
Infinitedimensional paracontrolled distributions: the Burgers generator
Regularity structures, paracontrolled distributions and all that provide pathwise, deterministic tools to solve and study singular stochastic PDEs over finitedimensional spaces. From a probabilistic point of view we would also like to understand the associated Kolmogorov backward equations, which can be interpreted as infinitedimensional 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 wellposedness of "energy solutions", without using the ColeHopf 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 selfavoiding 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 longrange 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 phi43 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 phi43 model''.


SRQW01 
6th September 2018 14:30 to 15:30 
Lorenzo Zambotti 
Renormalisation in regularity structures  part 4
This should be a minicourse 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 BrascampLieb inequality, for the measure recursively in terms of spectral gap or BrascampLieb 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 SineGordon and the Discrete Gaussian models in the rough phase (KosterlitzThouless 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.
Coauthor: 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 selfavoiding 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 longrange 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 selfavoiding 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 longrange 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
Coauthor: 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
FroehlichSimonSpencer 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 YangMills: a review of nogo 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  2dimensional YangMills theory and the MakeenkoMigdal equations (I)  
SRQ 
3rd October 2018 15:30 to 16:30 
Thierry Levy  2dimensional YangMills theory and the MakeenkoMigdal 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 nonintegrable perturbations of the classical dimer model
on the square lattice. In the integrable situation, the model is freefermionic
and the largescale fluctuations of its height function tend to a
twodimensional massless Gaussian field (GFF). We prove that convergence to GFF
holds also for sufficiently small nonintegrable perturbations. At the same
time, we show that the dimerdimer correlations exhibit nontrivial 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 noninteracting dimer model: Kasteleyn theory,
thermodynamiclimit,
longdistance asymptotics of correlations, GFF fluctuations.
Fermionic representation of the noninteracting and of the
interacting dimer model.
3. Multiscale analysis of the free propagator, Feynman
diagrams and dimensional
estimates. Determinant expansion.
Nonrenormalized
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. SchwingerDyson
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 nonintegrable perturbations of the classical dimer model
on the square lattice. In the integrable situation, the model is freefermionic
and the largescale fluctuations of its height function tend to a
twodimensional massless Gaussian field (GFF). We prove that convergence to GFF
holds also for sufficiently small nonintegrable perturbations. At the same
time, we show that the dimerdimer correlations exhibit nontrivial 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 noninteracting dimer model: Kasteleyn theory,
thermodynamiclimit,
longdistance asymptotics of correlations, GFF fluctuations.
Fermionic representation of the noninteracting and of the
interacting dimer model.
3. Multiscale analysis of the free propagator, Feynman
diagrams and dimensional
estimates. Determinant expansion.
Nonrenormalized
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. SchwingerDyson
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 nonintegrable perturbations of the classical dimer model
on the square lattice. In the integrable situation, the model is freefermionic
and the largescale fluctuations of its height function tend to a
twodimensional massless Gaussian field (GFF). We prove that convergence to GFF
holds also for sufficiently small nonintegrable perturbations. At the same
time, we show that the dimerdimer correlations exhibit nontrivial 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 noninteracting dimer model: Kasteleyn theory,
thermodynamiclimit,
longdistance asymptotics of correlations, GFF fluctuations.
Fermionic representation of the noninteracting and of the
interacting dimer model.
3. Multiscale analysis of the free propagator, Feynman
diagrams and dimensional
estimates. Determinant expansion.
Nonrenormalized
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. SchwingerDyson
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 nonintegrable perturbations of the classical dimer model
on the square lattice. In the integrable situation, the model is freefermionic
and the largescale fluctuations of its height function tend to a
twodimensional massless Gaussian field (GFF). We prove that convergence to GFF
holds also for sufficiently small nonintegrable perturbations. At the same
time, we show that the dimerdimer correlations exhibit nontrivial 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 noninteracting dimer model: Kasteleyn theory,
thermodynamiclimit,
longdistance asymptotics of correlations, GFF fluctuations.
Fermionic representation of the noninteracting and of the
interacting dimer model.
3. Multiscale analysis of the free propagator, Feynman
diagrams and dimensional
estimates. Determinant expansion.
Nonrenormalized
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. SchwingerDyson
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 nonintegrable perturbations of the classical dimer model
on the square lattice. In the integrable situation, the model is freefermionic
and the largescale fluctuations of its height function tend to a
twodimensional massless Gaussian field (GFF). We prove that convergence to GFF
holds also for sufficiently small nonintegrable perturbations. At the same
time, we show that the dimerdimer correlations exhibit nontrivial 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 noninteracting dimer model: Kasteleyn theory,
thermodynamiclimit,
longdistance asymptotics of correlations, GFF fluctuations.
Fermionic representation of the noninteracting and of the
interacting dimer model.
3. Multiscale analysis of the free propagator, Feynman
diagrams and dimensional
estimates. Determinant expansion.
Nonrenormalized
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. SchwingerDyson
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 nonintegrable perturbations of the classical dimer model
on the square lattice. In the integrable situation, the model is freefermionic
and the largescale fluctuations of its height function tend to a
twodimensional massless Gaussian field (GFF). We prove that convergence to GFF
holds also for sufficiently small nonintegrable perturbations. At the same
time, we show that the dimerdimer correlations exhibit nontrivial 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 noninteracting dimer model: Kasteleyn theory,
thermodynamiclimit,
longdistance asymptotics of correlations, GFF fluctuations.
Fermionic representation of the noninteracting and of the
interacting dimer model.
3. Multiscale analysis of the free propagator, Feynman
diagrams and dimensional
estimates. Determinant expansion.
Nonrenormalized
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. SchwingerDyson
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 JonaLasinio 
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 spinboson model in terms of the propagator generated by a free effective Hamiltonian. Our construction rests on the renormalization group induced by the isospectral FeshbachSchur 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 nonGaussian 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 almostsure 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 
Nonequilibrium 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 nonequilibrium 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 nonequilibrium stationary fluctuations. The main ingredient to prove these results is the derivation of precise bounds on the twopoint spacetime correlation functions.


SRQW02 
22nd October 2018 16:00 to 17:00 
Manfred Salmhofer  Functional Integrals for BoseFermi 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 bulkedge 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 bulkedge duality for a class of interacting 2d topological insulators, including the HaldaneHubbard model and the KaneMeleHubbard model. Our theorems give a precise characterization of edge transport: besides the bulkedge 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 FirstOrder 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 firstorder 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 twodimensional Qstate 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 Phi4quantum field model on the threedimensional torus
We consider the invariant measure and flow of the Phi4model on the threedimensional 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
Nonabelian YangMills 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 EpsteinGlaser 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 HaagKastler axioms, in the sense of formal power series in hbar. 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 KardarParisiZhang (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 righthand side is
a regularized spacetime white noise. The exponential of $h$  its socalled ColeHopf
transform  is known to satisfy a
linear PDE with multiplicative noise.
We prove a largescale diffusive limit for the solution, in particular a
timeintegrated heatkernel 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/momentumdecoupling expansion allows for perturbative
estimates of the bare resolvent of the ColeHopf linear PDE in the smallfield region where the noise is not too large, following the broad lines of IagolnitzerMagnen. Standard large deviation estimates for $\eta$ make it possible to extend the above estimates to the largefield region. Finally,
we show, by resumming all the byproducts of the expansion, that the solution $h$ may be written in the largescale limit (after a suitable Galilei transformation) as a small perturbation of the solution of the underlying linear EdwardsWilkinson 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 NavierStokes equations with random perturbation
In the past years there has been intense research on Euler equations with multiplicative transport type noise and NavierStokes 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 NavierStokes equations. Remarkable is the difference of the noises. And the inversion with
respect to usual paradigms which consider Euler equations as limit of NavierStokes 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 selfcontained 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. nonGaussianity). 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 SchrammLoewner Evolution (SLE), a canonical model of noncrossing 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 4dimensional $\Phi_4$ model at the critical point and its approach from the high temperature side, as well as a hierarchical 2dimensional SineGordon 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 VignesTourneret 
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 stateoftheart 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 
FeshbachSchur 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 renormalizationgroup framework based on a sequence of FeshbachSchur maps. Each map produces an effective Hamiltonian on a lowerdimensional space by localizing modes in space and in energy. Randomness in everlarger 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 
Nonequilibrium 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 largescale 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 largescale limits of nonequilibrium
interacting particle systems out of these ideas.


SRQ 
31st October 2018 15:00 to 16:30 
Milton Jara 
Nonequilibrium 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 largescale 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 largescale limits of nonequilibrium
interacting particle systems out of these ideas.


SRQ 
1st November 2018 11:00 to 12:30 
Milton Jara 
Nonequilibrium 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 largescale 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 largescale limits of nonequilibrium
interacting particle systems out of these ideas.


SRQ 
2nd November 2018 11:00 to 12:30 
Giovanni JonaLasinio 
Towards a nonequilibrium thermodynamics: the role of large fluctuations
In nonequilibrium
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 JonaLasinio 
Towards a nonequilibrium thermodynamics: the role of large fluctuations
In
nonequilibrium 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 spacetime 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 spacetime 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 solutiondependent regularisation procedure.
The fact that our
bounds do not depend on spacetime 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 nonconvex 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 wellknown 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 nontrivial 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 nontrivial 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 nontrivial 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 2dimensional 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
finitedimensional. 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
nonintersecting 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 
YangMills measure on the twodimensional torus as a random distribution
The YangMills measure on a twodimensional
compact manifold has been completely constructed as a stochastic process
indexed by loops. In this talk, I will present a construction of the YangMills
measure on the twodimensional torus as a random distribution. More
specifically, I will introduce a space of distributional oneforms for which
holonomies (i.e. Wilson loop observables) along axis paths are welldefined,
and show that there exists a random variable in this space which induces the
YangMills holonomies. An important feature of this space of oneforms is its
embedding into HölderBesov 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 Landautype gauge applied to lattice
approximations.


SRQ 
26th November 2018 11:00 to 12:30 
Mircea Petrache 
LargeN asymptotics of energyminimizing measures on Npoint configurations
If N points interact by Coulomb 2point 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 "energyminimizing
configurations".
What is the simplest problem that we get if we move
from variational problems on Npoint configurations, to variational problems on
measures on Npoint configurations? In that case there is a more natural
replacement of the "confinement", previously played by V(x): it is to
just "fix the 1point marginal" of our measure on configurations. We
obtain a generalization of optimal transport, for Nmarginals instead of the
usual 2marginals case.
In my talk I'll describe the above two types of
largeN 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 
Quasiinvariant Gaussian Measures for the 3D Nonlinear Wave Equation
We show that a class of Gaussian measures, supported on Sobolev spaces of high regularity, are quasiinvariant 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 SmoluchowskiKramers approximation
I will discuss the validity of the socalled
SmoluchowskiKramers 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 semilinear 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 semilinear parabolic equation obtained in
the SmoluchowskiKramers approximation.


SRQ 
3rd December 2018 11:00 to 12:30 
Tyler Helmuth 
Isomorphism theorems, random walks, and spin systems.
The celebrated
BFSDynkin 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
vertexreinforced jump process and hyperbolic spin models. If time permits I
will also discuss an application: proving that the vertexreinforced 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 nonabelian gauge fields. 

SRQ 
7th December 2018 11:00 to 12:30 
Roman Kotecky 
An abstract framework for a nonperturbative 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 BoseEinstein 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 (GrossPitaevskii regime). We determine the lowenergy spectrum, i.e. the ground state energy and lowlying 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) HamiltonJacobi equations
I will discuss two new regularity results (regularizing effect and propagation of regularity) for viscosity solutions of uniformly convex HamiltonJacobi equations. In turn, the new estimates yield new intermittent stochastic regularization for pathwise (stochastic) viscosity solutions of HamiltonJacobi 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 HamiltonJacobi 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 nearcriticality 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 longtime 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 longtime 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 onedimensional decaying Burgers turbulence with the covariance of initial profile of Gaussiandistributed 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 lowviscosity phase the onepoint probability density of velocities becomes nonGaussian 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 socalled 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 
SineGordon model revisited (again)
In this talk, I will discuss the SineGordon 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 SineGordon 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 energyenergy correlations and the central charge (computed from the leading subleading 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 modularinvariant function associated with the subleading 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 
Spacetime 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 spacetime 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 spacetime 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 solutiondependent regularisation procedure. The fact that our bounds do not depend on spacetime 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 onedimensional 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 masscritical stochastic nonlinear Schrodinger equation
We report some recent joint works with Chenjie Fan on construction of global solutions to defocusing masscritical 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 sixvertex model
The theme of the talk is deriving stochastic PDE limits as description of largescale fluctuations of the sixvertex (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 recentering 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 oneparameter family of Gibbs states converge to solution of stationary stochastic Burgers. Again for stochastic 6V, in a regime where the cornershape 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 LiCheng Tsai, and a joint work with LiCheng 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 manybody 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 nonreversible 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 Kortewegde Vries equation, the ultradiscrete Kortewegde Vries equation, the ultradiscrete Toda equation, the boxball 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 fastslow
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. 