After four successful TMS Seminars related to the theory of rough paths (RPs) with various perspectives, this time, as the title indicates, we wish to invite leading experts working in RPs theory, quantum field theory (QFT), and renormalization theory, to discuss recent trends and novel results, and to encourage collaboration across the disciplines.

Monday, 02.10.
0850 OPENING
0900-0945 Kasia Rejzner 
1000-1045 Claudio Dappiaggi
1100-1145 Francesco De Vecchi
1200-1330 LUNCH
1330-1415 Ajay Chandra
1430-1515 Nils Berglund  
1800 DINNER

Tuesday, 03.10.
0900-0945 Nikolay Barashkov 
1000-1045 Harprit Singh
1100-1145 Lorenzo Zambotti
1200-1330 LUNCH

• Nikolay Barashkov — Gluing for \Phi^4_3 on cylinders
  Abstract: The $\Phi^4_3$ model is a 3-dimensional non-Gaussian Euclidean QFT. Showing existence of such a measure was one of the highlights of the constructive QFT programme in the '70s. In this talk, I will describe joint work with Trishen Gunaratnam in analysing how  $\Phi^4_3$ models glue together on cylinders.

• Nils Berglund - Perturbation theory for the Phi^4_3 model, revisited with Hopf algebras
  Abstract: The static Phi^4 model on the d-dimensional torus is a well-known toy model in Euclidean quantum field theory. It is well-posed for d = 1, and its renormalisation is well-understood for d = 2 and d = 3, thanks to works by Glimm, Jaffe, and many others. In this talk, I will argue that recent progress in Wiener chaos expansions, Hopf-algebraic methods, and bounds on the value of Feynman diagrams obtained through BPHZ renormalisation can help us improve our understanding of this important result. In particular, I will sketch a relatively short, almost self-contained proof of the fact that the partition function of the suitably renormalised Phi^4_3 measure admits an asymptotic expansion, the coefficients of which converge as the ultraviolet cut-off is removed. We will also briefly address the question of Borel-summability of the asymptotic series, although this is not the main focus of our work.
  This is joint work with Tom Klose (Berlin/Warwick)

• Ajay Chandra - A priori bounds for the generalised parabolic Anderson model in the singular regime
  Abstract: While our understanding of local theory for parabolic singular SPDE is fairly mature, we still remain unable to control global behavior of many of these dynamics. In this talk, we'll discuss progress on this for the generalised parabolic Anderson model which, like the $\Phi^4_d$ equations, are straightforward to estimate when not rough but become much more difficult in the rough setting. However, unlike the $\Phi^4_d$ equations, we will not have a strong damping term to help us with the difficulties that appear in the rough setting.
  This is joint work with Guilherme Feltes and Hendrik Weber.

• Claudio Dappiaggi - Stochastic Partial Differential Equations and Renormalization à la Epstein-Glaser
  Abstract: We present a novel framework for the study of a large class of nonlinear stochastic partial differential equations, which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use specific techniques proper for microlocal analysis. These allow us to deal with renormalization using an Epstein-Glaser perspective, hence without resorting to any specific regularization scheme.  As a concrete example, we shall use this method to discuss the stochastic \Phi^3_d model and we shall comment on its applicability to the stochastic nonlinear Schrödinger equation.
  Based on joint works with A. Bonicelli, B. Costeri, N. Drago, P. Rinaldi and L. Zambotti.

• Francesco De Vecchi - Non-commutative probability and the quantization of Euclidean fermionic fields
  Abstract: The use of probabilistic concepts and techniques in Euclidean quantum field theory allowed the rigorous construction of many interacting bosonic quantum fields. In this talk, we show how it is possible to generalize some of these ideas, such as $L^p$ spaces, conditional expectation, and stochastic calculus, in order to obtain a probabilistic-like construction of fermionic quantum fields.
  The talk is based on a joint work with Luca Fresta, Maria Gordina and Massimiliano Gubinelli.

• Torstein Kastberg Nilssens - Parameter estimation in rough differential equations using scaled quadratic variation
  Abstract: In this talk, I will present a method for estimating the diffusion-coefficients and Hurst parameter in a rough path differential equation driven by fractional Brownian motion. The method is based on an observed trajectory of the solution and a type of quadratic variation formula generalized to accommodate non-martingale sources of noise. Finally, we will look at convergence rates of the method as well as some numerical experiments.

• Kasia Rejzner - Renormalization of gauge theories in (perturbative) algebraic quantum field theory
  Abstract: In this talk, I will briefly introduce the formalism of perturbative algebraic quantum field theory and then proceed to present more recent results concerning the non-perturbative formulation and the treatment of gauge theories.
  This is based on a series of joint papers with Brunetti, Fredenhagen and Duetsch.

• Harprit Singh - Singular SPDEs on Geometric Spaces
  Abstract: We shall discuss the solution theory to a large class of singular SPDEs in various non-translation invariant settings. In particular, I shall present results on Riemannian manifolds and homogeneous Lie groups as well as discuss some results on non-translation invariant elliptic and hypoelliptic equations on Euclidean space.
  Based on joint work with M. Hairer, respectively A. Mayorcas.

• Lorenzo Zambotti - On the multi-indices approach to rough paths and regularity structures
  Abstract: I will present some results on the approach to rough paths and regularity structures recently developed by Linares, Otto and Tempelmayr and based on multi-indices rather than on trees. While they insisted on using a pre-Lie approach, we argue that a post-Lie structure is much more natural, as noted also by Bruned and Katsetsiadis.
  Joint work with Jean-David Jacques.

This year the workshop will be located at NTNU, Campus Gjøvik, Norway. Directions:  NTNU in Gjøvik. For directions to the rooms at NTNU campus you can use NTNUs mazemap.

Monday the workshop will take place in 

K113

Tuesday the room is

K109

• Charles Curry - NTNU, Gjøvik 

• Kurusch Ebrahimi-Fard -  NTNU, Trondheim

• Fabian A. Harang - BI Norwegian Business School, Oslo

• Alexander Schmeding -  NTNU, Trondheim

TMS - Trond Mohn Stiftelsen through the national project Pure Mathematics in Norway.