(Location: UP-PHYS-B23+, School of Physics, University Park Campus)
If you would like to attend this meeting, please fill out the registration form (there is no registration fee).
For further information please contact Alexander Schenkel.
11:00 - 11:30 Welcome and refreshments
11:30 - 12:30 Claudio Dappiaggi (Pavia): Interplay between Stochastic Partial Differential Equations and AQFT
12:30 - 14:00 Lunch
14:00 - 14:30 Harkan Kirk-Karakaya (York): Aspects of Quantum Backflow
14:30 - 15:00 Nivedita (Oxford): Towards construction of fully-extended functorial chiral CFTs from Conformal Nets
15:00 - 16:00 Daan Janssen (York): Characteristic renormalization and applications to black hole formation
16:00 - 17:00 Informal discussions
We review 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 of 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 other models such as the stochastic nonlinear Schrödinger equation and the stochastic Thirring equation.
Based on joint works with A. Bonicelli, B. Costeri, N. Drago, P. Rinaldi and L. Zambotti.
In 1D quantum mechanics, quantum backflow is the phenomenon whereby a state consisting purely of positive momenta can exhibit an increase in probability of being measured in the region x < 0. Of particular interest is the maximum amount by which this probability can increase, the backflow constant, and the associated states that exhibit this maximum backflow. In this talk, I will discuss a new method for answering these questions by taking matrix elements of the Bracken-Melloy operator with respect to a sequence of non-orthonormal $L^2(\mathbb{R}^+)$ vectors. I will present progress towards obtaining a more accurate estimate of the backflow constant. Aspects of various multiple extended backflow problems will also be discussed.
Two-dimensional chiral conformal field theories have three mathematical formulations, namely VOAs, conformal nets and Segal (functorial) CFTs. The former two are in the spirit of AQFT and the last one is formulated as an anomalous FQFT. We are working on the construction of a fully extended 2d chiral functorial field theory given the data of a conformal net. We introduce some ingredients of the target 3-category of Bicommutant Categories (a model for 3-Hilb) as a categorification of the Morita category of von Neumann algebras. We further give equivalent constructions of the category of solitons that we assign to a point with a germ of a 1-manifold in the conformal cobordism category. This is a bicommutant category, further at the level of 1-morphisms, the composition maps to categorified Connes-Fusion.
We present a regularization prescription for Hadamard two-point functions defined on the boundary of a lightcone, which can be used to analyze renormalized quantities for linear scalar fields in a curved background. This can be applied to formulate the semi-classical Einstein equations as a characteristic initial value problem. Furthermore, we shall discuss how these tools may be used to estimate backreaction effects of quantum fields near gravitationally collapsing bodies and study formation of horizons and singularities in semi-classical gravity.
Some general info is available here: https://www.nottingham.ac.uk/about/visitorinformation/mapsanddirections/universityparkcampus.aspx
The talks will take place in the lecture theatre UP-PHYS-B23+ in the School of Physics. The latter is located directly next to the School of Mathematical Sciences. See also the map below: