Collection Number C21002
Collection Date -
Collection Type Conference/School

Entropy and energy fluctuations in non-equilibrium quantum statistical mechanics

Annalisa Panati University of Toulon
"Non-equilibrium statistical mechanics has seen some impressive developments in the last three decades, thank to the pioneering works of Evans, Cohen, Morris and Searles on the violation of the second law, soon followed by the ground-breaking formulation of the Fluctuation Theorem by Gallavotti and Cohen for entropy fluctuation in the early nineties.

On hidden quantum group symmetries in CFT

Eveliina Peltola University of Bonn
"I discuss applications of a hidden $U_q(\mathfrak{sl}_2)$-symmetry in CFT with central charge $c \leq 1$ (focusing on the generic, semisimple case, with $c$ irrational). This symmetry provides a systematic method for solving Belavin-Polyakov-Zamolodchikov PDE systems, and in particular for explicit calculation of the asymptotics and monodromy properties of the solutions. Using a quantum Schur-Weyl duality, one can understand solution spaces of such PDE systems in a detailed way.

Change the coefficients of conditional entropies in extensivity

Asuka Takatsu Tokyo Metropolitan University
The Boltzmann--Gibbs entropy is a functional on the space of probability measures. One characterization of the Boltzmann--Gibbs entropy is given by the Shannon--Khinchin axioms, which consist of continuity, maximality, expandability and extensivity. The extensivity is expressed in terms of the linear combinations of conditional probabilities. Replacing the coefficients in the linear combinations with a power function provides a characterization of the Tsallis entropy. I talk about the impossibility to replace the coefficients with a non-power function.

From gauge fields to direct connections on gauge groupoids

Alessandra Frabetti Université Claude Bernard Lyon 1 - Institut Camille Jordan
"Geometrically, a gauge theory consists of a spinor bundle describing the matter fields, associated to some principal bundle whose gauge group rules the internal symmetries of the system. The gauge fields are the local expressions of a principal connection inducing a covariant derivative which settles the dynamics of the matter fields. Principal connections can be seen as parallel displacements on the fibres of the principal bundle along curves on the base manifold.

A gentle introduction to (modular tensor) categories

Ana Ros Camacho Cardiff University
In this talk we will introduce categories, a notion that packages mathematical objects of any kind and provides an abstract language to study them. We will build up our way towards so-called modular tensor categories, which roughly speaking are categories with a tensor product, duals, and quite a bit of extra categorical structure. They arise in (rational) conformal field theory and its study poses many interesting questions on their classification, internal structure and generalizations. I will give an overview of these questions and some current lines of research in this topic.

Exploring spacetime beyond classicality

Renate Loll Radboud Universiteit Nijmegen
The physics of General Relativity is deeply intertwined with the mathematics of Lorentzian differentiable manifolds. The latter provide excellent models of spacetime across a vast range of physical scales, encoding gravitational interactions into the curvature properties of smooth metric spaces. However, describing geometry in terms of the infinitesimal line element "ds" does not seem appropriate in the quantum regime near the Planck scale.

On generalized hyperpolygons

Laura Schaposnik University of Illinois at Urbana-Champaign (UIUC)
In this talk we will introduce generalized hyperpolygons, which arise as Nakajima-type representations of a comet-shaped quiver, following recent work joint with Steven Rayan. After showing how to identify these representations with pairs of polygons, we shall associate to the data an explicit meromorphic Higgs bundle on a genus-g Riemann surface, where g is the number of loops in the comet. We shall see that, under certain assumptions on flag types, the moduli space of generalized hyperpolygons admits the structure of a completely integrable Hamiltonian system.