XV Modave Summer School in Mathematical Physics
© Fiorucci Adrien, 2018.

Lectures: topics and speakers

Asymptotic Symmetries in Gauge Theories and the BMS Group    by Romain RUZZICONI (ULB, Brussels).

In these lectures, we will discuss some general aspects of asymptotic symmetries in gauge theories. We will explain how to impose consistent sets of boundary conditions, and how to compute the asymptotic symmetry parameters. The different procedures to obtain the associated charges will be presented. As an illustration of these concepts, the example of 4d General Relativity in asymptotically flat spacetime will be covered. This will enable us to discuss the different extensions of the Bondi-Metzner-Sachs (BMS) group and their relevance for soft gravitons theorems, memory effects, and black hole information paradox.

A bird's eye view on background-independent quantum gravity    by Philipp HÖHN (University of Vienna).

We will revisit arguments for why gravity should be quantized in the first place, before developing a wish list of what features a putative theory of quantum gravity should have. For concreteness, we will discuss how this wish list may or may not be fulfilled by attempting to quantize geometric degrees of freedom directly, while respecting key properties of general relativity such as its diffeomorphism symmetry. In contrast to the usual quantization of fields on a fixed spacetime, this calls for a background-independent quantization of spacetime. I will give an overview of canonical and path integral approaches attempting to meet such requirements, such as loop quantum gravity and spin foam models, focusing on their main ideas, achievements and challenges.

Topological Field Theory    by Wolfger PEELAERS (University of Oxford).

Topological quantum field theory (TQFT) is a vast and rich subject that relates in a profound way physical observables to mathematical quantities. In these lectures, we will define TQFTs both from a physical and a mathematical point of view, formalizing the intuition that only the topology of the underlying manifold matters. In particular, we will introduce Witten's topological twist as a means to obtain so-called Witten-type or cohomological TQFTs, and we will look into Atiyah's axiomatic definition, which for one- and two-dimensional TQFTs provides a particularly intuitive, pictorial representation of their algebraic structure. Further, we will explore some of their applications in both physics and mathematics.

Renormalization Group    by Manuel REICHERT (University of Southern Denmark).

Non-perturbative regimes of quantum field theories, such as QCD and quantum gravity, are highly relevant for the understanding of fundamental interactions. In this course I will introduce the functional renormalisation group as tool for non-perturbative computations. I will show applications of the functional renormalisation group, where I will put the emphasis on asymptotically safe quantum gravity.
Asymptotically safe quantum gravity conjectures a non-trivial ultraviolet fixed point of the renormalisation group flow of the gravitational couplings, which makes the theory non-perturbatively renormalisable and thus fundamental. I will review the evidence in favour of this quantum gravity scenario and show how Standard Model parameters can be post-dicted by it.

Bottom-up Holography and its Applications    by Andrea AMORETTI (INFN, Genova).

The main goal of the course is to provide an overview of bottom-up models of holography applied to condensed matter systems.
The bottom up approach consists in applying the AdS/CFT duality starting directly from a classical gravity model, without caring about its possible string theory embedding. After introducing the basic idea beyond the holographic principle, I will describe the advantages and the limitations of the bottom-up approach. Eventually I will outline the properties of the most relevant bottom-up holographic models appeared in the literature, discussing their applications to study the transport properties of strongly coupled condensed matter systems.


Here is the schedule of lectures and peripheric activities.

Monday Tuesday Wednesday Thursday Friday
08:00-09:00 Breakfast Breakfast Breakfast Sleeping Sleeping
09:00-10:00 Quantum Gravity Topological F.T. Quantum Gravity Breakfast Breakfast
10:00-11:00 Quantum Gravity Topological F.T. Quantum Gravity Topological F.T. Exercises
11:00-11:15 Coffee break Coffee break Coffee break Coffee break Coffee break
11:15-12:15 B.M.S. B.M.S. R.G. Flow B.M.S. B.M.S.
12:15-14:15 Lunch Lunch Lunch Lunch Lunch
14:15-15:15 Gong-show Quantum Gravity Castle


Applied Holography B.M.S.
15:15-16:15 R.G. Flow R.G. Flow Topological F.T. Applied Holography
16:15-16:30 Coffee break Coffee break Coffee break Coffee break
16:30-17:30 R.G. Flow R.G. Flow Topological F.T. Applied Holography
17:30-18:30 Topological F.T. Applied Holography Exercises Exercises Free Time
18:30-19:30 Free Time Free Time Free Time Game
19:30- ... Dinner Dinner Dinner Dinner Dinner