# Past Lecture Days

**18 Nov 2021**Geoffrey Compère (Université Libre de Bruxelles)Advanced General Relativity: Charges and black hole thermodynamics

9:15–16:15 Lecture Hall Central Building AEI

Clément Mouhot (U Cambridge)**13/14 Feb 2020**

Introduction to Vlasov systems

We will present an introduction to the mathematical analysis of the main nonlinear transport equations, in particular the Vlasov-Poisson system that models plasmas and galaxies. If time permits, we will overview the (far) less complete Cauchy theory for the related Vlasov-Maxwell system. We will present the Cauchy problem and the key estimates and results known about the construction of solutions. If time permits, we will give a brief overview of more recent results on the asymptotic behaviour of such solutions.

Thursday 13 February from 10:15--12:30;

Friday 14 February from 10:15--12:30

Place: AEI seminar room 0.01

Stijn van Tongeren (HU Berlin)**14/15 Nov 2019**

Introduction to integrability

**24/25 Oct 2019**Richard Jozsa (U Cambridge)

Introduction to quantum information theory

24 Oct

10:15-11:15 Lecture 1

11:15-11:30 Break

11:30-12:30 Lecture 2

12:30-14:00 Break

14:00-15:00 Lecture 3

25 Oct

10:15-11:15 Lecture 4

**22 and 23 Jul 2019**Gustav Holzegel (U Cambridge)

Wave Equations on Black Hole spacetimes and (In)stability of Black Holes

Abstract: In this series of lectures I will begin by introducing the mathematical tools required for a rigorous study of wave equations on black hole spacetimes. The main focus will be on the geometric phenomena associated with black holes (which are briefly reviewed) and their manifestation in the analysis. In particular, the differences in the behaviour of waves on asymptotically flat and cosmological black holes will be explained. In the remaining time, I will make connection to the stability problem for black hole and review in some detail a proof of the linear stability of the Schwarzschild solution. Time permitting, the non-linear stability result will also be discussed.**19 and 20 Mar 2019**Ben Gripaios (U Cambridge)

Physics beyond the standard model

Abstract: The lectures will provide a brief introduction to a selection of current topics in physics Beyond the Standard Model. Time permitting, the following topics will be covered:

(i) miracles of the Standard Model; (ii) Effective Field Theory; (iii) Grand Unification; (iv) approaches to the Hierarchy Problem; (v) the Axion.

**18 and 19 Oct 2018**Chris Fewster (U York)

Introduction to Algebraic Quantum Field Theory

**7 and 8 June 2018**Kirone Mallick (IPhT Saclay, Paris)Non-equilibrium physics

Abstract: In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us with a unified description of many physical situations. These functions are expected to play, for systems far from of equilibrium, a role akin to that of the thermodynamic potentials. We shall review the Jarzynski and Crooks Work Identities, the Gallavotti-Cohen Fluctuation Theorem and the Macroscopic Fluctuation Theory. These concepts will be illustrated on simple systems such as the Brownian ratchet model for molecular motors and the asymmetric exclusion process.**9 and 10 May 2018**Daniele Dorigoni (Durham)Resurgence in quantum field theory

**14 Mar 2018**Christian Bär (U Potsdam)Introduction to characteristic classes and applications

10:00-11:00 Lecture 1: Homology and Cohomology (Room 0.01 AEI Golm)

11:30-12:30 Lecture 2: Vector bundles (Room 0.01 AEI Golm)

14:00-15:00 Lecture 3: Characteristic classes (Room K.-2.155 - K.-2.153, MPI for Colloids and Interfaces Golm)

15:30-16:30 Lecture 4: Applications (Room K.-2.155 - K.-2.153, MPI for Colloids and Interfaces Golm)Abstract:

Lecture 1: Homology and cohomology are quantities which are associated to a space and measure its "complexity". We will discuss deRham cohomology which is based on solvability of certain partial differential equations and simplicial homology which controls how a space can be built from simple pieces. We will see that the two theories are dual to each other.

Lecture 2: The target space in which a field takes its values typically depends on the point at which the field is evaluated. For example, a vector field must always be tanget to the space, a condition which changes with the base point. This gives rise to the concept of vector bundle. We will discuss geometric aspects of vector bundles such as curvature.

Lecture 3: We will see how the curvature of a vector bundle gives rise to interesting differential forms and corresponding cohomology classes which measure the "twistedness" of the bundle. This includes the famous Poincare and Chern classes.

Lecture 4: Consider the Dirac operator as an operator mapping left-handed to right-handed spinors. In general, it is hard to compute the solution space but the index is quite accessible. This is the difference of the dimension of the solution space and the codimension of the image. The index can be expressed in terms of characteristic classes, hence in geometric terms. This is the famous Atiyah-Singer index theorem. We will also see how this relates to anomalies and topological charges.

**14 + 15 December 2017**Stefan Theisen (AEI)Conformal Field Theories, Trace Anomalies and their Applications, 10:15 – 12:30 (AEI Golm, seminar room 0.01)

Abstract: I will introduce general properties of conformal field theories in arbitrary dimensions. In even dimensions, the symmetry is anomalous, giving rise to a conformal or Weyl anomaly. Its use in the proof of the a-theorem and in the computation of partition functions will be discussed.

**20, 22, 24 November 2017**GQFI independent research groupIMPRS Bootcamp Holography (GQFI), 09:30 – 13:45 (AEI Golm, seminar room 0.01)

Abstract: "The Gravity, Quantum Fields and Information Bootcamp is going to provide a hands-on introduction to holography (also known as AdS/CFT correspondence or gauge-gravity duality) and related subjects. The course will first introduce the basic notions of holography and then discuss recent connections with quantum information science and black hole physics, as well as applications to studies of strongly-coupled systems. No prior knowledge of holography is required. The goal of the meeting is to provide the basic knowledge about this vast subject and in this way help interested and determined IMPRS students to participate in GQFI seminars and collaborate with GQFI members."

**10 – 11 August 2017**David Tong (DAMTP Cambridge)

Gauge Theories in d=2+1 Dimensions, 10:00 – 12:15 (AEI Golm, seminar room 0.01)Abstract: The purpose of these lectures is to describe a recently-discovered web of dualities in non-supersymmetric gauge theories in d=2+1 dimensions. I will start by explaining some basic phenomenology of the quantum Hall effect, and how this is captured by Chern-Simons theories. I will then go on to describe the key idea of bosonization. This is the seed for many other dualities, including bosonic particle-vortex duality and its more surprising fermionic cousin.

**21 – 22 June 2017**Kirill Krasnov (Nottingham)

Formulations of General Relativity, 10:00 – 12:15 (AEI Golm, seminar room 0.01)Abstract: In his Nobel lecture Richard Feynman pointed out that important physical theories tend to admit many not obviously equivalent formulations. He went further as to suggest the availability of not obviously equivalent reformulations of a physical theory as a criterion of its simplicity. General Relativity admits many reformulations. Some of them make this theory almost unrecognisable. The goal of this lecture series is to review and contrast the known formulations of GR. The lectures will cover: The usual metric formulation, the first order metric-affine Palatini formulation, the second order pure affine formulation of Eddington-Schroedinger. The tetrad plus spin connection Einstein-Cartan formulation, the corresponding pure spin connection formulation. MacDowell-Mansouri formulation and its fully invariant version due to Stelle-West. BF-type formulation with the spin connection and a 2-form field, its pure connection version. Chiral formulations of 4D GR that retain only the self-dual part of the spin connection. This includes Plebanski and all related formulations. Each of the above is a Lagrangian formulation. The lectures will NOT cover the question of performing the 3+1 split and giving the corresponding initial value (=Hamiltonian) formulation. This is an interesting topic in its own right. We will contrast the different formulations of GR by looking at the type of perturbative expansion they generate when expanded around an appropriate background.

**9 March 2017**Mihalis Dafermos (Cambridge/Princeton)

Black hole stability inside and outside, 10:00 – 16:30 (AEI Golm, seminar room 0.01)Abstract: These lectures will discuss aspects of the evolution of waves in both the interior and exterior of black holes and how this relates to the stability of the spacetimes themselves as well as the nature of their internal structure and the question of cosmic censorship.

**16 January 2017**Edvard Musaev (AEI Potsdam)

Geometry in physics and string compactifications, 10:00-16:30 (AEI Potsdam, room 0.01)The lectures will contain a basic introduction to the geometry of fibre bundles, connections and spin geometry with a view to application in string theory compactifications.

**15 November 2016**Henrik Johansson (Uppsala University & Nordita)

Introduction to color-kinematics duality, and gravity as a double copy of gauge theory, 12:00 – 17:45 (Berlin, Humboldt University, room ZGW 6 2’21, IRIS building (Zum Grossen Windkanal 6))**15 June 2016**Krzysztof Meissner (Warsaw University)

The standard model of elementary particles and conformal symmetry, 10:00-16:30 (AEI Potsdam, room 0.01)

Glenn Barnich (Université Libre de Bruxelles)**4 May 2016**

BMS symmetry in 3 and 4 dimensions, 10:00-16:30 (AEI Golm, room 0.01)

Topics:

1) Symmetries of asymptotically AdS and flat spacetimes in d dimensions

2) Results in 3 dimensions: Solution space as coadjoint representation, classically dual 2d field theories

3) Results in 4 dimensions: BMS current algebra at null infinity

**9 March and 16 March 2016**Jan Metzger (University of Potsdam)

Partial differential equations, 10-15:30 (AEI Golm, room 0.01)

Abstract: In the six talks of these IMPRS lecture days we start from the very basic principles of classical physics: Ordinary and Partial Differential equations. We briefly visit the topic of ordinary differential equations and consider the setting in a somewhat general sense. Crucial topics are existence, uniqueness and stability analysis. In the second lecture we study examples of partial differential equations and inspect their qualitative behavior. In the third lecture we consider methods to analyze non linear equations with the help of the linear theory. Lectures 4 to 6 deal with the solution of the Cauchy Problem for the Einstein equations starting from the elliptic constraint system. After a brief look into the theory of symmetric hyperbolic systems we rephrase the Einstein equations as such a system and obtain a short time solution. To get the maximal development these solutions have to be stiched together.

**13 January 2016**Emil Akhmedov (High School of Economics, Moscow, and ITEP)

Introduction to Hawking Radiation, 10:00-16:30 (AEI Golm, room 0.01)

Abstract: I will start with the description of the thin shell collapse background and Penrose diagrams. Then will describe free scalar harmonics on such a background. Finally, I will derive the Hawking flux in Gaussian theory and explain why loop corrections to it in the interacting theory are not suppressed. If there will be enough time, I will discuss Unruh effect, its relation and distinction with Hawking effect, and the notion of particle.

**27 November 2015**Anastosios Petkou (Aristotle University, Thessaloniki):

Conformal field theory in various dimensions, 10:00-16:30 (AEI Golm, room 0.01)

Topics: Conformal symmetry in two and higher dimensions, AdS/CFT

**20 August 2015**Marc Henneaux (Université Libre de Bruxelles):

Constrained Hamiltonian systems and BRST symmetry, 10:00-16:30 (AEI Golm, room 0.01)

Topics: Gauge invariance and Hamiltonian constraints, BRST theory, Quantization of gauge systems

**25 June 2015**Song He (Perimeter Institute):Scattering Amplitudes of Massless Particles, 10:00-16:30 (HU Adlershof, IRIS-Building 2'07)

**18 March 2015**Daniel Persson (Chalmers University of Technology, Gothenburg):

Automorphic Forms, 10:00-12:30 (Room 0.01), 14:00-16:30 (Room 1.63)

Automorphic forms are ubiquitous in theoretical physics and in particular in string theory where they capture a wide variety of different phenomena such as loop amplitudes and black hole partition functions. In the mathematics literature automorphic forms on higher rank Lie groups are mainly analyzed using representation theory, a viewpoint which is particularly prominent in connection with the Langlands program. In recent years it has become evident that this perspective is also very useful in string theory, notably in the study of U-duality and higher derivative corrections. In these lectures I will give an introduction to the theory of automorphic forms from the representation theoretic point of view. The presentation will be example-driven and will focus on the special case of non-holomorphic Eisenstein series on the upper-half plane SL(2,R)/SO(2), for which everything can be done very explicitly.

**9 January 2015**Jakob Palmkvist (Texas A&M):

Group theory, Lie (super)algebras and representations, 10:00-12:30, 14:00-16:30

The course addresses basic and advanced topics in the structure and

representation theory of Lie (super)algebras, spread over four

lectures, according to the following rough schedule:

1. Basic concepts: finite groups, Lie groups and Lie algebras.

2. Classification of simple finite-dimensional Lie algebras: root

systems, Cartan matrices and Dynkin diagrams.

3. Representations of simple finite-dimensional Lie algebras:

(generalized) Young tableaux/diagrams, weights and characters.

4. Advanced topics: infinite-dimensional Kac-Moody algebras, Lie

superalgebras and other generalizations.

Gerhard Huisken (Universitaet Tuebingen & Mathematisches Forschungsinstitut Oberwolfach):**3 September 2014**

Mean curvature flow with surgery. 10:00-12:30, 14:00-16:30

The course describes a recent construction of Brendle and Huisken for the deformation of 2-dimensional embedded meanconvex hypersurfaces in Riemannian 3-manifolds along mean curvature flow, interrupted by only finitely many surgeries. The construction relies on new non-collapse and pseudolocality estimates for embedded surfaces and has applications to asymptotically flat 3-manifolds arising in General relativity.

**9****July**Filippo Guarnieri and Teake Nutma (AEI):**2014**

The Ins and Outs of Mathematica. 10:00-12:30, 14:00-16:30

See this website for material from the lecture.**11 June 2014**Amitabh Virmani (Institute of Physics, Bhubaneshwar, Odisha):

Black Holes in String Theory, 10:00-12:30, 14:00-16:30

(i) higher-dimensional black holes

(ii) string theory black holes

(iii) Strominger-Vafa counting

(iv) information paradox

Claude Duhr (IPPP Durham):**9 April 2014**

The mathematics of multiple polylogarithms and Feynman integrals, 10:00-12:30, 14:00-16:30

I will discuss how the mathematical structures underlying multiple polylogarithms are useful to compute certain classes of Feynman integrals that are of interest in high-energy physics. I will introduce the Hopf algebra of multiple polylogarithms and show how it can be used to be derive functional equations among these functions. In a second part, I will focus on applications of these ideas to the computation of integrals that appear in high-energy physics computations.

**8 January 2014**Jens Hoppe (KTH Stockholm):

Introduction to integrable systems,

11:00-12:30, 14:00-15:30