Related papers: Cargese Lectures on the Kerr/CFT Correspondence
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and…
The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
These lectures present a brief introduction to measurement theory for QFT in possibly curved spacetimes introduced by the author and R. Verch [Comm. Math. Phys. 378 (2020) 851-889]. Topics include: a brief introduction to algebraic QFT,…
In the nearly twenty years that have elapsed since its discovery, the gauge-gravity correspondence has become established as an efficient tool to explore the physics of a large class of strongly-coupled field theories. A brief overview is…
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
What should these lectures be? The subject assigned to us is so broad that many books can be written about it. So, in planning these lectures I had several options. One would be to focus on a narrow subset of topics and to cover them in…
We construct a new type of Chandrasekhar transformation in Kerr spacetime using the different tortoise coordinate, which is useful for exact analysis to study Teukolsky equation with arbitrary frequency. We also give the interpretation of…
Geometric complexity theory (GCT) is an approach to the $P$ vs. $NP$ and related problems. A high level overview of this research plan and the results obtained so far was presented in a series of three lectures in the Institute of Advanced…
In this work we study in detail new kinds of motions of the metric tensor. The work is divided into two main parts. In the first part we study the general existence of Kerr-Schild motions --a recently introduced metric motion. We show that…
This presentation intends to illustrate the specific capabilities of an e$^+$e$^-$ sub-TeV collider to provide answers on the basic issues in physics: origin of mass, hierarchy of masses, cosmological problems. Some foreseeable scenarios…
This is a write-up of a two hour talk at the Simons workshop. It contains an elementary introduction to F-theory and may be useful for people new to the subject.
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
These are the notes accompanying three lectures given by the second author at the Motivic Geometry program at CAS, which aim to give an introduction and an overview of some recent developments in the field of reciprocity sheaves.
This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count…
We consider a certain linear recursive relation with integer parameters and study some of its algebraic and geometric properties, with the purpose of estimating the number of chains of valences in the Farey series.