Related papers: Lectures on Polyfolds and Symplectic Field Theory
This PhD Thesis is devoted to the study of Hodge structures on a special type of complex algebraic varieties, the so-called character varieties. For this purpose, we propose to use a powerful algebro-geometric tool coming from theoretical…
We construct Symmetry Topological Field Theories (SymTFTs) for continuous subsystem symmetries, which are inherently non-Lorentz-invariant. Our framework produces dual bulk descriptions -- gapped foliated and exotic SymTFTs -- that generate…
These notes are a transcript of lectures given by the author in the XVIII Modave summer school in mathematical physics. The introduction is devoted to a detailed review of the literature on asymptotic symmetries, flat holography, and the…
In this expository paper written for physicists and geometers we introduce the notions of TQFT and of orbifold. Then we survey the construction of TQFT's originating from orbifolds such as Chen-Ruan theory and Orbifold String Topology.
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
The AdS/CFT correspondence provides quantum theories of gravity in which spacetime and gravitational physics emerge from ordinary non-gravitational quantum systems with many degrees of freedom. Recent work in this context has uncovered…
These are lecture notes expanding upon a set of lectures given by G.M. at the TASI 2023 School. Part I is an introduction to topological field theory, including extended topological field theory. Part II is an introduction to generalized…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
The symmetry data of a $d$-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory (SymTFT). In top down (i.e., stringy) realizations of this structure, the QFT in…
The standard model of particle physics represents the cornerstone of our understanding of the microscopic world. In these lectures we review its contents and structure, with a particular emphasis on the central role played by symmetries and…
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact…
This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics…
Lecture notes of a block course explaining why quantum field theory might be in a better mathematical state than one gets the impression from the typical introduction to the topic. It is explained how to make sense of a perturbative…
A self-consistent string field theory with interaction is formulated. The symmetry algebra of this theory includes, in the low-energy limit, local space-time symmetries, and the Brans-Dicke equation describes a class of low-energy…
In this paper, we propose an approach based on the theory of an axiomatic $S$ matrix and partially switching on an interaction, which is extremely suitable for describing the phenomenon of oscillations within the framework of quantum field…
We analyze the symplectic structure of two-dimensional dilaton gravity by evaluating the symplectic form on the space of classical solutions. The case when the spatial manifold is compact is studied in detail. When the matter is absent we…
We present a detailed discussion of AdS_3 black holes and their connection to two-dimensional conformal field theories via the AdS/CFT correspondence. Our emphasis is on deriving refined versions of black hole partition functions, that…
Proceedings of the workshop "Boundary and Defect Conformal Field Theory: Open Problems and Applications," Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017.
The present notes are based on three lectures, each ninety minutes long, prepared for the school 'Integrability, Dualities and Deformations', that ran from 23 to 27 August 2021 in Santiago de Compostela and virtually. These lectures, aimed…
These are the extended notes of a talk I gave at the Geometric Topology Seminar of the Max Planck Institute for Mathematics in Bonn on January 30th, 2012. My goal was to familiarize the topologists with the basics of arithmetic hyperbolic…