Related papers: Lecture notes on torsions
The present review is based on the lectures that the author had been giving during several years at the Swiss Federal Institute of Technology in Zurich (ETH Zurich). Being bounded by lecture frames, the selection of the material, by…
These notes are from a 4-lecture mini-course taught by the author at the conference on von Neumann algebras as part of the ``Geometrie non commutative en mathematiques et physique'' month at CIRM in 2004.
In 1971, Ray and Singer proposed an analytic equivalent of a classical topological invariant, the R-torsion. This Ray-Singer torsion has had many ramifications in mathematics and physics. I will describe the background, the Ray-Singer…
Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…
These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate…
These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.
We describe torsion classes in the first cohomology group of $\text{SL}_2(\mathbb{Z})$. In particular, we obtain generalized Dickson's invariants for p-power polynomial rings. Secondly, we describe torsion classes in the zero-th homology…
Construction of immersions with "small" curvatures between Riemannian manifolds and indicating obstructions to such immersions
This is more or less the content of a 5-hour mini-course that I have given at KTH in the program ``Master class in low-dimensional dynamics'' during May 1-5, 2023. It was not intended to be exhaustive but to give the students a grasp of…
These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…
These notes are a written version of a set of lectures given at TASI-02 on the topic of effective field theories. They are meant as an introduction to some of the latest techniques and applications in the field.
These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…
These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as…
This is an expanded version of a three-hour minicourse given at the winterschool Winterbraids IV held in Dijon in February 2014. The aim of these lectures was to present some aspects of the dimer model to a geometrically minded audience. We…
Preliminary version No.~2 of the lecture notes for the talk ``Quantum theory of gravitational collapse'' given at the 271. WE-Heraeus-Seminar ``Aspects of Quantum Gravity'' at Bad Honnef, 25 February--1 March 2002
These informal lecture notes describe the progress in semiconductor spintronics in a historic perspective as well as in a comparison to achievements of spintronics of ferromagnetic metals. After outlining motivations behind spintronic…
This is lecture notes for a course given at the PCMI Summer School "Quantum Field Theory and Manifold Invariants" (July 1 -- July 5, 2019). I describe basics of gauge-theoretic approach to construction of invariants of manifolds. The main…
Witten- Helffer-Sj\"ostrand theory is a considerable addition to the De Rham- Hodge theory for Riemannian manifolds and can serve as a general tool to prove results about comparison of numerical invariants associated to compact manifolds…
These are the lecture notes for the introductory graduate course I taught at Yale during Spring 2007. I mostly followed [GS], [BGV], [AB], [Par2], and there are no original results in these notes.
The present notes are based on a course on Cherednik algebras given by the first author at MIT in the Fall of 2009. Their goal is to give an introduction to Cherednik algebras, and to review the web of connections between them and other…