Related papers: Lecture on Langlands Functoriality Conjecture
This is an expanded version of lectures given at a Summer School "Geometric methods in Representation Theory" (Grenoble, 2008).
These are informal notes written in 2007 that outline the local and global quantum Langlands program. (I decided to make them public in view of the revived interest in the subject.)
Lecture notes on selected topics in the theory of gravitation.
These are extended lecture notes of a PhD course that the author gave at the Universita degli studi di Torino in Italy in spring 2013.
This paper gives an overview from the perspective of Lie group theory of some of the recent advances in the rapidly expanding research area of quantum entanglement. This paper is a written version of the last of eight one hour lectures…
The present overview and gentle introduction to Grassmannian calculus and some of its applications to probability collects the notes of a mini-course given by the authors at the Brazilian School of Probability, August 5-9, 2024, in…
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
An expository lecture on the analogy between the subjects of the title. Delivered at the International Conference on Number Theory at the Korea Institute for Advanced Study in December 1997.
Lecture notes for the proceedings of the workshop "Algebraic Combinatorics related to Young diagram and statistical physics", Aug. 6-10 2012, I.I.A.S., Nara, Japan.
These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were…
A School on Loop Quantum Gravity was held at the IMSc during Sept 8 -- 18, 2009. In the first week a basic introduction to LQG was provided while in the second week the focus was on the two main application, to cosmology (LQC) and to the…
Lecture notes of a course on birational geometry (taught at College de France, Winter 2011, with the support of Fondation Sciences Math\'ematiques de Paris). Topics covered: introduction into the subject, contractions and extremal rays,…
This is an introduction to orientifolds with emphasis on applications to duality. Based on lectures given at the 1997 Trieste Summer School on Particle Physics and Cosmology, Italy.
These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…
These are lecture notes (by the first author) from a course (by the second author) given over two extended semesters at the University of Sydney. The first part provides an introduction to the Langlands correspondence from an arithmetical…
We present some of the topics covered in a series of lectures under the same title that was given at the "Summer School on High Energy Physics at the LHC: New trends in HEP" in Natal, Brazil. In particular, after some general thoughts on…
A short lecture given at the Summer School on "Modern perspectives in lattice QCD", Les Houches, August 3-28, 2009.
The present volume is the written version of the series of lectures the author delivered at the Catholic University of Leuven, Belgium during the period of June-July, 1990. The main purpose of these talks is to present some of author's work…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…
We describe the applications of localization methods, in particular the functorial localization formula, in the proofs of several conjectures from string theory. Functorial localization formula pushes the computations on complicated moduli…