Related papers: Height inequalities and canonical class inequaliti…
In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…
This update to my article on Congruent numbers, elliptic curves, and the passage from the local to the global, which appeared in Resonance, December 2009, pp. 1183--1205 (https://www.ias.ac.in/describe/article/reso/014/12/1183-1205) and was…
This is a report of the concluding talk presented at the International Symposium on QCD Corrections and New Physics which was held during October 27-29, 1997 at Mielparque Hiroshima, Hiroshima, Japan. The report will be published in the…
This is an expanded version of lectures given at a Summer School "Geometric methods in Representation Theory" (Grenoble, 2008).
In the case of the scientometric evaluation of multi- or interdisciplinary units one risks to compare apples with oranges: each paper has to assessed in comparison to an appropriate reference set. We suggest that the set of citing papers…
This is a brief reminder, with extensions, from a different angle and for a less specialized audience, of my presentation at WGMP32 in July 2013, to which I refer for more details on the topics hinted at in the title, mainly deformation…
These are the revised notes of my lectures at the 1995 Santa Cruz summer institute. Changes from the Jan.26,1996 version: Major: 7.1--2; Medium: 3.7, 3.11, 5.3.3, 7.9.2, 9.8.
Introductory lectures on SCET mainly following the first chapters of arXiv:1410.1892
We contribute to the program of extending computable structure theory to the realm of metric structures by investigating lowness for isometric isomorphism of metric structures. We show that lowness for isomorphism coincides with lowness for…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
We give an algebraic proof of a class number formula for dihedral extensions of number fields of degree $2q$, where $q$ is any odd integer. Our formula expresses the ratio of class numbers as a ratio of orders of cohomology groups of units…
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…
Scientific attention is unevenly distributed, creating inequities in recognition and distorting access to opportunities. Using citations as a proxy, we quantify disparities in attention by gender and institutional prestige. We find that…
In these lecture notes for a summer mini-course, we provide an exposition on quantum groups and Hecke algebras, including (quasi) R-matrix, canonical basis, and $q$-Schur duality. Then we formulate their counterparts in the setting of…
These are the notes of a series of lectures delivered by the author at the Graduate School of Mathematics of the University of Tokyo, during the month of October 2015. They were meant to be as self-contained as possible, taking into account…
This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.
Lecture notes prepared for the 2021 SAGEX PhD School in Amplitudes hosted by the University of Copenhagen August 10th through 13th. Topics covered include: the manifestation of asymptotic symmetries via soft theorems, their organization…
Lecture Notes for the Les Houches Summer School LXIII on Quantum Fluctuations in July 1995 to appear in Elsevier Science Publishers B.V. 1997, edited by E. Giacobino and S. Reynaud.
This paper is an expanded version of two talks given by the author at the Summer School on the Interactions between Homotopy Theory and Algebra at the University of Chicago, July 26 to August 6, 2004. It describes a connection between model…
These are lecture notes from the IMPANGA 2010 Summer school. They give an introduction to log canonical thresholds, covering some basic properties, examples, and some recent results and open questions.