Related papers: Lecture notes on Geometric Crystals and their comb…
Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…
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…
A previous work gave a combinatorial description of the crystal $B(\infty)$, in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present…
This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic…
We generalize Lusztig's nilpotent varieties, and Kashiwara and Saito's geometric construction of crystal graphs from the symmetric to the symmetrizable case. We also construct semicanonical functions in the convolution algebras of…
Selected highlights of the theoretical developments reported at the 2004 Quark Matter conference are discussed, with emphasis on open issues.
This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…
In the following few pages an account is given of a theme, which I began in 1966 and followed to the present.
These notes are the write-up of my 2008 PCMI lectures on multiplier ideals. They aim to give an introduction to the algebro-geometric side of the theory, with an emphasis on its global aspects. The focus is on concrete examples and…
Notes for the author's MSRI lecture in January 2014.
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. We give an introduction focusing on the example of unitary groups and highlight…
The source of these notes is a series of lectures given at the CIMPA's summer school "Recent Topics in Geometric Analysis".
These are lecture notes of a course on Calogero-Moser systems and their connections with representation theory and geometry, given by the author in Zurich in May-June 2005.
The goal of this introduction to symmetries is to present some general ideas, to outline the fundamental concepts and results of the subject and to situate a bit the following lectures of this school. [These notes represent the write-up of…
Similarly to the theory of crystalline cohomology, we give a local description of a prismatic crystal and its cohomology in terms of a $q$-Higgs module and the associated $q$-Higgs complex on the bounded prismatic envelope of an embedding…
We show that theory predictions for volume reflection in bent crystals agree with recent experimental data. This makes possible to predict volume reflection angle and efficiency in a broad range of energy for various crystals. A simple…
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
A new kind of diagrams is presented, showing the causal structure of bimetric interactions.
This paper is the augmented notes of a course I gave jointly with Laurent Berger in Rennes in 2014. Its aim was to introduce the periods rings B crys and B dR and state several comparison theorems between{\'e}tale and crystalline or de Rham…