Related papers: Arithmetic lattices and weak spectral geometry
The aim of these Lectures is to provide a brief overview of the subject of asymptotic symmetries of gauge and gravity theories in asymptotically flat spacetimes as background material for celestial holography.
We compute the Laplacian spectra of singular area-minimising hypersurfaces in the hyperbolic space with prescribed asymptotic data. We also obtain similar results in higher codimension, and explore related extremal properties of the bottom…
Late Winter Lecture Notes, Short Course (10 hours) of Relativistic Astrophysics held at the Department of Physics and Astronomy of the University of Padova, March 13-17, 2017. Third version.
A brief survey of real algebraic structures on topological spaces is given. This article is written for the Gokova Gemetry/Topology Conference proceedings.
This article contains a collection of problems contributed during the course of the conference.
The magnetic Laplacian on hyperbolic surfaces provides a rich analytic framework in which a variety of quantum phenomena emerge. The present note, written for the \emph{Proceedings of the Journ\'ees EDP 2025}, is a concise overview of the…
This is a survey of known algorithms in algebraic topology with a focus on finite simplicial complexes and, in particular, simplicial manifolds. Wherever possible an elementary approach is chosen. This way the text may also serve as a…
This workshop about triangulations of manifolds in computational geometry and topology was held at the 2014 CG-Week in Kyoto, Japan. It focussed on computational and combinatorial questions regarding triangulations, with the goal of…
These are (not updated) notes from the lectures I gave at the NATO ASI ``Symmetric Functions 2001'' at the Isaac Newton Institute in Cambridge (June 25 -- July 6, 2001). Their goal is an informal introduction to asymptotic combinatorics…
These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March…
These are expanded notes of some lectures given by the author for a workshop held at the Indian Statistical Institute, Bangalore in June, 2010, giving an exposition on the modular representations of finite groups of Lie type and $p$-adic…
These are notes of the lectures given during the Toric Topology Workshop at the Korea Advanced Institute of Science and Technology in February 2010. We describe several approaches to moment-angle manifolds and complexes, including the…
We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.
This is a recent conference report on the Kobayashi Problem on hyperbolicity of generic projective hypersurfaces. As an appendix, a (non-updated) author's survey article of 1992 on the same subject, published in an edition with a limited…
We give a precise estimate for the number of lattice points in certain bounded subsets of $\mathbb{R}^{n}$ that involve `hyperbolic spikes' and occur naturally in multiplicative Diophantine approximation. We use Wilkie's o-minimal structure…
This is an expanded version of the author's lecture at the Conference in Commutative Algebra and Algebraic Geometry in Messina Italy in June 1999. The purpose of the talk was to give a brief introduction to the subject of tight closure,…
This is a revised version of a tutorial lecture that I presented at the \`Ecole de Physique des Houches on July 26-31 2020. Topics include Non-parametric Information Geometry, the Statistical bundle, exponential Orlicz spaces, and Gaussian…
These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa,…
We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives…
In these lecture notes I give an elementary introduction to elliptic hypergeometric functions. I focus on motivating the main ideas and constructions, rather than giving a comprehensive survey. The lectures include a brief explanation of…