Related papers: Park City lectures on Eigenfunctions

The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and…

These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…

Special functions have always played a central role in physics and in mathematics, arising as solutions of particular differential equations, or integrals, during the study of particular important physical models and theories in Quantum…

Talk given at ICM '98, Berlin, reviewing some of the recent developments in understanding of string theory for a mathematical audience (to appear in Documenta Mathematica).

We find an infinite set of eigenfunctions for the Laplacian with respect to a flat metric with conical singularities and acting on degree zero bundles over special Riemann surfaces of genus greater than one. These special surfaces…

These are the notes for an eponymous course given by the authors at the summer school on p-adic arithmetic geometry in Hangzhou.

These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and…

These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of root systems, generalized associahedra, and the combinatorics of clusters. Lectures 1-2 cover classical material:…

This is a remark on a recent post by P. Denton, S. Parke, T. Tao, X. Zhang, Eigenvectors from eigenvalues, arXiv:1908.03795v1

This is an essay to accompany the author's lecture at the introductory workshop on `Nonabelian fundamental groups in arithmetic geometry' at the Newton Institute, Cambridge in July, 2009.

These lecture notes were prepared as a basic introduction to the theory of constrained systems which is how the fundamental forces of nature appear in their Hamiltonian formulation. Only a working knowledge of Lagrangian and Hamiltonian…

For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is…

The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the…

This manuscript provides a more detailed treatment of the material from my lecture series at the 2022 Arizona Winter School on Automorphic Forms Beyond $GL_2$. The main focus of this manuscript is automorphic forms on unitary groups, with a…

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…

This is a series of lecture notes explaining topos theory and its application in physics.

This paper, which is a summary (in which considerable creative license has been taken) of the author's talk at the sixth international conference on $p$-adic mathematical physics and its applications (CINVESTAV, Mexico City, October 2017),…

A modestly revised version of lecture notes that were distributed to accompany my four lectures at the 2017 Spring School of Analysis at Paseky, sponsored by Charles University, Prague. They are an introductory survey of Rubio de Francia…

To be published in the proceedings of IAU Symposium 239 "Convection in Astrophysics" (ed. F. Kupka, I. W. Roxburgh, K. L. Chan). Content: 1. From Nice to Prague, 2. The triumph of 3-D simulations, 3. How to lower the cost - what else can be…

This work details worked solutions to the various problems set by the lecturers during the course of the Les Houches summer school 2017 on effective field theories in particle physics and cosmology.