Related papers: Automorphic Forms and the Theta Correspondence
This is an expanded set of notes based on two lectures given by the author at the 2022 IHES summer school on the Langlands program, on explicit techniques for the construction of automorphic representations.
These notes are an extension of the rough notes provided for my four lecture graduate level course on "Quadratic Forms and Automorphic Forms" at the March 2009 Arizona Winter School on Quadratic Forms. They are meant to give a survey of…
Motivated by issues in string theory and M-theory, we provide a pedestrian introduction to automorphic forms and theta series, emphasizing examples rather than generality.
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…
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…
This set of lecture notes is an expanded version of a mini-course the author gave in March of 2025 for the program ``Representation Theory \& Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris. The goal is to provide a survey…
These are the notes from my courses on the arithmetic of quadratic forms.
This is my talk delivered at the workshop 'Automorphic L-Functions and related prpblems' (March 10--13, 2012, Tokyo University). We showed an instance of applications of the theory of automorphic representations to a genuinely traditional…
A general framework of constructions of endoscopy correspondences via automorphic integral transforms for classical groups is formulated in terms of the Arthur classification of the discrete spectrum of square-integrable automorphic forms.…
In our previous paper we gave proofs of Ibukiyama's correspondences on holomorphic Siegel modular forms of degree 2 of half-integral weight and integral weight. In this paper, we formulate and prove similar correspondences on automorphic…
This is a note constructing a certain weight 4 automorphic form on the moduli space of cubic surfaces, posted here because it is referred to in math.AG/0002066
We describe some recent developments and formulate some conjectures in the genuine representation theory and the study of automorphic forms of the metaplectic group $\mathrm{Mp}(2n)$, from the point of view of the theta correspondence as…
The classical theta correspondence establishes a relationship between automorphic representations on special orthogonal groups and automorphic representations on symplectic groups or their double covers. This correspondence is achieved by…
These are lectures given at the 2022 Arizona Winter School. It gives an introduction to the rigidity method for constructing automorphic forms for semisimple groups over function fields. The rigidity method leads to explicit constructions…
These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets.
This article is a brief survey of the theory of topological modular forms (TMF) and the theory of topological automorphic forms (TAF). It will be a chapter in forthcoming "Handbook of Homotopy Theory" edited by Haynes Miller.
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
This set of lecture notes on local theta correspondence is the written version of a mini-course the author gave in March of 2025 for the program ``Representation Theory and Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris.…
The zeros and poles of standard automorphic $L$-functions attached to representations of classical groups are linked to the nonvanishing of lifts in the theory of the theta correspondence. The results of this paper show that when a cuspidal…
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…