Frank Calegari | |
---|---|
Alma mater | University of California, Berkeley |
Scientific career | |
Fields | Mathematics |
Institutions | University of Chicago Institute for Advanced Study |
Thesis | Ramification and Semistable Abelian Varieties (2002) |
Doctoral advisor | Ken Ribet |
Notes | |
Brother of Danny Calegari |
Francesco Damien "Frank" Calegari is a professor of mathematics at the University of Chicago working in number theory and the Langlands program.
Calegari won a bronze medal and a silver medal at the International Mathematical Olympiad while representing Australia in 1992 and 1993 respectively. [1] Calegari received his PhD in mathematics from the University of California, Berkeley in 2002 under the supervision of Ken Ribet. [2]
Calegari was a von Neumann Fellow of mathematics at the Institute for Advanced Study from 2010 to 2011. [3] He is a professor of mathematics at the University of Chicago. [4]
As of 2020, Calegari is an Editor at Mathematische Zeitschrift and an Associate Editor of the Annals of Mathematics. [5] [6]
Calegari works in algebraic number theory, including Langlands reciprocity and torsion classes in the cohomology of arithmetic groups. [4]
Calegari was a 5-year American Institute of Mathematics Fellow. [7]
Mathematician Danny Calegari is Frank Calegari's brother. [8]
In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and consequential conjectures about connections between number theory and geometry. Proposed by Robert Langlands, it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Widely seen as the single biggest project in modern mathematical research, the Langlands program has been described by Edward Frenkel as "a kind of grand unified theory of mathematics."
In mathematics, the local Langlands conjectures, introduced by Robert Langlands, are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of G. This correspondence is not a bijection in general. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups.
Danny Matthew Cornelius Calegari is a mathematician and, as of 2023, a professor of mathematics at the University of Chicago. His research interests include geometry, dynamical systems, low-dimensional topology, and geometric group theory.
In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscopic groups. It was conjectured by Robert Langlands (1983) in the course of developing the Langlands program. The fundamental lemma was proved by Gérard Laumon and Ngô Bảo Châu in the case of unitary groups and then by Ngô (2010) for general reductive groups, building on a series of important reductions made by Jean-Loup Waldspurger to the case of Lie algebras. Time magazine placed Ngô's proof on the list of the "Top 10 scientific discoveries of 2009". In 2010, Ngô was awarded the Fields Medal for this proof.
Michael Rapoport is an Austrian mathematician.
In mathematics, the Fontaine–Mazur conjectures are some conjectures introduced by Fontaine and Mazur (1995) about when p-adic representations of Galois groups of number fields can be constructed from representations on étale cohomology groups of a varieties. Some cases of this conjecture in dimension 2 were already proved by Dieulefait (2004).
Kari Kaleva Vilonen is a Finnish mathematician, specializing in geometric representation theory. He is currently a professor at the University of Melbourne.
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Anton Yurevich Alekseev is a Russian mathematician.
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Jacques Tilouine is a professor of mathematics at Université Sorbonne Paris Nord working in number theory and automorphic forms, particularly Iwasawa theory.
Sug Woo Shin is a professor of mathematics at the University of California, Berkeley working in number theory, automorphic forms, and the Langlands program.
Philipp Habegger is a Swiss mathematician and a professor of mathematics at the University of Basel who works in Diophantine geometry.
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