About

Matthew Emerton is a professor in the Department of Mathematics at the University of Chicago. His area of research is number theory. The page provides links to his preprints, papers, and additional information about his research, indicating his active engagement in mathematical research and scholarship. He also offers educational resources such as homework sheets and notes for various courses, including first-year algebra, class field theory, and prismatic cohomology, reflecting his involvement in teaching and mentoring students. His professional profile includes his contact information and links to colleagues and collaborators, emphasizing his active participation in the mathematical community.

Research topics

• Mathematics
• Pure mathematics
• Artificial Intelligence
• Sociology
• Mathematical analysis
• Computer Science
• Geometry
• Discrete mathematics
• Combinatorics

Selected publications

• A categorical p-adic Langlands correspondence for GL_2(Q_p)

  arXiv (Cornell University) · 2026-03-27

  preprintOpen access

  Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a derived category of Ind-coherent sheaves on a stack of (phi,Gamma)-modules.

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• A categorical p-adic Langlands correspondence for GL_2(Q_p)

  arXiv (Cornell University) · 2026-03-27

  articleOpen access

  Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a derived category of Ind-coherent sheaves on a stack of (phi,Gamma)-modules.

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• EXPLICIT RECIPROCITY LAWS AND IWASAWA THEORY FOR MODULAR FORMS

  Duke Mathematical Journal · 2025-08-15

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• An introduction to the categorical 𝑝-adic Langlands program

  Proceedings of symposia in pure mathematics · 2025-12-03

  other1st authorCorresponding

  We give an introduction to the “categorical” approach to the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -adic Langlands program, in both the “Banach” and “analytic” settings.

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• The geometric Breuil–Mézard conjecture fortwo-dimensional potentially Barsotti–Tate Galois representations

  Algebra & Number Theory · 2025-01-31 · 1 citations

  articleOpen access

  We establish a geometrization of the Breuil-Mzard conjecture for potentially Barsotti-Tate representations, as well as of the weight part of Serre's conjecture, for moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field.These results are first proved for the stacks of our earlier papers, and then transferred to the stacks of Emerton and Gee by means of a comparison of versal rings.r / 297 5.A case of the classical geometric Breuil-Mzard conjecture 300 6.The geometric Breuil-Mzard conjecture for the stacks Z dd,1 303 7. The geometric Breuil-Mzard conjecture for the stacks X 2,red 305 Appendix: A lemma on formal algebraic stacks 308

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• Components of moduli stacks of two-dimensional Galois representations

  Forum of Mathematics Sigma · 2024-01-01 · 1 citations

  articleOpen access

  Abstract In the article [CEGS20b], we introduced various moduli stacks of two-dimensional tamely potentially Barsotti–Tate representations of the absolute Galois group of a p -adic local field, as well as related moduli stacks of Breuil–Kisin modules with descent data. We study the irreducible components of these stacks, establishing, in particular, that the components of the former are naturally indexed by certain Serre weights.

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• Appendix F Breuil–Kisin–Fargues modules and potentially semistable representations (by Toby Gee and Tong Liu)

  Princeton University Press eBooks · 2022-11-11

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  Appendix F Breuil–Kisin–Fargues modules and potentially semistable representations (by Toby Gee and Tong Liu) was published in Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts on page 279.

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• Appendix B Graded modules and rigid analysis

  Princeton University Press eBooks · 2022-11-11

  book-chapter1st authorCorresponding
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• Index

  Princeton University Press eBooks · 2022-11-11

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• Chapter Two Rings and coefficients

  Princeton University Press eBooks · 2022-11-11

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Recent grants

• Automorphic Forms and Galois Representations

  NSF · $390k · 2019–2023

• P-adic aspects of the Langlands program

  NSF · $110k · 2012–2014

• p-adic aspects of the Langlands program

  NSF · $320k · 2013–2017

• P-adic Aspects of the Langlands Program

  NSF · $330k · 2016–2020

• p-adic Aspects of the Langlands Program

  NSF · $186k · 2007–2010

Frequent coauthors

• Toby Gee

  46 shared

• Frank Calegari

  23 shared

• Vytautas Paškūnas

  11 shared

• Ana Caraiani

  Imperial College London

  10 shared

• David Savitt

  Johns Hopkins University

  9 shared

• Davide A. Reduzzi

  University of Chicago

  7 shared

• Liang Xiao

  7 shared

• David Helm

  5 shared

Education

• B.S.

  University of Melbourne

• Ph.D.

  Harvard University