About

Kiran Kedlaya received his Ph.D. in Mathematics from MIT in 2000. For the next three years, he held postdoctoral positions at the Mathematical Sciences Research Institute in Berkeley, at the University of California at Berkeley, and at the Institute for Advanced Study in Princeton. Since then, Kedlaya has been a faculty member at MIT, first as Assistant Professor and then as Associate Professor. Kedlaya is an expert on a broad range of topics related to arithmetic algebraic geometry and number theory, especially p-adic cohomology, p-adic Hodge theory, and computational number theory.

Research topics

• Biology
• Mathematical economics
• Economics
• Ecology

Selected publications

• Compatibility of $F$-isocrystals on adjoint Shimura varieties

  ArXiv.org · 2025-04-25

  preprintOpen access

  In this article, we extend past results of the last two authors to include compatibility of canonical $\ell$-adic local systems and canonical $F$-isocrystals on adjoint Shimura varieties in the superrigid regime. Our method relies on the crystallinity of canonical $p$-adic local systems due to Esnault--Groechenig as well as Margulis superrigidity and the crystalline-to-étale companion construction of Drinfeld and Kedlaya.

  PublisherOA PDFDOI

• Sato–Tate Groups of Abelian Threefolds

  Memoirs of the American Mathematical Society · 2025-07-23 · 5 citations

  articleOpen access

  Given an abelian variety over a number field, its Sato–Tate group is a compact Lie group which conjecturally controls the distribution of Euler factors of the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -function of the abelian variety. It was previously shown by Fité, Kedlaya, Rotger, and Sutherland that there are 52 groups (up to conjugation) that occur as Sato–Tate groups of abelian surfaces over number fields; we show here that for abelian threefolds, there are 410 possible Sato–Tate groups, of which 33 are maximal with respect to inclusions of finite index. We enumerate candidate groups using the Hodge-theoretic construction of Sato–Tate groups, the classification of degree-3 finite linear groups by Blichfeldt, Dickson, and Miller, and a careful analysis of Shimura’s theory of CM types that rules out 23 candidate groups; we cross-check this using extensive computations in <sc>GAP</sc> , <sc>SageMath</sc> , and <sc>Magma</sc> . To show that these 410 groups all occur, we exhibit explicit examples of abelian threefolds realizing each of the 33 maximal groups; we also compute moments of the corresponding distributions and numerically confirm that they are consistent with the statistics of the associated <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -functions.

  PublisherOA PDFDOI

• The William Lowell Putnam Mathematical Competition 2001–2016

  2020

  1st authorCorresponding
  • Mathematical economics
  • Economics
  • Biology
  PublisherDOI

• COM volume 153 Issue 12 Cover and Back matter

  Compositio Mathematica · 2017-11-17

  paratextOpen access

  An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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• An application of the effective Sato-Tate conjecture

  Contemporary mathematics - American Mathematical Society · 2016-01-01 · 17 citations

  otherOpen accessSenior authorCorresponding

  Based on the Lagarias-Odlyzko effectivization of the Chebotarev density theorem, Kumar Murty gave an effective version of the Sato-Tate conjecture for an elliptic curve conditional on analytic continuation and Riemann hypothesis for the symmetric power Lfunctions. We use Murty's analysis to give a similar conditional effectivization of the generalized Sato-Tate conjecture for an arbitrary motive. As an application, we give a conditional upper bound of the form O((log N ) 2 (log log 2N ) 2 ) for the smallest prime at which two given rational elliptic curves with conductor at most N have Frobenius traces of opposite sign.

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• Motivic Serre group, algebraic Sato-Tate group and Sato-Tate conjecture

  Contemporary mathematics - American Mathematical Society · 2016-01-01 · 7 citations

  otherSenior authorCorresponding

  We make explicit Serre's generalization of the Sato-Tate conjecture for motives, by expressing the construction in terms of fiber functors from the motivic category of absolute Hodge cycles into a suitable category of Hodge structures of odd weight.This extends the case of abelian varietes, which we treated in a previous paper.That description was used by Fité-Kedlaya-Rotger-Sutherland to classify Sato-Tate groups of abelian surfaces; the present description is used by Fité-Kedlaya-Sutherland to make a similar classification for certain motives of weight 3. We also give conditions under which verification of the Sato-Tate conjecture reduces to the identity connected component of the corresponding Sato-Tate group.

  PublisherDOI

• Sato-Tate groups of some weight 3 motives

  Contemporary mathematics - American Mathematical Society · 2016-01-01 · 16 citations

  otherOpen accessCorresponding

  We establish the group-theoretic classification of Sato-Tate groups of\nself-dual motives of weight 3 with rational coefficients and Hodge numbers\nh^{3,0} = h^{2,1} = h^{1,2} = h^{0,3} = 1. We then describe families of motives\nthat realize some of these Sato-Tate groups, and provide numerical evidence\nsupporting equidistribution. One of these families arises in the middle\ncohomology of certain Calabi-Yau threefolds appearing in the Dwork quintic\npencil; for motives in this family, our evidence suggests that the Sato-Tate\ngroup is always equal to the full unitary symplectic group USp(4).

  PublisherOA PDFDOI

• Putnam Trivia for the Nineties

  American Mathematical Society eBooks · 2002-01-16

  book-chapterOpen access1st authorCorresponding
  PublisherOA PDFDOI

• Solutions

  American Mathematical Society eBooks · 2002-01-16

  book-chapter1st authorCorresponding
  PublisherDOI

• The William Lowell Putnam Mathematical Competition 1985–2000

  American Mathematical Society eBooks · 2002-01-16 · 16 citations

  book1st authorCorresponding
  PublisherDOI

Frequent coauthors

• Bjorn Poonen

  Massachusetts Institute of Technology

  4 shared

• Ravi Vakil

  4 shared

• Kazuhiro Fujiwara

  The University of Tokyo

  2 shared

• Evan M. O’Dorney

  1 shared

• Shigeyuki Kondō

  1 shared

• Jonathan S. Kane

  University of Wisconsin–Madison

  1 shared

• Shigeru Mukai

  1 shared

• Шигефуми Мори

  1 shared

Awards & honors

• International Congress of Mathematicians Speaker - 2010
• Fellow of the American Mathematical Society
• Alfred P. Sloan Research Fellowship
• Presidential Early Career Award for Scientists and Engineers
• Clay Liftoff Fellowship