Jordan S. Ellenberg

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Jordan S. Ellenberg is an American mathematician and author known for his work in number theory and algebraic geometry. He is a professor of mathematics at the University of Wisconsin–Madison. Ellenberg has made significant contributions to arithmetic geometry and has published numerous research papers in prestigious mathematical journals.


In addition to his academic work, Ellenberg is recognized for his ability to communicate complex mathematical ideas to a general audience. He is the author of the bestselling book "How Not to Be Wrong: The Power of Mathematical Thinking" (2014), which explores the profound ways in which mathematical thinking influences our understanding of the world. In 2021, he published "Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else," where he delves into the role of geometry in various fields and its impact on modern life.


Ellenberg has also written articles and essays for publications like The New York Times, The Wall Street Journal, and Slate, where he discusses mathematical concepts and their relevance to everyday life and current events. He is known for his engaging writing style that makes mathematics accessible and interesting to a broad audience.


As a young mathematician, Ellenberg demonstrated exceptional talent by earning gold medals at the International Mathematical Olympiad. He holds a Ph.D. from Harvard University and has been influential both as a researcher and an educator, inspiring many through his teaching and public outreach efforts in mathematics.

All published works
Action Title Year Authors
+ PDF Chat Certifying nontriviality of Ceresa classes of curves 2024 Jordan S. Ellenberg
Adam Logan
P. Srinivasan
+ PDF Chat PatternBoost: Constructions in Mathematics with a Little Help from AI 2024 François Charton
Jordan S. Ellenberg
Ascher Wagner
Geordie Williamson
+ PDF Chat THE CERESA CLASS: TROPICAL, TOPOLOGICAL AND ALGEBRAIC 2023 Daniel Corey
Jordan S. Ellenberg
Wanlin Li
+ PDF Heights on stacks and a generalized Batyrev–Manin–Malle conjecture 2023 Jordan S. Ellenberg
Matthew Satriano
David Zureick-Brown
+ Homological stability for generalized Hurwitz spaces and Selmer groups in quadratic twist families over function fields 2023 Jordan S. Ellenberg
Aaron Landesman
+ PDF Chat Sparsity of Integral Points on Moduli Spaces of Varieties 2022 Jordan S. Ellenberg
Brian Lawrence
Akshay Venkatesh
+ Intracounty modeling of COVID-19 infection with human mobility: Assessing spatial heterogeneity with business traffic, age, and race 2021 Xiao Hua Hou
Song Gao
Qin Li
Yuhao Kang
Nan Chen
Kaiping Chen
Jinmeng Rao
Jordan S. Ellenberg
Jonathan A. Patz
+ PDF Chat Rational Points on Solvable Curves over ℚ via Non-Abelian Chabauty 2021 Jordan S. Ellenberg
Daniel Rayor Hast
+ Heights on stacks and a generalized Batyrev-Manin-Malle conjecture 2021 Jordan S. Ellenberg
Matthew Satriano
David Zureick-Brown
+ Sparsity of Integral Points on Moduli Spaces of Varieties 2021 Jordan S. Ellenberg
Brian Lawrence
Akshay Venkatesh
+ PDF Geometry, inference, complexity, and democracy 2020 Jordan S. Ellenberg
+ Intra-county modeling of COVID-19 infection with human mobility: assessing spatial heterogeneity with business traffic, age and race 2020 Xiao Hua Hou
Song Gao
Qin Li
Yuhao Kang
Nan Chen
Kaiping Chen
Jinmeng Rao
Jordan S. Ellenberg
Jonathan A. Patz
+ PDF Chat Nonvanishing of hyperelliptic zeta functions over finite fields 2020 Jordan S. Ellenberg
Wanlin Li
Mark Shusterman
+ Geometry, Inference, Complexity, and Democracy 2020 Jordan S. Ellenberg
+ The Ceresa class: tropical, topological, and algebraic 2020 Daniel Corey
Jordan S. Ellenberg
Wanlin Li
+ Geometry, Inference, Complexity, and Democracy 2020 Jordan S. Ellenberg
+ Convergence rates for ordinal embedding 2019 Jordan S. Ellenberg
Lalit Jain
+ Convergence rates for ordinal embedding 2019 Jordan S. Ellenberg
Lalit Jain
+ PDF Sumsets as unions of sumsets of subsets 2018 Jordan S. Ellenberg
+ Approximate Gradient Coding via Sparse Random Graphs 2017 Zachary Charles
Dimitris Papailiopoulos
Jordan S. Ellenberg
+ PDF Chat On ℓ-torsion in class groups of number fields 2017 Jordan S. Ellenberg
Lillian B. Pierce
Melanie Matchett Wood
+ Rational points on solvable curves over $\mathbb{Q}$ via non-abelian Chabauty 2017 Jordan S. Ellenberg
Daniel Rayor Hast
+ PDF Chat Homology of FI-modules 2017 Thomas M. Church
Jordan S. Ellenberg
+ Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle's conjecture for function fields 2017 Jordan S. Ellenberg
TriThang Tran
Craig Westerland
+ Approximate Gradient Coding via Sparse Random Graphs 2017 Zachary Charles
Dimitris Papailiopoulos
Jordan S. Ellenberg
+ Fox-Neuwirth-Fuks cells, quantum shuffle algebras, and Malle's conjecture for function fields 2017 Jordan S. Ellenberg
TriThang Tran
Craig Westerland
+ Sumsets as unions of sumsets of subsets 2016 Jordan S. Ellenberg
+ PDF On large subsets of $\mathbb{F}_q^n$ with no three-term arithmetic progression 2016 Jordan S. Ellenberg
Dion Gijswijt
+ PDF New bounds on curve tangencies and orthogonalities 2016 Jordan S. Ellenberg
József Solymosi
Joshua Zahl
+ New bounds on curve tangencies and orthogonalities 2016 Jordan S. Ellenberg
József Solymosi
Joshua Zahl
+ PDF Furstenberg sets and Furstenberg schemes over finite fields 2016 Jordan S. Ellenberg
Daniel Erman
+ On large subsets of $F_q^n$ with no three-term arithmetic progression 2016 Jordan S. Ellenberg
Dion Gijswijt
+ PDF Chat Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields 2016 Jordan S. Ellenberg
Akshay Venkatesh
Craig Westerland
+ PDF AN INCIDENCE CONJECTURE OF BOURGAIN OVER FIELDS OF POSITIVE CHARACTERISTIC 2016 Jordan S. Ellenberg
Márton Hablicsek
+ On large subsets of $F_q^n$ with no three-term arithmetic progression 2016 Jordan S. Ellenberg
Dion Gijswijt
+ Sumsets as unions of sumsets of subsets 2016 Jordan S. Ellenberg
+ PDF Chat FI-modules and stability for representations of symmetric groups 2015 Thomas M. Church
Jordan S. Ellenberg
Benson Farb
+ Detection of Planted Solutions for Flat Satisfiability Problems 2015 Quentin Berthet
Jordan S. Ellenberg
+ Algebraic structures on cohomology of configuration spaces of manifolds with flows 2015 Jordan S. Ellenberg
John D. Wiltshire-Gordon
+ Detection of Planted Solutions for Flat Satisfiability Problems 2015 Quentin Berthet
Jordan S. Ellenberg
+ New bounds on curve tangencies and orthogonalities 2015 Jordan S. Ellenberg
József Solymosi
Joshua Zahl
+ PDF FI-modules over Noetherian rings 2014 Thomas M. Church
Jordan S. Ellenberg
Benson Farb
Rohit Nagpal
+ PDF Chat Representation stability in cohomology and asymptotics for families of varieties over finite fields 2014 Thomas M. Church
Jordan S. Ellenberg
Benson Farb
+ An incidence conjecture of Bourgain over fields of positive characteristic 2013 Jordan S. Ellenberg
Márton Hablicsek
+ The Beauty of Bounded Gaps: A Huge Discovery about Prime Numbers and What It Means for the Future of Mathematics 2013 Jordan S. Ellenberg
+ Random Dieudonné modules, random -divisible groups, and random curves over finite fields 2013 Bryden Cais
Jordan S. Ellenberg
David Zureick-Brown
+ An incidence conjecture of Bourgain over fields of positive characteristic 2013 Jordan S. Ellenberg
Márton Hablicsek
+ Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II 2012 Jordan S. Ellenberg
Akshay Venkatesh
Craig Westerland
+ Superstrong approximation for monodromy groups 2012 Jordan S. Ellenberg
+ PDF Chat Expander graphs, gonality, and variation of Galois representations 2012 Jordan S. Ellenberg
Chris Hall
Emmanuel Kowalski
+ FI-modules: a new approach to stability for S_n-representations 2012 Thomas M. Church
Jordan S. Ellenberg
Benson Farb
+ PDF Chat Arithmetic Veech sublattices of SL(2,Z) 2012 Jordan S. Ellenberg
D. B. McReynolds
+ PDF Chat Arithmetic Veech sublattices of $\operatorname{SL}(2,\mathbf{Z})$ 2012 Jordan S. Ellenberg
D. B. McReynolds
+ Random Dieudonne modules, random p-divisible groups, and random curves over finite fields 2012 Bryden Cais
Jordan S. Ellenberg
David Zureick-Brown
+ Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II 2012 Jordan S. Ellenberg
Akshay Venkatesh
Craig Westerland
+ Superstrong approximation for monodromy groups 2012 Jordan S. Ellenberg
+ Random Dieudonne modules, random p-divisible groups, and random curves over finite fields 2012 Bryden Cais
Jordan S. Ellenberg
David Zureick-Brown
+ Modeling λ‐invariants by <i>p</i>‐adic random matrices 2011 Jordan S. Ellenberg
Sonal Jain
Akshay Venkatesh
+ Statistics of Number Fields and Function Fields 2011 Akshay Venkatesh
Jordan S. Ellenberg
+ PDF Random pro-$p$ groups, braid groups, and random tame Galois groups 2011 Nigel Boston
Jordan S. Ellenberg
+ III.21 Elliptic Curves 2010 Jordan S. Ellenberg
+ IV.5 Arithmetic Geometry 2010 Jordan S. Ellenberg
+ THE DIOPHANTINE EQUATION A<sup>4</sup> + 2<sup>δ</sup>B<sup>2</sup> = C<sup>n</sup> 2010 Michael A. Bennett
Jordan S. Ellenberg
Nathan Ng
+ PDF Positive motivic measures are counting measures 2010 Jordan S. Ellenberg
Michael Larsen
+ Upper bounds for the growth of Mordell-Weil ranks in pro-p towers of Jacobians 2010 Jordan S. Ellenberg
+ Linnik's ergodic method and the distribution of integer points on spheres 2010 Jordan S. Ellenberg
Philippe Michel
Akshay Venkatesh
+ PDF A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ 2010 Jordan S. Ellenberg
Julianna Tymoczko
+ PDF Chat THE KAKEYA SET AND MAXIMAL CONJECTURES FOR ALGEBRAIC VARIETIES OVER FINITE FIELDS 2009 Jordan S. Ellenberg
Richard Oberlin
Terence Tao
+ Every curve is a Teichm ¨ uller curve 2009 Jordan S. Ellenberg
D. B. McReynolds
+ PDF Non-simple abelian varieties in a family: geometric and analytic approaches 2009 Jordan S. Ellenberg
Christian Elsholtz
Chris Hall
Emmanuel Kowalski
+ Positive motivic measures are counting measures 2009 Jordan S. Ellenberg
Michael Larsen
+ Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields 2009 Jordan S. Ellenberg
Akshay Venkatesh
Craig Westerland
+ Non-simple abelian varieties in a family: geometric and analytic approaches 2008 Jordan S. Ellenberg
Christian Elsholtz
Chris Hall
Emmanuel Kowalski
+ Points of low height on ℙ¹ over number fields and bounds for torsion in class groups 2008 Jordan S. Ellenberg
+ PDF Chat Local-global principles for representations of quadratic forms 2007 Jordan S. Ellenberg
Akshay Venkatesh
+ Counting maximal arithmetic subgroups 2007 Mikhail Belolipetsky
Jordan S. Ellenberg
Akshay Venkatesh
+ PDF Asymptotics of coinvariants of Iwasawa modules under non-normal subgroups 2007 Jordan S. Ellenberg
Adam Logan
+ Reflection Principles and Bounds for Class Group Torsion 2007 Jordan S. Ellenberg
Akshay Venkatesh
+ PDF Selmer groups and Mordell–Weil groups of elliptic curves over towers of function fields 2006 Jordan S. Ellenberg
+ Counting extensions of function fields with bounded discriminant and specified Galois group 2006 Jordan S. Ellenberg
Akshay Venkatesh
+ PDF Pro–<i>p</i>groups and towers of rational homology spheres 2006 Nigel Boston
Jordan S. Ellenberg
+ PDF The number of extensions of a number field with fixed degree and bounded discriminant 2006 Jordan S. Ellenberg
Akshay Venkatesh
+ PDF On the Error Term in Duke's Estimate for the Average Special Value of <i>L</i>-Functions 2005 Jordan S. Ellenberg
+ Corrigendum to "Galois representations attached to Q-curves and the generalized Fermat equation A 4 + B 2 = C p" 2005 Jordan S. Ellenberg
+ PDF Serre’s conjecture over 𝔽<sub>9</sub> 2005 Jordan S. Ellenberg
+ A sharp diameter bound for unipotent groups of classical type over Z/pZ 2005 Jordan S. Ellenberg
Julianna Tymoczko
+ PDF Chat Galois representations attached to [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-curves and the generalized Fermat equation A 4 + B 2 = C P 2004 Jordan S. Ellenberg
+ ℚ-Curves and Galois Representations 2004 Jordan S. Ellenberg
+ PDF K3 Surfaces Over Number Fields with Geometric Picard Number One 2004 Jordan S. Ellenberg
+ PDF On the average number of octahedral modular forms 2003 Jordan S. Ellenberg
+ Galois representations attached to Q-curves and the generalized Fermat equation A^4 + B^2 = C^p 2003 Jordan S. Ellenberg
+ On the error term in Duke's estimate for the average special value of L-functions 2003 Jordan S. Ellenberg
+ The number of extensions of a number field with fixed degree and bounded discriminant 2003 Jordan S. Ellenberg
Akshay Venkatesh
+ PDF Galois invariants of dessins d’enfants 2002 Jordan S. Ellenberg
+ Endomorphism Algebras of Jacobians 2001 Jordan S. Ellenberg
+ On the modularity of ℚ-curves 2001 Jordan S. Ellenberg
Chris Skinner
+ On the modularity of ?-curves 2001 Chris Skinner
Jordan S. Ellenberg
+ Finite flatness of torsion subschemes of Hilbert-Blumenthal abelian varieties 2001 Jordan S. Ellenberg
+ Serre's conjecture over F_9 2001 Jordan S. Ellenberg
+ Congruence ABC implies ABC 2000 Jordan S. Ellenberg
+ Congruence ABC implies ABC 1999 Jordan S. Ellenberg
Common Coauthors
Commonly Cited References
Action Title Year Authors # of times referenced
+ The critical order of vanishing of automorphicL-functions with large level 1995 William Duke
6
+ PDF Chat Galois representations attached to [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-curves and the generalized Fermat equation A 4 + B 2 = C P 2004 Jordan S. Ellenberg
5
+ Endlichkeitss�tze f�r abelsche Variet�ten �ber Zahlk�rpern 1983 Герд Фалтингс
5
+ PDF Growth and generation in SL<sub>2</sub>(ℤ∕pℤ) 2008 H. A. Helfgott
4
+ Twists of newforms and pseudo-eigenvalues ofW-operators 1978 A. O. L. Atkin
W Li
4
+ On the size of Kakeya sets in finite fields 2008 Zeev Dvir
4
+ On the density of discriminants of cubic fields. II 1971 H. Davenport
H. Heilbronn
4
+ Representation theory and homological stability 2013 Thomas M. Church
Benson Farb
4
+ On the Distribution of Galois Groups 2002 Gunter Malle
4
+ PDF Chat Finite covers of random 3-manifolds 2006 Nathan M. Dunfield
William P. Thurston
4
+ PDF Chat FI-modules and stability for representations of symmetric groups 2015 Thomas M. Church
Jordan S. Ellenberg
Benson Farb
4
+ Density of discriminants of cubic extensions. 1988 B. Datskovsky
D. J. Wright
4
+ PDF Recent work connected with the Kakeya problem 2003 Thomas Wolff
4
+ On the modularity of ℚ-curves 2001 Jordan S. Ellenberg
Chris Skinner
4
+ On Sets of Integers Which Contain No Three Terms in Arithmetical Progression 1946 Felix Behrend
4
+ Bounds for arithmetic multiplicities 1998 William Duke
4
+ PDF Lectures on the Mordell-Weil Theorem 1989 Jean-Pierre Serre
4
+ PDF The inverse Galois problem and rational points on moduli spaces 1991 Michael D. Fried
Helmut V�lklein
4
+ Éléments de géométrie algébrique 1964 Alexandre Grothendieck
4
+ On the 4-rank of class groups of quadratic number fields 2006 Étienne Fouvry
Jürgen Klüners
3
+ PDF Noncongruence subgroups in H(2) 2005 Pascal Hubert
Samuel Lelièvre
3
+ PDF The congruence subgroup property for Aut $F_2$: A group-theoretic proof of Asada’s theorem 2011 Kai‐Uwe Bux
Mikhail Ershov
Andrei S. Rapinchuk
3
+ Composition Factors of Monodromy Groups 2001 Daniel Frohardt
Kay Magaard
3
+ PDF Teichmüller curves, triangle groups, and Lyapunov exponents 2010 Irene I. Bouw
Martin Möller
3
+ Advanced Topics in the Arithmetic of Elliptic Curves 1994 Joseph H. Silverman
3
+ PDF Comparison Techniques for Random Walk on Finite Groups 1993 Persi Diaconis
Laurent Saloff‐Coste
3
+ Residually reducible representations and modular forms 1999 Christopher Skinner
Andrew Wiles
3
+ The faithfulness of the monodromy representations associated with certain families of algebraic curves 2001 Mamoru Asada
3
+ Every curve is a Hurwitz space 1989 Steven Diaz
Ron Donagi
David Harbater
3
+ PDF Nearly ordinary deformations of irreducible residual representations 2001 Claire Skinner
Andrew Wiles
3
+ Affine mappings of translation surfaces: geometry and arithmetic 2000 Eugène Gutkin
Chris Judge
3
+ On the distribution of divisor class groups of curves over a finite field 1989 Eduardo Friedman
Lawrence C. Washington
3
+ Big symplectic or orthogonal monodromy modulo ℓ 2007 Chris Hall
3
+ The Distribution of Galois Groups and Hilbert's Irreducibility Theorem 1981 Stephen D. Cohen
3
+ PDF On the ring of Hilbert modular forms over Z 1983 Shōyū Nagaoka
3
+ PDF Finding rational points on bielliptic genus 2 curves 1999 E. V. Flynn
Joseph L. Wetherell
3
+ On Relations between Jacobians of Certain Modular Curves 2000 Imin Chen
3
+ PDF On the Error Term in Duke's Estimate for the Average Special Value of <i>L</i>-Functions 2005 Jordan S. Ellenberg
3
+ On Deformation Rings and Hecke Rings 1996 Fred Diamond
3
+ Arithmetic moduli of elliptic curves 1985 Nicholas M. Katz
Barry Mazur
3
+ ON ARITHMETIC CURVES IN THE MODULI SPACES OF CURVES 2005 Pierre Lochak
3
+ Topics in Classical Automorphic Forms 1997 Henryk Iwaniec
3
+ Teichm�ller curves in moduli space, Eisenstein series and an application to triangular billiards 1989 William A. Veech
3
+ Distribution of Discriminants of Abelian Extensions 1989 D. J. Wright
3
+ PDF None 1999 Nils Bruin
3
+ Cohomology of Number Fields 2008 Jürgen Neukirch
Alexander Schmidt
Kay Wingberg
3
+ Teichmüller curves, Galois actions and $ \widehat {GT} $‐relations 2005 Martin Möller
3
+ PDF Mod 2 and mod 5 icosahedral representations 1997 N. I. Shepherd-Barron
Richard Taylor
3
+ Sur les représentations modulaires de degré 2 de Gal(Q¯/Q) 1987 Jean-Pierre Serre
3
+ Closed trajectories for quadratic differentials with an application to billiards 1986 Howard Masur
3