David P. Roberts

A presentation I gave several years ago for non-mathematicians gives a good sense of my approach to research. Publications, preprints, and talks:

Publications and Preprints

Listed in reverse chronological order. Documents posted here usually differ slightly from the published versions.

Preprints

Mixed degree number fields computations, with John Jones

PDF, 16 pages.

Chebyshev covers and exceptional number fields.

PDF, 22 pages.

Rigid Jordan tuples.

dvi ps, 17 pages.

Publications

34. PGL₂(F_l) number fields with rational companion forms

PDF, to appear in International Journal of Number Theory, 18 pages.

33. Newforms with rational coefficients

PDF, to appear in the Ramanujan journal, 23 pages.

32. Artin L-functions of small conductor, with John Jones.

PDF, to appear in Research in Number Theory, 32 pages.

31. A three-parameter clan of Hurwitz-Belyi maps

PDF , to appear in Publications Mathématiques de Besançon, Algèbre et Théorie des Nombres. Accompanying Mathematica File.

30. Hurwitz-Belyi maps

PDF , to appear in Publications Mathématiques de Besançon, Algèbre et Théorie des Nombres. Accompanying Mathematica File.

29. Hurwitz number fields

PDF , New York Journal of Mathematics 23 (2017) 227-272. Accompanying Mathematica File.

28. Serre weights and wild ramification in two-dimensional Galois representations, with Lassina Dembélé and Fred Diamond

PDF, Forum Math. Sigma 4 (2016), e33, 49 pages.

27. Hurwitz monodromy and full number fields with Akshay Venkatesh.

PDF , Algebra and Number Theory 9 (2015), no. 4, 1115-1148.

26. Division polynomials with Galois group SU3(3).2 = G2(2)

PDF , Advances in the theory of numbers, 169–206, Fields Inst. Commun., 77. Accompanying Mathematica File.

25. Polynomials with prescribed bad primes

PDF, International Journal of Number Theory 11 (2015), no. 4, 1115-1148.

24. Lightly ramified number fields with Galois group S.M12.A

PDF, J. Théor. Nombres Bordeaux 28 (2016), no. 2, 435–460.

23. A database of number fields, with John Jones.

PDF, London Journal of Mathematics and Computation, 17 (1) (2014) 595--618. Database at http://hobbes.la.asu.edu/NFDB/.

22. The tame-wild principle for discriminant relations for number fields, with John Jones.

PDF, Algebra and Number Theory 8 (2014), no. 3, 609-645.

21. Nonsolvable polynomials with field discriminant 5A

PDF, International Journal of Number Theory 7 (2011), 289-322. File containing polynomials

20. Octic 2-adic fields, with John Jones.

PDF, Journal of Number Theory 128 (2008), 1410-1429.

19. Number fields ramified at one prime, with John Jones.

PDF, ANTS VIII, Springer Lecture Notes in Computer Sciences 5011 (2008), 226-239.

18. Intersection numbers of Heegner divisors on Shimura curves, with Kevin Keating.

PDF, Pure and Applied Mathematics Quarterly, Vol. 4 Num. 4 (2008), 1165-1204.

17. Wild partitions and number theory.

PDF, ps, dvi, Journal of Integer Sequences, Vol. 10, (2007), Article 07.6.6, 34 pages.

16. Nash equilibria in Cauchy-random zero-sum and coordination matrix games.

PDF, International Journal of Game Theory, 34 (2006), 167-184.

15. Galois number fields with small root discriminant, with John Jones.

PDF, Journal of Number Theory, 122 (2007), 379-407.

14. Fractalized cyclotomic polynomials.

PDF, Proceedings of the American Mathematical Society, 135 (2007), 1959-1967.

13. A database of local fields, with John Jones.

PDF, Journal of Symbolic Computation, Volume 41 no. 1 (2006), 80-97. Database at http://math.la.asu.edu/~jj/localfields .

12.Pure Nash equilibria of coordination matrix games.

PDF, Economics Letters, Volume 89, Issue 1 (2005), 7-11.

11. Number fields with discriminant ±2a3b and Galois group An or Sn, with Gunter Malle.

PDF, London Mathematical Society Journal of Computation and Mathematics, 8, (2005). 80-101.

10. Nonic 3-adic Fields, with John Jones.

PDF, ANTS-VI, Springer Lecture Notes in Computer Science, 3076 (2004), 293-308.

9. An ABC construction of number fields.

PDF, CNTA-VII, CRM Proceedings and Lecture Notes, 36, (2004), 237-267.

8. Frobenius classes in alternating groups.

PDF, Rocky Mountain Journal of Mathematics, Volume 34, Number 4, Winter 2004, 1483--1496. Accompanying Mathematica file.

7. Septic fields with discriminant ±2a3b, with John Jones.

ps , dvi, Mathematics of Computation, 72 (2003), 1975-1985.

6. Discriminants of some Painlevé polynomials

ps , dvi without pictures, Number Theory for the Millennium III, AK Peters, (2002) 205-221. Accompanying Mathematica file.

5. Density of cubic field discriminants.

dvi, Mathematics of Computation, 70 (2001), 1699-1705.

4. Sextic number fields with discriminant -j2a3b, with John Jones.

PDF, CNTA-V, CRM Proceedings and Lecture Notes, 19, (1999) 141-172.

3. Timing analysis of targeted Hunter searches, with John Jones.

ANTS-III, Springer Lecture Notes in Computer Science, 1423, (1998), 412-423.

2. Twin sextic algebras.

Rocky Mountain Journal of Mathematics, 28, (1998) 341-368.

1. Composita of sextic fields, theory and examples.

Communications in Algebra, 24, (1996) 3311-3334.

Thesis

Shimura curves analogous to X0(N).

PDF, 97 pages.

Talks on my research

This list also includes some general talks about my research area. Some of the material in these talks has not yet appeared in papers.

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1988

ICERM, Brown U

Oberwolfach, Germany

U of Wisconsin, Madison

UMM

New York Number Theory Seminar

U of Bonn, Germany

ICTP, Trieste, Italy

CNTA XIII, Ottawa

U of Warwick, England

U of Nebraska, Omaha

Oberwolfach, Germany

University of Chicago

Northwestern University

Oberwolfach, Germany

U of Sydney, Australia

UNC Greensboro

Arizona State

Collège de France

Stanford

ICTP, Trieste, Italy

U of Wisconsin, Madison

Arizona State

Stanford

CNTA-11, Nova Scotia

Stanford

U of Calgary

Arizona State

ANTS-8, Banff

UMM

Arizona State

U of Nebraska, Omaha

U of Texas, Austin

SJTN Madrid

Arizona State

UMM

U of Florida

Arizona State

U of Wisconsin, Madison

U of Nebraska, Omaha

CNTA-8 Toronto

Arizona State

UMM

CNTA-7 Montreal

Arizona State

Millennial NT conference, U of Illinois

AMS meeting, San Antonio

UMM

Arizona State

ANTS-III, Portland

Rutgers

U of California at Irvine

CNTA-5 Ottawa

Caltech

Arizona State

AMS meeting, Chicago

U of Southern California

U of Chicago

U of Toronto

U of Saskatoon

Arizona State

CMS meeting, Montreal

U of Chicago

U of Illinois

U of Chicago

U of Michigan

Motives with small conductor

Mod l congruences and p-adic ramification

Complete Hypergeometric L-functions (video)

Hypergeometric Motives

What is a motive? (video)

Hurwitz Belyi Maps

A database of number fields

Division polynomials with Galois group SU3 (3).2 = G2(2)

Some Belyi covers unexpectedly defined over Q

Numerical verification of Deligne's conjecture for HGMs

Division polynomials with Galois group SU3 (3).2 = G2(2)

An LMFDB perspective on motives

Primitive extensions of Qp

A database of number fields

Lightly ramified number fields (with an eye to automorphic forms)

Hypergeometric motives and their wild ramification

Hurwitz number fields

Motivic computations in Magma

Hurwitz number fields

Computing Galois groups II

Computing Galois groups I

Introduction to number fields

Number fields coming from covers of M0,5

The exotic dodecahedron M0,5

Hypergeometric motives and their division polynomials

Covers of M0,5 and number fields

Hypergeometric motives and their division polynomials

The inverse Galois problem

Lightly ramified S.M12.A number fields

Hurwitz number fields

Ramification in moduli fields

Chebyshev covers and exceptional number fields

Nonsolvable polynomials with discriminant 5 A

Arboreal dessins d'enfants

Number fields ramified at one prime

Dessins d'enfants (video)

Chebyshev covers and exceptional number fields

Una conjetura de finitud para cuerpos de números

Wild Partitions and Number Theory

A new result in game theory

Fractalized cyclotomic polynomials

A database of local fields

Fractalized cyclotomic polynomials

Octic 2-adic fields

Fractalized cyclotomic polynomials

A database of local fields

Singular primes for three point covers

Generic polynomials with small discriminant

Discriminants of Yablonsky-Vorobiev polynomials

An ABC construction of number fields

Discriminants of some Painleve polynomials

Roots of generalized Jacobi polynomials

Number fields with prescribed ramification

Rigid Matrix Tuples

Three point covers and remarkable polynomials

Searches for number fields

ABC construction of PQ fields

Modular forms with conductor 2a

Number fields with prescribed ramification

Motivic Galois groups of some genus two curves

Sextic number fields with discriminant -j 2a 3b

Character measures I,II,III

Character measures

Computing motivic Galois groups

A motivic inverse problem and some solutions

Equidistribution in motivic Galois groups I,II

Motives and de Rham cohomology

Motivic Galois groups

Numerical computation with motivic L-functions

Equidistribution in motivic Galois groups

Introduction to motives I,II,III,IV,V

Motives and Langlands reciprocity

Gross-Zagier formula for Shimura curves