David P. Roberts
David P. Roberts
Professor of Mathematics
University of Minnesota, Morris
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.
Publications
34.
PGL_{2}(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
ICERM, Brown U
ICERM, Brown U
ICERM, Brown U
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
U of Nebraska, Omaha
Oberwolfach, Germany
University of Chicago
Northwestern University
Oberwolfach, Germany
U of Sydney, Australia
UNC Greensboro
UNC Greensboro
UNC Greensboro
UNC Greensboro
Arizona State
Arizona State
Collège de France
Stanford
ICTP, Trieste, Italy
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
U of Florida
Arizona State
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
Rutgers
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
Arizona State
CMS meeting, Montreal
U of Chicago
U of Illinois
U of Chicago
U of Michigan
Mod l congruences and p-adic ramification
Complete Hypergeometric L-functions
(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
Lightly ramified number fields (with an eye to automorphic forms)
Hypergeometric motives and their wild ramification
Hypergeometric motives and their wild ramification
Number fields coming from covers of M0,5
Hypergeometric motives and their division polynomials
Covers of M0,5 and number fields
Hypergeometric motives and their division polynomials
Lightly ramified S.M12.A number fields
Lightly ramified S.M12.A number fields
Chebyshev covers and exceptional number fields
Nonsolvable polynomials with discriminant 5
A
Number fields ramified at one prime
Chebyshev covers and exceptional number fields
Chebyshev covers and exceptional number fields
Chebyshev covers and exceptional number fields
Una conjetura de finitud para cuerpos de números
Wild Partitions and Number 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
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
Gross-Zagier formula for Shimura curves
The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.