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

PGL2(Fl) number fields with rational companion forms

PDF, 17 pages.


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

33. Newforms with rational coefficients

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


32. Artin L-functions of small conductor

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 .


  1. 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


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

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

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

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

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


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

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


About About.html
Teaching Teaching.html
Research
Other Other.html
 

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.