Mathematics Department

C D Haessig

C. Douglas Haessig

Assistant Professor, Mathematics
Ph.D., University of California, Irvine, 2005
B.S., University of California, Santa Barbara, 1998

CV | Seminars

Research Summary

A large part of my research is aimed at understanding various properties of L-functions of Galois representations which arise from families of exponential sums. Galois representations encode many deep and significant problems within number theory. In fact, it was through their study that the celebrated Fermat's Last theorem was finally settled affirmatively by Wiles et al. in 1995. More recently, Serre's conjecture, which implies Fermat, and the Sato-Tate conjecture, also came down to statements about Galois representations. Galois representations are frequently studied by their associated L-function. This is simply a function which encodes much, if not essentially all, of the Galois representation. Even the most elementary questions about these L-functions are still largely unknown. For instance, the Riemann hypothesis is a conjecture describing the precise location of the zeros of the L-function attached to a specific Galois representation. I use techniques from geometry and p-adic analysis to study such L-functions.

Selected Publications

Haessig, Rojas-Leon. L-functions of symmetric powers of the generalized Airy family of exponential sums: ell-adic and p-adic methods. Submitted

Haessig, On the zeta function of divisors of projective varieties with large rank divisor class group, J. Number Theory. Vol 129, Issue 5, May 2009, Pages 1161-1177

Haessig, L-functions of symmetric powers of cubic exponential sums. J. Reine Angew. Vol 2009, Issue 631, Pages 1 - 57

Haessig. On the p-adic meromorphy of the function field height zeta function. J. Number Theory (2007) Vol 128/7, pp. 2063-2069.

Haessig. Equalities, congruences, and quotients of zeta functions in Arithmetic Mirror Symmetry. Appendix to D. Wan's Mirror symmetry for zeta functions. Mirror Symmetry V, AMS/IP Studies in Advanced Mathematics, Vol. 38, (2007) 159-184.

D. Wan and C. D. Haessig. On the p-adic Riemann hypothesis for the zeta function of divisors. J. Number Theory. 104 (2004) 335-352.

Expositions

Haessig. Exponentials sums and the Chevalley-Warning theorem (Michigan number theory days. 2010)

Courses

   2010 (F) Math 436 (Syllabus)
   2010 (S) Math 130 (Syllabus) and Math 285 (Syllabus)
   2009 (F) Math 141, 163 and Topics in Number theory
   2009 (S) Math 200, 235
   2008 (F) Math 233
   2008 (S) Math 141A, 282
   2007 (F) Math 162Q, 230
   2007 (S) Math 142, 236
   2006 (F) Math 141, 230

Opportunities for Undergraduates and Graduates

  Fellowships - UR database


Past Student Projects