David Zywina

Curriculum Vitae

Teaching: I am currently teaching Math 1120.  Registered students can access course information through the course's blackboard page.

• The inverse Galois problem for orthogonal groups
• Modular forms and some cases of the inverse Galois problem
• An explicit Jacobian of dimension 3 with maximal Galois action
• Bounds for the Lang-Trotter conjectures
• On the surjectivity of mod l representations associated to elliptic curves
• On the possible images of the mod l representations associated to elliptic curves over Q
• The inverse Galois problem for PSL2(Fp)
• The splitting of reductions of an abelian variety
• Explicit class field theory for global function fields
• The Sato-Tate Law for Drinfeld modules
• Bounds for Serre's open image theorem
• Abelian varieties over large algebraic fields with infinite torsion
• Hilbert's irreducibility theorem and the larger sieve
• Splitting fields of characteristic polynomials of random elements in arithmetic groups with F. Jouve and E. Kowalski
• The Chebotarev invariant of a finite group with E. Kowalski (short version)
• A refinement of Koblitz's conjecture
• Drinfeld modules with maximal Galois action on their torsion points
• Elliptic curves with maximal Galois action on their torsion points
• The Lang-Trotter conjecture and mixed representations (old preprint, main results are now part of "Bounds for the Lang-Trotter conjectures")
• The large sieve and Galois representations
• Arithmetic E8 lattices with maximal Galois action with Tony Várilly-Alvarado
• An explicit integral polynomial whose splitting field has Galois group W(E8) with F. Jouve and E. Kowalski

• Inverse Galois problem for small simple groups