David Helm

Imperial College
Office: 672 Huxley

Curriculum Vitae (last updated Sep 2021)


  1. Moduli of Langlands parameters (With Jean-Francois Dat, Gilbert Moss, and Robert Kurinczuk)
  2. Coherent Springer theory and the categorical Deligne-Langlands correspondence (With David Ben-Zvi, Harrison Chen, and David Nadler)
  3. An ordinary abelian variety with an etale self-isogeny of p-power degree and no isotrivial factors
  4. Potential automorphy over CM fields (With Patrick Allen, Frank Calegari, Ana Caraiani, Toby Gee, Bao Le Hung, James Newton, Peter Scholze, Richard Taylor, and Jack Thorne)
  5. Converse Theorems and the local Langlands correspondence in families (With Gilbert Moss) Invent. Math. 214 (2018), 999-1022.
  6. Curtis Homomorphisms and the integral Bernstein center for GL_n Algebra and Number Theory 14 (2020), no. 10, 2607-2645. Note that the paper Helm-Moss, above, references an earlier version of this paper with different section numbering; in particular sections 9,10, and 11 of the version referenced in Helm-Moss correspond to sections 8,9, and 10 of the current version. The numbering of individual results within these sections remains the same.
  7. Whittaker models and the integral Bernstein center for GL_n(F) Duke Math. Journal 165 (2016), no. 9, 1597-1628.
  8. The local Langlands correspondence for GL_n in families (With Matthew Emerton) Ann. Sci. Ec. Norm. Sup. 47 (2014), no. 4, 655-722.
  9. The Bernstein center of the category of smooth $W(k)[GL_n(F)]$-modules Forum Math. Sigma 4 (2016), e11.
  10. On the modified mod $p$ local Langlands correspondence for GL_2(Q_l) Math. Res. Lett. 20 (2013), no. 3, 489-500.
  11. Finite descent obstruction on curves and modularity (With Jose Felipe Voloch) Bull. London Math. Soc. 2011; doi: 10.1112/blms/bdr015.  
  12. On $l$-adic families of cuspidal representations of $\GL_2(Q_p)$ Math. Res. Let. 17 (2010), no. 5, 805-822.
  13. Towards a geometric Jacquet-Langlands correspondence for unitary Shimura varieties Duke Math. J. 155 (2010), no. 3, 483-518.
  14. Monodromy filtrations and the topology of tropical varieties (With Eric Katz) Canadian J. Math 64 (2012) 845-868.
  15. A geometric Jacquet-Langlands correspondence for U(2) Shimura varieties Israel J. Math. 187 (2012), 37-80.
  16. On maps between modular Jacobians and Jacobians of Shimura curves, Israel J. Math. 160 (2007), 61-117.  
  17. Mazur's principle for U(2,1) Shimura varieties
  18. Algorithms for graded injective resolutions and local cohomology over semigroup rings (with Ezra Miller), Journal of Symbolic Computation, 39, no. 3-4 (2005), 373-395.  
  19. Bass numbers of Semigroup-Graded Local Cohomology (With Ezra Miller), Pacific Journal of Math. 209, no. 1 (2003), 41-66.  
  20. Jacobians of Shimura curves and Jacquet-Langlands Correspondences (Thesis)