Hugh Roberts Geller

Research

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Research Interests:

Homological Algebra:

  • Differential graded algebras (DGAs), DGA resolutions, and DGA modules

  • Minimal resolutions

  • Fiber Products

Number Theory:

  • Congruences of Fourier coefficients of Siegel modular forms

  • Integrality of Siegel-Eisenstein and Klingen-Eisenstein series

  • Siegel’s phi operator

  • Fourier-Jacobi coefficients of Siegel modular forms, particularly those for genus 2, non-Maass, cuspidal eigenforms

 

Publications:

Eigenform Product Identities for Degree-Two Siegel Modular Forms, with Jim Brown, Rico Vicente, and Alexandra Walsh, Journal of Number Theory (to appear), 14 pages.

 

Invited Talks

Towards DG-Algebra Resolutions of Fiber Products, AMS Southeastern Sectional, Special Session on Developments in Commutative Algebra, II; Auburn University, March 2019

 

Upcoming Invited Talks

Title TBD, AMS Southeastern Sectional, Special Session on Homological Methods in Algebra; University of Florida, November 2019

Title TBD, AMS Southeastern Sectional, Special Session on Commutative Algebra; University of Virginia, March 2020

Posters

DG-Algebra Resolutions for Products of Ideals, Thematic Program in Commutative Algebra and its Interactions with Algebraic Geometry; University of Notre Dame, June 2019

Towards DG-Algebra Resolutions for Fiber Products, Morgantown Algebra Days; West Virginia University, April 2019