Hugh Roberts Geller

Research

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Research Interests:

Commutative and Homological Algebra:

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

  • Minimal resolutions

  • Fiber Products

  • Applications to neural rings

Publications:

Eigenform Product Identities for Degree-Two Siegel Modular Forms, with Jim Brown, Rico Vicente, and Alexandra Walsh, Journal of Number Theory, 204 (2019), 25-40.

Minimal Resolutions of Fiber Products, Proc. Amer. Math. Soc., 150 (2022), no. 10, 4159-4172 DOI: https://doi.org/10.1090/proc/15963

Canonical Forms of Neural Ideals, with Rebecca R.G., To Appear in La Matematica arXiv:2209.09948

Semidualizing Modules over Numerical Semigroup Rings, with Ela Celikbas and Toshinori Kobayashi, arXiv:2306.14989, To Appear in the International Journal of Algebra and Computation

Submitted:

Betti Numbers of Fiber Products of Complete Local Algebras, with Ela Celikbas and Tony Se, arXiv:2307.05715

Invited Talks

Semidualizing Modules Over Numerical Semigroup Rings, Algebra and Number Theory Seminar, Texas Tech University, October 3, 2023 (3:00 pm Central on Zoom)

Classifying Betti Numbers of Fiber Products, AMS Central Sectional, Special Session on Commutative Algebra with Connections to Combinatorics and Geometry; University of Cincinnati, April 2023

DG Structures for Products of Ideals, AMS Southeastern Sectional, Special Session on Recent Developments in Commutative Algebra; Georgia Institute of Technology, March 2023

Minimal DGA Resolutions for Complete Bipartite Graphs, Algebra Seminar, West Virginia University, October 2022

Minimal DG Algebras for Families of Edge Ideals, Joint Mathematics Meetings, Special Session on Commutative Algebra; Seattle, WA, April 2022 (postponed due to Omicron)

Classifying Two Generated Neural Ideals, AMS Eastern Sectional, Special Session on Combinatorial Methods in Commutative Algebra; Tufts University, March 2022

Minimal DG Algebras for Families of Edge Ideals, AMS Southeastern Sectional, Special Session on Combinatorial and Homological Commutative Algebra; University of South Alabama, November 2021

Minimal Differential Graded Resolutions of Fiber Products, Dissertation Defense; Clemson University, July 2021

Explicit Minimal Free Resolutions of Fiber Products, AMS Eastern Sectional, Special Session on Commutative Algebra; Brown University, March 2021

DG-Module Resolutions of Certain Fiber Products, AMS Southeastern Sectional, Special Session on Differential Graded Methods in Commutative Algebra; Georgia Institute of Technology, March 2021

Explicit Minimal Free Resolutions of Fiber Products, Algebra Seminar, West Virginia University, February 2021

DG-Structures on Minimal Free Resolutions of Fiber Products, Joint Mathematics Meetings, Special Session on Commutative Algebra; Washington, DC, January 2021

DG-Structures on Minimal Free Resolutions of Fiber Products, Algebra and Number Theory Seminar, Texas Tech University, November 2020

Minimal Free Resolutions of Fiber Products, Combinatorics, Algebra, and Geometry Seminar, George Mason University, October 2020

DG-Structures for Fiber Products, AMS Eastern Sectional, Special Session on Homological Methods in Algebra; Pennsylvania State University (Online), October 2020

DG-Structures on Minimal Free Resolutions of Fiber Products, Commutative and Homological Algebra Market Presentations (CHAMP); Virtual Seminar, September 2020

Minimal Free Resolutions of Fiber Products, AMS Central Sectional, Special Session on Free Resolutions, Combinatorics, and Geometry; University of Texas at El Paso (Online), September 2020

DG-Structures for Fiber Products, AMS Western Sectional, Special Session on DG Methods in Commutative Algebra and Representation Theory; California State University, Fresno, May 2020
*Held on Zoom due to COVID-19.

DG-Algebra Resolutions for Products of Ideals, AMS Southeastern Sectional, Special Session on Commutative Algebra; University of Virginia, March 2020
*Held on Zoom due to COVID-19. All recordings posted to Eloísa Grifo’s page

DG-Algebra Resolutions for Products of Ideals, AMS Southeastern Sectional, Special Session on Homological Methods in Algebra; University of Florida, November 2019

DG-Algebra Resolutions for Products of Ideals, Commutative Algebra Seminar; University of Utah, October 2019

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

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