Jonas T. Hartwig, Ph.D.

Research

Interests

• Representation theory
  • Lie theory
  • quantum groups
  • symmetry breaking
• Mathematical physics
  • field theory
  • Kaluza-Klein reductions
  • supergravity

Grants

• Symmetry Algebras in Relative Representation Theory, funded by the Army Research Office grant W911NF-24-1-0058

Recent Talks

• Spring 2024: Slides for my talk Differential Reduction Algebras
• May 5, 2022: Slides and video for my talk The Diagonal Reduction Algebra of the Lie Superalgebra 𝖔𝖘𝖕(1|2) given at Xiamen University, China.

Recent Papers

For a complete list, see the arXiv.

• Dirac Reduction Algebra
  with Matthew Dorang and Dwight Anderson Williams II
• Parabolic Stabilization and Cutting for Reduction Superalgebras
• Structure of Galois rings and the Gelfand-Kirillov Conjecture
  with Vyacheslav Futorny, Erich C. Jauch, João Schwarz
• Subcategories of Module Categories via Restricted Yoneda Embeddings
  with Dylan Fillmore
• Exact Solutions to the Klein—Gordon Equation via Reduction Algebras
  with Lillian Ryan Uhl and Dwight Anderson Williams II
• Hilbert—Samuel Polynomials for Algebras with Special Filtrations
  with Erich C. Jauch and João Schwarz
• Galois Order Realization of Noncommutative Type D Kleinian Singularities
• Symplectic Differential Reduction Algebras and Generalized Weyl Algebras
  with Dwight Anderson Williams II

Teaching

During Fall 2025 and Spring 2026, I am on Faculty Professional Development Assignment (colloquially known as sabbatical).

Classes

• Past teaching

Mentees

• Sagar Shrivastava (Postdoc 2025-2027)
• Dustin Baker (PhD expected Spring 2027)
• Lillian Ryan Uhl (MSc Fall 2024)
• Dylan Fillmore (PhD Spring 2024)
• Jordan Disch (PhD Spring 2022)
• Dwight Anderson Williams II (Postdoc 2020-2021)
• Fox Hobart (MSc Summer 2021)
• O'Neill Kingston (PhD Spring 2020)
• Erich Jauch (PhD Spring 2020)

Notes

• Locally finite modules over commutative algebras
• Highest weight representations of the Virasoro algebra

Activities

• QuaSy-Con III, the third installment of the Quantum Symmetries Conference Series, will be held at Iowa State University, November 8-9, 2025.
• Algebra and Geometry Seminar
• The Sioson Collection

Recent and Upcoming Travel

• Special Session on Geometry, Representation Theory and Noncommutative Algebra at AMS meeting in St. Louis MO, Oct 18-19, 2025
• Special Session on Interactions Between Lie Theory and Combinatorics of Symmetric Functions at AMS meeting in Albany NY, Oct 19-20, 2024
• The Representation Theory and Geometry of Quantum Algebras at CMS meeting in Saskatchewan, May 31-June 4, 2024
• QuaSy-Con II in Notre Dame, May 24-26, 2024
• Representations of Lie Algebras and Lie Superalgebras at AMS meeting in University of San Francisco, May 4-5, 2024
• Geometric Methods in Representation Theory and The Algebras and Special Functions around Association Schemes at AMS meeting in Milwaukee, April 20-21, 2024
• Gone Fishing at Northwestern, April 11-14, 2024

Recent Conferences Organized

• New Directions in Noncommutative Algebras and Representation Theory at the 2023 Fall Southeastern Sectional Meeting of the AMS at University of South Alabama, Mobile, AL, October 13–15, 2023
• Representation Theory, Geometry and Mathematical Physics at the 2023 Spring Central Sectional Meeting of the AMS at University of Cincinnati, Cincinnati, OH, April 15–16, 2023