- Representation theory
- Lie theory
- quantum groups
- symmetry breaking

- Mathematical physics
- field theory
- Kaluza-Klein reductions
- supergravity

*Symmetry Algebras in Relative Representation Theory*, funded by the Army Research Office

- 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.

*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 skew-affine generalized Weyl algebras*

with Dwight Anderson Williams II

- MWF 3:10pm–4:00pm

- Fall 2024
- Spring 2025
- MATH 6180 Representation Theory
- MATH 6800 Mathematical Aspects of Fundamental Physics

- Past teaching

- Lillian Uhl (MSc expected 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)

- 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

- 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

- April 8, 2022: Slides for my talk
*Galois Orders and Deformation Quantization*given at the Poisson geometry conference Gone Fishing. - March 26, 2022: Slides for my talk
*On the Diagonal Reduction Algebra of 𝖔𝖘𝖕(1|2)*given in the Special Session on Combinatorics and Representations of Noncommutative Algebras at the Spring Central Sectional Meeting of the AMS. - Oct 5, 2021: Video recording of my talk on the diagonal reduction algebra for the Lie superalgebra 𝖔𝖘𝖕(1|2).
- Jan 26, 2021: Slides for my talk
*Harish-Chandra modules over orders in smash products*at the UTA-KSU Representation Theory and Mathematical Physics Seminar.

*Symplectic differential reduction algebras and skew-affine generalized Weyl algebras*

with Dwight Anderson Williams II*Ghost center and representations of the diagonal reduction algebra of 𝖔𝖘𝖕(1|2)*

with Dwight Anderson Williams II (in Journal of Geometry and Physics)*Diagonal reduction algebra for 𝖔𝖘𝖕(1|2)*

with Dwight Anderson Williams II (in Theoretical and Mathematical Physics)*Principal Galois orders and Gelfand-Zeitlin modules*

(in Advances in Mathematics)*Harish-Chandra modules over Hopf Galois orders*

(in International Mathematics Research Notices)*Gelfand-Tsetlin crystals*

with O'Neill Kingston*The q-difference Noether problem for complex reflection groups and quantum OGZ algebras*

(in Communications in Algebra)*De Concini-Kac filtration and Gelfand-Tsetlin generators for quantum gl*_{N}

with Vyacheslav Futorny (in Linear Algebra and its Applications)*Solution to a q-difference Noether problem and the quantum Gelfand-Kirillov conjecture for gl*_{N}

with Vyacheslav Futorny (in Mathematische Zeitschrift)

*Grothendieck rings of towers of generalized Weyl algebras in the finite orbit case*

with Daniele Rosso (in Journal of Algebra)*Grothendieck rings of towers of twisted generalized Weyl algebras*

with Daniele Rosso (in Algebras and Representation Theory)*Classification of twisted generalized Weyl algebras over polynomial rings*

with Daniele Rosso (in Journal of Algebra)*Unitarizability of weight modules over noncommutative Kleinian fiber products*

(Preprint)*Noncommutative fiber products and lattice models*

(in Journal of Algebra)*Cylindrical Dyck paths and the Mazorchuk-Turowska equation*

with Daniele Rosso (in Journal of Algebraic Combinatorics)*Twisted generalized Weyl algebras and primitive quotients of enveloping algebras*

with Vera Serganova (in Algebras and Representation Theory)*The isomorphism problem for multiparameter quantized Weyl algebras*

with Ken Goodearl (in São Paulo Journal of Mathemaical Sciences)*Locally finite simple weight modules over twisted generalized Weyl algebras*

(in Journal of Algebra)*Multiparameter twisted Weyl algebras*

with Vyacheslav Futorny (in Journal of Algebra)*On the consistency of twisted generalized Weyl algebras*

with Vyacheslav Futorny (in Proceedings of the AMS)*Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras*

with Johan Öinert (in Journal of Algebra)*Twisted generalized Weyl algebras, polynomial Cartan matrices and Serre-type relations*

(in Communications in Algebra)*Pseudo-unitarizable weight modules over generalized Weyl algebras*

(in Journal of Pure and Applied Algebra)

*Clifford and Weyl superalgebras and spinor representations*

with Vera Serganova (in Transformation Groups)*Simple Whittaker modules over free bosonic orbifold vertex operator algebras*

with Nina Yu (in Proceedings of the AMS)*Dynamical decomposition of bilinear control systems subject to symmetries*

with Domenico D'Alessandro (in Journal of Dynamical and Control Systems)*Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials*

with Jasper Stokman (in Journal of Mathematical Physics)

*Quantum affine modules for non-twisted affine Kac-Moody algebras*

with Vyacheslav Futorny and Evan Wilson (in Proceedings of the AMS)*Irreducible completely pointed modules for quantum groups of type A*

with Vyacheslav Futorny and Evan Wilson (in Journal of Algebra)*The elliptic GL(n) dynamical quantum group as an 𝖍-Hopf algebroid*

(in International Journal of Mathematics and Mathematical Sciences)*Hopf structures on ambiskew polynomial rings*

(in Journal of Pure and Applied Algebra)

*Deformations of Lie algebras using σ-derivations*

with Daniel Larsson and Sergei Silvestrov (in Journal of Algebra)

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