Jonas T. Hartwig, Ph.D.

Associate Professor in the Department of Mathematics at Iowa State University

Contact

• Carver Hall 470
• jth@iastate.edu
• jthartwig.net

Teaching

• Spring 2022
  • MATH 365 Complex Variables
  • MATH 620X Lie Algebras
  • Office Hours MT 4:10pm – 6:00pm
• Previous teaching

Research

• Representation theory, Lie algebras, quantum groups
• Invariant theory, Gelfand-Tsetlin theory, Galois orders
• Twisted generalized Weyl algebras, graded rings
• Connections to geometry, integrable systems, mathematical physics

Activities

• Algebra and Geometry Seminar

Recent Talks

• 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.
• 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.

Notes

These are various introductory texts and surveys intended for graduate students and others who wish to learn about these topics.

• Highest weight representations of the Virasoro algebra Basics of the Virasoro algebra (this was part of my master's thesis).

Current Mentees

• Dylan Fillmore
• Jordan Disch

Past Mentees

• Dwight Anderson Williams II (Postdoc 2020-2021)
• Fox Hobart (MSc Summer 2021)
• O'Neill Kingston (PhD Spring 2020)
• Erich Jauch (PhD Spring 2020)

Publications

2022

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

2021

• Diagonal reduction algebra for 𝖔𝖘𝖕(1|2)
  with Dwight Anderson Williams II (in Theoretical and Mathematical Physics)
• Harish-Chandra modules over Hopf Galois orders
  (Preprint)

2020

• Gelfand-Tsetlin crystals
  with O'Neill Kingston (Preprint)
• Grothendieck rings of towers of twisted generalized Weyl algebras
  with Daniele Rosso (in Algebras and Representation Theory)

2019

• Classification of twisted generalized Weyl algebras over polynomial rings
  with Daniele Rosso (in Journal of Algebra)

2018

• 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)

2017

• Principal Galois orders and Gelfand-Zeitlin modules
  (in Advances in Mathematics)
• Unitarizability of weight modules over noncommutative Kleinian fiber products
  (Preprint)

2016

• Noncommutative fiber products and lattice models
  (in Journal of Algebra)

2015

• The q-difference Noether problem for complex reflection groups and quantum OGZ algebras
  (in Communications in 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)

2014

• Quantum affine modules for non-twisted affine Kac-Moody algebras
  with Vyacheslav Futorny and Evan Wilson (in Proceedings of the AMS)
• The isomorphism problem for multiparameter quantized Weyl algebras
  with Ken Goodearl (in São Paulo Journal of Mathemaical Sciences)
• Irreducible completely pointed modules for quantum groups of type A
  with Vyacheslav Futorny and Evan Wilson (in Journal of Algebra)

2012

• De Concini-Kac filtration and Gelfand-Tsetlin generators for quantum gl_N
  with Vyacheslav Futorny (in Linear Algebra and its Applications)

2011

• Solution to a q-difference Noether problem and the quantum Gelfand-Kirillov conjecture for gl_N
  with Vyacheslav Futorny (in Mathematische Zeitschrift)
• Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials
  with Jasper Stokman (in Journal of Mathematical Physics)
• 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)

2010

• Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras
  with Johan Öinert (in Journal of Algebra)

2009

• Twisted generalized Weyl algebras, polynomial Cartan matrices and Serre-type relations
  (in Communications in Algebra)

2008

• The elliptic GL(n) dynamical quantum group as an 𝖍-Hopf algebroid
  (in International Journal of Mathematics and Mathematical Sciences)
• Pseudo-unitarizable weight modules over generalized Weyl algebras
  (in Journal of Pure and Applied Algebra)

2005

• Hopf structures on ambiskew polynomial rings
  (in Journal of Pure and Applied Algebra)
• Locally finite simple weight modules over twisted generalized Weyl algebras
  (in Journal of Algebra)

2004

• Deformations of Lie algebras using σ-derivations
  with Daniel Larsson and Sergei Silvestrov (in Journal of Algebra)

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