I am interested in applying the representation theory of Lie groups and Lie algebras to problems from quantum computing and mathematical physics.

Current topics of research include: dynamical Lie algebras, quantum signal processing, quantum machine learning, quantum many body systems, quantum state tomography.

Prospective students need to have background in Analysis (MA 515, 715), Linear Algebra (MA 520), Lie Algebras (MA 720) and Lie Algebra Representation Theory (MA 725). Other recommended courses: Abstract Algebra I, II (MA 521, 721), Matrix Theory I, II (MA 523, 723), Manifold Theory (MA 555), Numerical Analysis I, II (MA 580, 780), Signal Processing (ECE 510, 710). Knowledge of Physics is not required.

Recommended special topics courses in Fall 2024: Applied Harmonic Analysis (591-002), Mathematical Foundations of Quantum Computation (MA 591-003), Lie Groups and Lie Algebras (MA 790-001).

Research Assistantships available starting Spring 2025 for NC State PhD students in Math or Applied Math who have passed their qualifying exams. Please contact me if interested.

Nicholas Brock

Chris Portwood

Hassan Hatam, PhD 2024. Dissertation: Advances in logarithmic vertex algebras

Ju Wang, PhD 2022. First job: Assistant Professor, University of Lynchburg, VA. Dissertation: On the cohomology of Poisson pseudoalgebras

Noufe Aloudah, PhD 2021. First job: Assistant Professor, Qassim University, Saudi Arabia. Dissertation: Hochschild-Serre spectral sequence for Lie conformal algebras

Samantha Kirk, PhD 2021. First job: Visiting Lecturer, Mount Holyoke College, MA. Dissertation: Toroidal Lie algebras and their vertex operator representations

Anila Yadavalli, PhD 2019. First job: MathCEP Assistant Professor, University of Minnesota. Dissertation: Darboux transformations and Fay identities for the extended bigraded Toda hierarchy 

McKay Sullivan, PhD 2017. First job: Assistant Professor, Utah Tech University. Dissertation: Twisted logarithmic modules of free field and lattice vertex algebras

William Wheeless, PhD 2015. First job: Department of Defense. Dissertation: Additional symmetries of the extended Toda hierarchy

Jason Elsinger, PhD 2014. First job: Assistant Professor, Spring Hill College, Mobile, AL. Dissertation: Classification of orbifold modules under an automorphism of order two

Daniel Fleisher, PhD 2013. First job: Postdoctoral Fellow, Weizmann Institute, Israel. Dissertation: Wakimoto modules, FMS bosonization and integrable hierarchies

Katie Liszewski, PhD 2011. First job: Federal Bureau of Investigation. Dissertation: The charged free boson integrable hierarchy 

Juan Villarreal, Visiting Postdoctoral Researcher, 2021

Maria Vega, NSF Alliance Postdoctoral Fellow, 2012-2015