Alexander Shapiro

Assistant Professor


Ph.D., University of California, Berkeley, 2016
M.Sc., Moscow State University, Russia, 2008

Research Area

Representation theory, integrable systems, quantum field theory, and cluster algebra


Research Interests

I am interested in problems on the interface of representation theory, integrable systems, quantum field theory, and cluster algebra. My main projects focus on

  • quantum character varieties
  • higher Teichmuller theory and non-compact Chern–Simons theory
  • positive representation theory of quantum groups
  • cluster structure on BFN Coulomb branches

Selected Publications

  • G. Schrader, A. Shapiro. “K-theoretic Coulomb branches of quiver gauge theories and cluster varieties.” arXiv:1910.03186 (2019).
  • G. Schrader, A. Shapiro. “A cluster realization of U q(sln) from quantum character varieties.” Inventiones Mathematicae 216, no. 3 (2019): 799-846.
  • G. Schrader, A. Shapiro. “On b -Whittaker functions.” arXiv:1806.00747 (2018).
  • G. Schrader, A. Shapiro. “Continuous tensor categories from quantum groups I: algebraic aspects.” arXiv:1708.08107 (2017).
  • G. Schrader, A. Shapiro. “Quantum groups, quantum tori, and the Grothendieck-Springer resolution.” Advances in Mathematics 321 (2017): 431-474.

Phone: 574-631-7957
Fax: 547-631-6579
Office: 126 Hayes-Healy Bldg