Alexander Shapiro

Assistant Professor

Education

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

Bio

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.

Email: ashapiro@nd.edu
Phone: 574-631-7957
Fax: 547-631-6579
Office: 126 Hayes-Healy Bldg