Steven Karp
Assistant Professor
Education
BMath, University of Waterloo, 2011
M.A.St., University of Cambridge, 2012
Ph.D., University of California - Berkeley, 2017
Research Groups
Algebra and Algebraic Geometry, Discrete Math, Operations Research, and Probability
Research Area
Algebraic combinatorics
Bio
Research Interests
My research centers around total positivity, which is the study of spaces and their positive parts. For example, a square matrix is called totally positive if all of its square submatrices have a positive determinant. Such matrices can be parametrized using networks, and all their eigenvalues are real and positive. I study the positive parts of matrix spaces and their generalizations, such as algebraic groups and flag varieties, and explore their connections with areas such as combinatorics, representation theory, topology, and theoretical physics.
Selected Publications
- with Hugh Thomas) q-Whittaker functions, finite fields, and Jordan forms. arXiv:2207.12590 12.
- (with Anthony M. Bloch) On two notions of total positivity for partial flag varieties. arXiv:2206.05806 11.
- Wronskians, total positivity, and real Schubert calculus. arXiv:2110.02301
Email: skarp2@nd.edu
Phone: 574-631-8706
Fax: 574-631-6579
Office: 108 Hayes-Healy Bldg.