Steven Karp

Steven Karp is an Assistant Professor in the Department of Mathematics at the University of Notre Dame, within the College of Science. He holds a BMath from the University of Waterloo (2011), an M.A.St. from the University of Cambridge (2012), and a Ph.D. from the University of California, Berkeley (2017). His research focuses on algebraic combinatorics and total positivity, particularly in the study of positive parts of matrix spaces and their generalizations to algebraic groups and flag varieties. Karp explores connections between these areas and combinatorics, representation theory, topology, and theoretical physics.

Steven Karp's educational background includes:

• BMath, University of Waterloo, 2011
• M.A.St., University of Cambridge, 2012
• Ph.D., University of California, Berkeley, 2017

His research interests are centered around total positivity, which examines the positive parts of mathematical spaces such as matrices, algebraic groups, and flag varieties. Key areas of exploration include the parametrization of totally positive matrices using networks, the study of eigenvalues and determinants in such contexts, and the interplay between total positivity and algebraic combinatorics, representation theory, and topology. Karp’s work also extends to applications in theoretical physics, particularly through connections with Schubert calculus and amplituhedra.

Karp’s recent publications highlight his contributions to the study of total positivity in flag varieties, Grassmannians, and amplituhedra. His work often integrates geometric and algebraic techniques, exploring topics such as Plücker coordinates, Wronskian determinants, Toda flows, and symmetric Toda lattices. These studies emphasize the role of positivity in understanding topological and combinatorial structures, with implications for both pure mathematics and theoretical physics.

Steven Karp has not been listed as having any scientific awards in the provided information.

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