Julianna Tymoczko

Julianna Tymoczko is the Louise Wolff Kahn 1931 Professor of Mathematical Sciences and Codirector of the Postbaccalaureate Program at Smith College, where she serves as an Associate Professor of Mathematics in the Department of Mathematics within the School of Mathematics & Statistics. Her office is located in Burton Hall 314, and she maintains regular office hours Monday through Thursday.

• Ph.D. and M.A. from Princeton University
• A.B. from Harvard University

Professor Tymoczko's research sits at the rich intersection of algebraic geometry and algebraic combinatorics, with particular focus on geometric representations of the symmetric group, modern Schubert calculus, and equivariant cohomology using combinatorial methods. Her work often centers on Hessenberg varieties, a family of subvarieties of the flag variety that includes Springer varieties as special cases. She approaches complex geometric questions through algebraic and combinatorial techniques, studying objects like circles, spheres, and more complicated varieties described as zero sets of polynomial equations.

Her extensive publication record shows consistent work on Poincare polynomials for Nilpotent Hessenberg Varieties across various dimensions (GL(2) through GL(9)), demonstrating deep exploration of the topological and combinatorial properties of these spaces. The progression of her work reveals increasing complexity from lower-dimensional cases to higher-dimensional generalizations.

• Alfred P. Sloan fellow
• Recipient of National Science Foundation grant support

Professor Tymoczko actively contributes to the mathematical community through teaching, research, and service. She currently teaches advanced mathematics courses including Math 300 (Dialogues in Math) and Math 301 (Topics in Math), co-organizes the Algebra/Combinatorics/Geometry seminar at Smith College, and participates regularly in the Valley Geometry Seminar and Representation Theory seminar. Her research is supported by NSF funding, and she frequently presents her work at major conferences including AMS Special Sessions and international venues like McMaster University.

Her research program involves detailed study of the connections between geometric structures, combinatorial patterns, and algebraic representations, with particular attention to how these fields inform one another in the study of Hessenberg varieties and related structures.