Exploring Tropical Geometry, Log-concavity, and Matroids: Women+ and Mathematics 2025

This May, the Institute for Advanced Study hosted its annual Women⁺ and Mathematics (W⁺AM) program, a weeklong mathematical symposium for educators, students, and researchers that aims to form fruitful research relationships and establish a mentoring network to support early career scholars.

Thirty-one participants gathered at the Institute to collaborate on this year’s theme, “Convexity and Combinatorics in Algebraic Geometry,” through joint problem-solving sessions, daily lightning talks, group meals, and two lecture courses.

These courses, the Terng and Uhlenbeck lectures––named for Chuu-Lian Terng, Member (1979, 1997–98) in the School of Mathematics, and Distinguished Visiting Professor Karen Uhlenbeck––form the centerpiece of the week’s activities each year. Terng and Uhlenbeck, pioneering women in their respective mathematical fields, played a key role in establishing the W⁺AM program at the Institute in 1994. 

This year, the Uhlenbeck lectures were delivered by Melody Chan with teaching assistant Raluca Vlad, both of Brown University. Chan’s course explored tropical geometry, a modern degeneration technique in algebraic geometry, through tropical curves, tropical abelian varieties, and their moduli spaces.

The Terng lecture course, taught by Josephine Yu from Georgia Institute of Technology and teaching assistant Tracy Chin from the University of Washington, took on the theory of matroids and their relationship to log-concave polynomials. The course explored the real and combinatorial geometry underlying log-concavity along with applications to matroids and the mixing times of random walks.

The 2025 program was organized by Wei Ho, W⁺AM Director and Visiting Professor in the School of Mathematics. Ho also holds appointments at Princeton University and the University of Michigan. Dusa McDuff, Member (1976, 2002) and Visitor (1977–78) in the School of Mathematics, now based at Barnard College and Columbia University, also organized the event, with the help of the Program Committee.

Founded in 1993 at the Park City Mathematics Institute, W⁺AM was established at IAS the following year, under the leadership of Uhlenbeck and Terng, with support from then-Director Phillip Griffiths. Ever since, the program has been dedicated to fostering a successful living and learning environment for emerging mathematicians of exceptional talent. W⁺AM is open to all who support its mission. In 2019, the program was recognized for its impact with the American Mathematical Society’s “Mathematics Programs that Make a Difference” Award.

W⁺AM receives generous support from the Institute for Advanced Study, Jane Street, Lisa Simonyi, the Minerva Research Foundation, the National Science Foundation, the Princeton University Department of Mathematics, and the Robert S. Hillas Fund.