School of Mathematics

Rahul Ilango, Member in the School of Mathematics, studies computational complexity theory, which quantifies the amount of resources—like time and hardware—needed to solve computational tasks. Ilango has a particular interest in problems that bridge complexity theory with other fields, such as cryptography and proof complexity. 

Federico Ardila, Friends of the Institute for Advanced Study Member in the School of Mathematics (2024–25), describes mathematics as a deeply human, emotional, and collaborative pursuit. He shares how working alongside world experts at IAS inspires creativity in problem solving, akin to playing soccer with the best in the world.

Yelena Mandelshtam, Member in the Institute for Advanced Study’s School of Mathematics (2024–25), discusses the power of complementary knowledge between mathematics and physics, and how this might drive forward advances in understanding problems such as the KP Equation.

Alex Fink, Member in the School of Mathematics (2025), expounds on the continuity in thought and research at the Institute for Advanced Study and discusses the power of its many collaborative spaces to facilitate “aha” moments. 

When visiting graduate student Gianmarco Caldini first arrived at IAS in spring 2024, a series of fortuitous connections on the Institute campus and beyond led him and Camillo De Lellis, IBM von Neumann Professor in the School of Mathematics, to both a collaboration and a friendship with renowned topologist and frequent IAS Member Bill Browder. Their work resulted in the publication of a decades-old theorem originally begun by Browder and Frederick J. Almgren Jr.

Catherine Eva Pfaff, Member in the School of Mathematics (2024–25), discusses the ways in which geometric group theorists and theoretical computer scientists at the Institute for Advanced Study approach mathematical constructions and learn from one another’s insights.

Theresa Arzadon-Labajo, Senior System Administrator in the Institute for Advanced Study's School of Mathematics, reflects on fond memories that she has of working alongside Professor Emeritus Pierre Deligne.

Mikaela Iacobelli, von Neumann Fellow in the School of Mathematics (2024–25), describes her work on plasma—often called "the first state of matter"—and her exploration of convex integration, a new field she is investigating at the Institute for Advanced Study.

Jean Gutt, von Neumann Fellow in the Institute for Advanced Study's School of Mathematics (2024–25), recounts how dialogue with a School of Historical Studies colleague over lunch revealed connections between disparate fields.

Bennett Chow, Member in the Institute for Advanced Study's School of Mathematics (2024–25), traces new paths of discovery being undertaken in the field of geometric analysis, influenced in particular by Professor Aaron Naber.