Geometry

Hong Wang, Member (2019–21) in the School of Mathematics, and her colleague Joshua Zahl have proven the three-dimensional Kakeya conjecture, a problem that has, until now, “eluded some of the greatest living mathematicians.” Their work has built on that of other IAS scholars, including Jean Bourgain, Professor (1994–2018) in the School, and Terence Tao, Member (2005, 2023) in the School.

In July, 184 participants from 17 countries travelled to Park City, Utah to attend the latest iteration of Park City Mathematics Institute (PCMI), an annual Institute for Advanced Study outreach program. The attendees explored motivic homotopy theory, which offers mathematicians the opportunity to better understand complex algebraic shapes by using flexible tools from homotopy theory.

Michael Magee, current von Neumann Fellow in the School of Mathematics, has won a Philip Leverhulme Prize for mathematical research, specifically his work on spectral geometry.

By Siobhan Roberts, frequent Director's Visitor:

"Lisanne Taams, a student at Radboud University in the Netherlands, is working on a Ph.D. about, in her words, 'computing motives of moduli stacks of vector bundles on stacky curves.'"

Anna Wienhard, current Member in the School of Mathematics, has received the Hector Science Award 2022 from the Hector Foundation, which honors outstanding scientists from German universities and research institutions. 

Past Members in the School of Mathematics Peter B. Kronheimer (1987–89) and Tomasz Mrowka (2003–04) have received the 2023 Leroy P. Steele Prize for Seminal Contribution to Research.

"'It’s easy to cover a floor with copies of squares, triangles or hexagons [...] but only in ways that never repeat. 'You want to understand the structure of such tilings,' said Rachel Greenfeld, a mathematician at the Institute for Advanced Study in Princeton, New Jersey. 'How crazy can they get?' Pretty crazy, it turns out."

"Like many people who would go on to become mathematicians, Wei Ho grew up competing in math contests. In eighth grade, she won the Mathcounts state competition in Wisconsin, and her team took third place at nationals."

Assaf Naor, Member in the School of Mathematics, has received the 2018 Frederic Esser Nemmers Mathematics Prize from Northwestern University for his profound work on the geometry of metric spaces, which has led to breakthroughs in the theory of...