Bhargav Bhatt Joins Mathematics Faculty at IAS

Recognized for Revolutionary Contributions to Arithmetic Geometry and Related Fields

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Lee Sandberg

Bhargav Bhatt, an internationally renowned expert in arithmetic algebraic geometry and commutative algebra, has joined the Institute for Advanced Study as Fernholz Joint Professor in the School of Mathematics, effective July 1, 2022. His new position is a joint appointment with Princeton University, with IAS serving as his home institution. Bhatt joins from the University of Michigan, where he is currently on leave as the Frederick W. and Lois B. Gehring Professor.

Among Bhatt’s principal achievements is the introduction—with frequent collaborator Peter Scholze, building on their previous joint work with Matthew Morrow—of the theory of prismatic cohomology. This fundamental discovery in arithmetic algebraic geometry is widely regarded for its simplicity and many applications. His original research, coupled with his skill as an expositor of ideas, have established Bhatt as a driving force of the field.

“Bhargav combines mathematical creativity with a penchant for collaboration and the ability to perceive analogies across seemingly dissimilar fields,” stated David Nirenberg, IAS Director and Leon Levy Professor. “His presence at the Institute will surely facilitate discovery, not only in his own work, but for many others in our mathematical community.”

Bhatt first came to IAS as a Member (2012–14) in the School of Mathematics and returned as a Visitor (2020). Primarily focused on algebraic geometry and its interactions with number theory, commutative algebra, homotopy theory, Bhatt’s work complements current research conducted in the School of Mathematics by fellow Faculty members Jacob Lurie and Robert and Luisa Fernholz Professor Akshay Venkatesh.

“There has been a real revolution in p-adic geometry over the last few years, with Bhargav Bhatt as one of its leading figures,” remarked Lurie. “I’m thrilled that he’ll be joining the Faculty of the School of Mathematics.”

Initially an engineering student, Bhatt worked to understand bridges from a physical standpoint. He ultimately found his calling in the bridges he built between disparate areas of mathematics, including commutative algebra, derived geometry, birational geometry, and p-adic Hodge theory.

In the field of commutative algebra, Bhatt has made several important contributions to the circle of ideas surrounding Hochster’s direct summand conjecture. Following a formal proof of the conjecture by Yves André, Bhatt proved a much stronger version of Hochster’s conjecture based on the Cohen–Macaulay property and Kodaira vanishing up to finite covers. His proof makes essential use of the theory of prismatic cohomology.

His work on extensions of de Rham (and crystalline) cohomology to singular algebraic varieties using derived methods builds on the work of Luc Illusie and Alexander Beilinson. Bhatt’s efforts resulted in new proofs of comparison theorems in p-adic Hodge theory, namely the crystalline comparison conjecture of Fontaine and the semi-stable comparison conjecture of Fontaine-Jannsen.

A prolific collaborator, Bhatt advances the mathematics community through the power of his ideas and the ease with which he communicates them. He is also a generous mentor, willingly sharing his time and insights with other researchers. Such interactions will enrich the collaborative atmosphere that is crucial to the Institute’s mission: to support the development of scholars and inspire research at the highest levels.

“I’m deeply honored (and frankly a bit daunted) by this appointment,” commented Bhatt. “The Institute and Princeton University have been home to many remarkable breakthroughs in mathematics in the last century. On a personal level, both institutions have played decisive roles in my own development. It is a privilege to be back, and I look forward to contributing to the intellectual community here.”

Bhatt earned a B.S. in Applied Mathematics from Columbia University (2005) and went on to receive his M.A. and Ph.D. in Mathematics from Princeton University (2010) under the advisement of Aise Johan de Jong.

Bhatt’s achievements have received wide international recognition. He received the 2021 New Horizons in Mathematics Prize from the Breakthrough Prize Foundation, “for outstanding work in commutative algebra and arithmetic algebraic geometry, particularly on the development of p-adic cohomology theories.” He is also the recipient of the 2021 Clay Research Award of the Clay Mathematics Institute. Bhatt received a Packard Fellowship (2015), was named Eilenberg Chair at Columbia University (Fall 2018), and was elected as a Simons Investigator (2019) and Fellow of the American Mathematical Society (2021). He is scheduled to deliver a plenary talk at the International Congress of Mathematicians on July 11, 2022.

About the Institute
The Institute for Advanced Study has served the world as one of the leading independent centers for theoretical research and intellectual inquiry since its establishment in 1930, advancing the frontiers of knowledge across the sciences and humanities. From the work of founding IAS faculty such as Albert Einstein and John von Neumann to that of the foremost thinkers of the present, the IAS is dedicated to enabling curiosity-driven exploration and fundamental discovery.

Each year, the Institute welcomes more than 200 of the world’s most promising post-doctoral researchers and scholars who are selected and mentored by a permanent Faculty, each of whom are preeminent leaders in their fields. Among present and past Faculty and Members there have been 35 Nobel Laureates, 44 of the 62 Fields Medalists, and 22 of the 25 Abel Prize Laureates, as well as many MacArthur Fellows and Wolf Prize winners.