Math Faculty and Emeriti
Faculty
Bhargav Bhatt
Fernholz Joint Professor
Email
Office: Simonyi Hall 213
Curriculum Vitae (PDF File)
Academic Assistant:
Madeleine Perez
Bhargav Bhatt is interested in algebraic geometry in a broad sense, and especially enjoys arithmetic questions. He has made fundamental contributions to p-adic Hodge theory and applied them to longstanding questions in commutative algebra and algebraic topology.
Camillo De Lellis
IBM von Neumann Professor
Email
Office: Fuld Hall 116
Curriculum Vitae (PDF File)
Publications (PDF File)
Preprints (PDF File)
Academic Assistant:
Nina Kowalski
Camillo De Lellis, a geometric analyst, has broad expertise in the calculus of variations, geometric measure theory, and fluid dynamics. Using modern tools and innovative approaches, De Lellis has contributed to central problems in analysis and geometry, resulting in the creation of a transparent proof of regularity and opening new lines of inquiry for geometric analysts to explore.
Irit Dveer Dinur
Betsey Lombard Overdeck Theory of Computing Professor
Email
Office: Simonyi Hall 103
Curriculum Vitae (PDF File)
Academic Assistant:
Andrea Lass
Irit Dinur is interested in error-correcting codes and probabilistically checkable proofs, both of which capture a certain “robustness” in computation. Over the course of her career, she has made numerous transformative contributions to the field of theoretical computer science, publishing groundbreaking work on optimization, expansion of graphs and hypergraphs, coding theory, and differential privacy.
Elon Lindenstrauss
Email
Office: Fuld Hall 119
Curriculum Vitae (PDF File)
Academic Assistant:
Suparna Mahableshwarkar
Elon Lindenstrauss is a leading authority in the field of ergodic theory, dynamical systems, and their applications to number theory. His major breakthroughs include the development of the theory of mean topological dimension, the proof of quantum unique ergodicity for arithmetic surfaces, and the characterization of the set of possible exceptions to the celebrated Littlewood conjecture in Diophantine approximation.
Jacob Lurie
Frank C. and Florence S. Ogg Professor
Email
Office: Simonyi Hall 203
Academic Assistant:
Nina Kowalski
Jacob Lurie’s research has influenced a diverse range of fields from topology to number theory, providing foundational work that has changed the way mathematicians describe and work with derived phenomena. His ideas have redefined the foundations of homotopy theory and topological aspects of algebraic geometry, providing a channel through which algebraic topology influences algebraic geometry. His proof of the Baez-Dolan cobordism hypothesis changed the field drastically, providing a precise dictionary between manifold theory and operadic algebra as well as an applicable language for topological field theory.
Aaron Naber
Email
Office: Fuld Hall 221
Curriculum Vitae (PDF File)
Academic Assistant:
Madeleine Perez
Aaron Naber, a world-renowned geometric analyst, has opened new horizons for studying singular sets arising in the calculus of variations. Powerful techniques that he has developed in the field of Riemannian geometry have also brought about new understandings of the structure of Gromov-Hausdorff limit spaces with lower Ricci bounds, Einstein manifolds, and their degenerations.
Tim Roughgarden
Email
Academic Assistant:
Andrea Lass
Widely regarded as a field-defining figure in algorithmic game theory, Tim Roughgarden works at the interface of computer science and economics, and on the design, analysis, and limitations of algorithms. His research spans many application areas, including networks, auctions, markets, and blockchain protocols. He has written or edited numerous books and monographs, including Twenty Lectures on Algorithmic Game Theory (Cambridge University Press, 2016), Beyond the Worst-Case Analysis of Algorithms (Cambridge University Press, 2021), and the Algorithms Illuminated series (Soundlikeyourself Publishing, 2017–2022).
Akshay Venkatesh
Robert & Luisa Fernholz Professor
Email
Office: Fuld Hall 315
Academic Assistant:
Nina Kowalski
Akshay Venkatesh is a mathematician who has worked on many topics at the interface between number theory and other fields, including representation theory, dynamics, and algebraic topology. His recent work examines new algebraic structures related to the topology of locally symmetric spaces.
Avi Wigderson
Herbert H. Maass Professor
Email
Office: Simonyi Hall 013
Academic Assistant:
Andrea Lass
Avi Wigderson is a widely recognized authority in the diverse and evolving field of theoretical computer science. His main research area is computational complexity theory. This field studies the power and limits of efficient computation and is motivated by such fundamental scientific problems as: Does P = NP? (Can mathematical creativity be efficiently automated?) Can every efficient process be efficiently reversed? (Is electronic commerce secure?) Can randomness enhance efficient computation? Can quantum mechanics enhance efficient computation? How do we learn, and can machines be taught to learn like us (or better)?
Emeriti
Enrico Bombieri
Professor Emeritus
Email
Office: Simonyi Hall 212
Academic Assistant:
Krista Carroll
Enrico Bombieri, a Fields Medalist for his work on the large sieve and its application to the distribution of prime numbers, is one of the world’s leading authorities on number theory and analysis. His work ranges from analytic number theory to algebra and algebraic geometry, and the partial differential equations of minimal surfaces. In the past decade, his main contributions have been in the active area of Diophantine approximation and Diophantine geometry, exploring questions on how to solve equations and inequalities in integers and rational numbers. Some of the above topics, in particular those related to prime number theory, have potential practical applications to cryptography and security of data transmission and identification.
Pierre Deligne
Professor Emeritus
Email
Office: Fuld Hall 210
Curriculum Vitae (PDF file)
Publications (Website) (PDF file)
Letters (PDF File)
Academic Assistant:
Andrea Lass
Pierre Deligne is known for his work in algebraic geometry and number theory. He pursues a fundamental understanding of the basic objects of arithmetical algebraic geometry—motive, L-functions, Shimura varieties—and applies the methods of algebraic geometry to trigonometrical sums, linear differential equations and their monodromy, representations of finite groups, and quantization deformation. His research includes work on Hilbert’s twenty-first problem, Hodge theory, the relations between modular forms, Galois representations and L-series, the theory of moduli, tannakian categories, and configurations of hyperplanes.
Phillip Griffiths
Professor Emeritus
Email
Office: Fuld Hall 214
Curriculum Vitae (PDF file)
Bibliography (PDF File)
Selected Works (PDF File)
Selected Works on Albert - The Digital Repository of the IAS (PDF File)
Academic Assistant:
Krista Carroll
Phillip Griffiths initiated with his collaborators the theory of variation of Hodge structure, which has come to play a central role in many aspects of algebraic geometry and its uses in modern theoretical physics. In addition to algebraic geometry, he has made contributions to differential and integral geometry, geometric function theory, and the geometry of partial differential equations. A former Director of the Institute (1991–2003), Griffiths chaired the Science Initiative Group, which fosters science in the developing world through programs such as the Carnegie–IAS African Regional Initiative in Science and Education.
Helmut Hofer
Professor Emeritus
Email
Office: Fuld Hall 112
Curriculum Vitae (PDF file)
Publications List (PDF file)
Academic Assistant:
Suparna Mahableshwarkar
One of the founders of the area of symplectic topology, Helmut Hofer works on symplectic geometry, dynamical systems, and partial differential equations. His fundamental contributions to the field have led to a new area of mathematics known as Hofer geometry.
Robert Langlands’s profound insights in number theory and representation theory include the formulation of general principles relating automorphic forms and algebraic number theory; the introduction of a general class of L-functions; the construction of a general theory of Eisenstein series; the introduction of techniques for dealing with particular cases of the Artin conjecture (which proved to be of use in the proof of Fermat’s theorem); the introduction of endoscopy; and the development of techniques for relating the zeta functions of Shimura varieties to automorphic L-functions. Mathematicians have been working on his conjectures, the Langlands Program, for the last three decades. He spent a good deal of time in the late eighties and nineties and with some success studying lattice models of statistical physics and the attendant conformal invariance. In recent years, he has been preoccupied by the geometric theory of automorphic forms. He has only now reached the stage at which he can contemplate publication.
Robert D. MacPherson
Professor Emeritus
Email
Office: Fuld Hall 213
Curriculum Vitae (Website)
Publications (PDF File)
Academic Assistant:
Suparna Mahableshwarkar
Robert MacPherson’s work has introduced radically new approaches to the topology of singular spaces and promoted investigations across a great spectrum of mathematics. He works in several fields of geometry-topology, algebraic geometry, differential geometry, and singularity theory. He is especially interested in aspects of geometry that interact with other areas of mathematics, such as the geometry of spaces of lattices, which interacts with modular forms, and the geometry of toric varieties, which interacts with combinatorics.
Peter Sarnak
Professor Emeritus
Email
Office: Simonyi Hall 113
Curriculum Vitae (PDF File)
Bibliography (PDF File)
Publications (Website)
Academic Assistant:
Madeleine Perez
Peter Sarnak has made major contributions to number theory and to questions in analysis motivated by number theory. His interest in mathematics is wide-ranging, and his research focuses on the theory of zeta functions and automorphic forms with applications to number theory, combinatorics, and mathematical physics.
Thomas Spencer
Professor Emeritus
Email
Office: Simonyi Hall 219
Academic Assistant:
Krista Carroll
Thomas Spencer has made major contributions to the theory of phase transitions and the study of singularities at the transition temperature. In special cases, he and his collaborators have proved universality at the transition temperature. Spencer has also worked on partial differential equations with stochastic coefficients, especially localization theory. He is presently developing a mathematical theory of supersymmetric path integrals to study the quantum dynamics of a particle in random media. His other interests include random matrices, chaotic behavior of dynamical systems, and nonequilibrium theories of turbulence.
Distinguished Visiting Professors
Karen Uhlenbeck
Professor Emeritus
Email
Office: Simonyi Hall 210
Karen Uhlenbeck works primarily on geometric partial differential equations. She has worked in the areas of the calculus of variations, minimal surfaces, harmonic maps, gauge theory, and integrable systems. Her current interest is in analysis connected with the best Lipschitz model for Teichmüller space of Thurston.
Michael Hutchings
Distinguished Visiting Professor
Email
Office: Fuld Hall 418
Michael Hutchings is interesed in low dimensional and symplectic topology and geometry.
Past Faculty
Past Faculty Members in the School of Mathematics.