Number Theory | University of Michigan

Faculty

Bhargav Bhatt — Frederick W and Lois B Gehring Professor of Mathematics

Professor Bhatt's research interests lie at the intersection of two fields of mathematics: algebraic geometry (which studies solutions to systems of polynomial equations in many variables) and number theory (which studies properties and relationship of numbers). The interaction between these fields is often mediated through a third field: topology (which studies the qualitative features of shapes). Bhatt's research exploits this connection to transport problems in one field to potentially more tractable problems in the other.

Charlotte Chan — Assistant Professor (starting fall 2021)

Professor Chan works in geometric representation theory and number theory. For example, she uses algebro-geometric methods in representation theory to understand phenomena within the framework of the Langlands program. She is also interested in automorphic representations and L-functions.

charchan@umich.edu | webpage | arXiv

Stephen DeBacker — Arthur F. Thurnau Professor

Professor DeBacker's research is directed towards questions in harmonic analysis for reductive p-adic groups. In particular, he has recently been interested in stability questions. His work uses a great deal of Bruhat–Tits theory, and, to this end, he also studies the structure of reductive groups over nonarchimedean local fields.

smdbackr@umich.edu | webpage | profile | genealogy | arXiv

Wei Ho — Associate Professor

Professor Ho's research interests lie in number theory and algebraic geometry. She uses techniques and ideas from (or finds applications in) other fields such as invariant theory, dynamics, and combinatorics.

Tasho Kaletha — Associate Professor

Professor Kaletha’s research interests include the stable topological trace formula, the local Langlands correspondence and endoscopy for p-adic groups, and the asymptotic behavior of divisibility functions for arithmetic groups. Currently, he is focusing on endoscopic character identities for L-packets on p-adic groups.

kaletha@umich.edu | webpage | profile | genealogy | arXiv

Jeff Lagarias — Harold Mead Stark Distinguished University Professor

Professor Lagarias' research interests are diverse. His initial training was in analytic and algebraic number theory. After receiving his PhD in 1974, Lagarias worked at Bell Laboratories and AT&T Labs until 2003, on problems in many pure and applied fields. Besides number theory, he has made contributions in harmonic analysis (wavelets and fractals), mathematical optimization (interior point methods), discrete geometry (tilings and quasicrystals), ergodic theory, low-dimensional topology (complexity of unknotting), and theoretical computer science.

James Milne — Professor Emeritus

Professor Milne likes to call his area "arithmetic geometry". Roughly speaking algebraic geometry studies the geometric objects (algebraic varieties) defined by polynomial equations over an algebraically closed field, and arithmetic geometry studies the same objects over arithmetically interesting fields such as the rational numbers. Thus it is a fascinating mixture of algebraic number theory and algebraic geometry.

Hugh Montgomery — Professor Emeritus

Professor Montgomery studies number theory and harmonic analysis, mainly analytic number theory, and most especially the distribution of prime numbers, properties of the Riemann zeta function, and the distribution of its zeros. Further interests include Diophantine approximation, the geometry of numbers, transcendence, power sums, irregularities of distribution, extremal properties of trigonometric polynomials, and analytic inequalities.

Kartik Prasanna — Professor

Professor Prasanna's interests lie in the arithmetic of L-functions and algebraic cycles and especially in the conjectures of Bloch–Beilinson and Bloch–Kato which are vast generalizations of the Birch and Swinnerton–Dyer conjecture. A related research interest that he is very fond of is the study of periods of motives/automorphic forms. Prasanna's collaborators include Massimo Bertolini, Henri Darmon, Atsushi Ichino, Chris Skinner and Akshay Venkatesh.

kartikp@umich.edu | webpage | profile | genealogy | arXiv

Andrew Snowden — Professor

Professor Snowden mostly works in the new field of representation stabiltiy, which combines commutative algebra and representation theory, often in infinite dimensional settings. The typical objects of study are infinite dimensional varieties, infinite polynomial rings, and representations of combinatorial categories. He also does some work within number theory and arithmetic geometry.

Mike Zieve — Professor

Professor Zieve studies questions with an algebraic flavor in various areas of math, including algebra, number theory, algebraic geometry, combinatorics, coding theory, complex analysis, and topology. For more information please see his homepage.

zieve@umich.edu | webpage | profile | genealogy | arXiv