# Research at UW-Madison in Algebra

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**Research at UW-Madison in algebra**

UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.

**Tenured and tenure-track faculty in algebra**

Eric Bach: (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)

Nigel Boston: (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)

Andrei Caldararu: (Cornell, 2000) Algebraic geometry, homological algebra, string theory.

Tullia Dymarz: (Chicago, 2007) (arrives Fall 2011) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis.

Jordan Ellenberg: (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.

Shamgar Gurevich: (Tel Aviv, 2005) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.

I. Martin Isaacs: (Harvard, 1964) Group theory, algebra.

Ken Ono: (UCLA, 1993) (on leave 2010-11) Combinatorics and number theory involving elliptic curves, L-functions, modular forms, Maass forms, and partitions.

Donald Passman: (Harvard, 1964) Ring theory, group theory, group rings and enveloping algebras of Lie algebras.

Paul Terwilliger: (Illinois, 1982) Combinatorics, representation theory and special functions.

Tonghai Yang: (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.

**Postdoctoral fellows in algebra**

David Brown: (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques.

Bryden Cais: (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias.

Sukhendu Mehrotra: (Penn, 2005) Algebraic geometry, homological algebra and string theory, specifically, derived categories of coherent sheaves on algebraic varieties.

**Seminars in algebra**

The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.

Algebraic Geometry Seminar (Fridays at 2:30)

Lie theory seminar (Mondays at 1:20 901VV)

Combinatorics Seminar (Mondays at 2:25)

Group Theory Seminar (Mondays at 3:30)

Number Theory Seminar (outside speakers)(Thursdays at 2:30)

Number Theory Seminar (grad student speakers) (Tuesdays at 2:30)

**Upcoming conferences in algebra held at UW**

Graduate student conference in algebraic geometry, Fall 2010

**Previous conferences in algebra held at UW**

Workshop on Pseudo-Anosovs with Small Dilatation, April 2010

Singularities in the Midwest, March 2010

Midwest Graduate Student Conference in Number Theory, November 2009

Midwest Number Theory Day, November 2009

Miniconference on pro-p groups in number theory, April 2008

Pro-p groups and pro-p algebras in number theory, April 2007

Groups, Rings and Algebras, June 2005

**Graduate study at UW-Madison in algebra**

Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. Here is a list of this fall's graduate courses.

The department holds an NSF-RTG grant in number theory and algebraic geometry, which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas.

Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Imperial (UK), MIT, Princeton, Stanford, and UT-Austin, to tenure-track jobs at McGill, Wake Forest, Bucknell, the University of New Mexico, and the University of South Carolina, and to non-academic positions at places such as Credit Suisse and the Center for Communications Research, La Jolla.