# Algebra

**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**

Dima Arinkin: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.

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) 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.

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

Melanie Matchett Wood: (Princeton, 2009) Number theory and arithmetic geometry.

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**

Matthew Ballard: (U Washington, 2008) Homological mirror symmetry.

Robert Harron: (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms.

Zev Klagsbrun: (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry.

Sean Rostami: (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties

Owen Sizemore: (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups

**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)

Combinatorics Seminar (Mondays at 2:25)

Lie Theory Seminar (Mondays at 1:20 in VV901)

Group Theory Seminar (being organized, maybe late Tuesday, contact Nigel Boston if interested)

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

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

SILO (Systems, Information, Learning and Optimization) (Wednesdays at 12:30)

**Upcoming conferences in algebra held at UW**

Midwest Algebraic Geometry Conference for Graduate Students -- watch this space!

**Previous conferences in algebra held at UW**

Applied Algebra Days, October 21-23 2011

Midwest Number Theory Conference for Graduate Students, November 2011

RTG Graduate Student Workshop in Algebraic Geometry, October 2010

Workshop on Pseudo-Anosovs with Small Dilatation, April 2010

Singularities in the Midwest, March 2010

RTG 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

**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, University of Cologne(Germany), 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.

**Emeritus faculty in algebra**

Richard Askey John Bascom Professor, Ph.D Princeton (1961) Research: Special Functions

Steven Bauman Professor, University of Illinois at Urbana-Champaign (1962) Research: Finite group theory

Georgia Benkart E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) Research: Lie Theory, Quantum Groups and Representation Theory.

Michael Bleicher Professor, Ph.D. Tulane University and University of Warsaw (1961) Research: Number theory and convex geometry

Richard A. Brualdi Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory

Donald Crowe Professor, Ph.D. University of Michigan (1959) Research: Classical geometry and African patterns

Hiroshi Gunji Professor, Ph.D. Johns Hopkins University (1962) Research: Algebraic geometry

I. Martin Isaacs Professor, Ph.D. Harvard University (1964) Research: Group Theory, Algebra

Arnold Johnson Professor, Ph.D. University of Notre Dame (1965) Research: Classical Groups

Lawrence Levy Professor, Ph.D. University of Illinois at Urbana-Champaign (1961) Research: Commutative and noncommutative ring theory

J. Marshall Osborn Professor, Ph.D. University of Chicago (1957) Research: Non-associative rings and Lie algebras

Donald Passman Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) Research: Associative Rings and Algebras, Group Theory

Hans Schneider J. J. Sylvester Professor of Mathematics, Ph.D. University of Edinburgh (1952) Research: Linear algebra and matrix theory

Louis Solomon Professor, Ph.D. Harvard University (1958) Research: Finite group theory and hyperplane arrangements

Robert Wilson Professor, Ph.D. University of Wisconsin-Madison (1969) Research: Algebra, Math. Education.