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. (Also in the geometry/topology group)
Jordan Ellenberg: (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.
Daniel Erman: (Berkeley, 2010) Algebraic geometry and commutative algebra
Shamgar Gurevich: (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.
Simon Marshall: (Princeton, 2010) Analytic number theory (also in the analysis group.)
Laurentiu Maxim: (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)
Steven Sam: (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics
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
Michael Brown: (Nebraska, 2015) K-theory, commutative algebra, (noncommutative) algebraic geometry.
Alexandra Kjuchukova: (Penn, 2015) Topology of algebraic varieties, branched covers
Alexander Pavlov: (U Toronto, 2015) Commutative algebra, algebraic geometry
Naser T. Sardari: (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces
John Wiltshire-Gordon: (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories
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)
Applied Algebra Seminar (Thursdays 11)
Combinatorics Seminar (Mondays at 2:25)
Lie Theory Seminar (Mondays at 1:20 in VV901)
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
ANTS XIII (Algorithmic Number Theory Symposium), July 2018
Arithmetic of Algebraic Curves, April 2018
Singularities in the Midwest V, March 2018
Previous conferences in algebra held at UW
Singularities in the Midwest IV, March 2017
Applied Algebra Days 3, May 2016
Upper midwest commutative algebra colloquium, November 2015
Applied Algebra Days 2, May 2014
Group Theory, Number Theory, and Topology Day, January 2013
Mirror Symmetry in the Midwest, November 2012
Midwest Algebraic Geometry Graduate Conference, November 2012
Applied Algebra Days, October 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, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, 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.