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.)
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
Vadim Gorin: (Moscow, 2011) Integrable probability, random matrices, asymptotic representation theory (also in the probability group.)
Shaoming Guo: (Bonn, 2015) Harmonic analysis, analytic number theory, combinatorics, geometric measure theory, partial differential equations (also in the analysis group.)
Shamgar Gurevich: (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.
Michael Kemeny: (Bonn, 2015) Algebraic geometry and commutative algebra, in particular the study of moduli and syzygies of algebraic varieties.
Hanbaek Lyu: (Ohio State, 2018) Discrete probability, dynamical systems, networks, optimization, machine learning (also in the probability group.)
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.)
Jose Israel Rodriguez: (Berkeley, 2014) Applied algebraic geometry and algebraic methods for statistics.
Amos Ron: (Tel Aviv, 1987) Approximation theory, wavelets, Gabor systems, splines, polynomial interpolation, data representation, frames, scientific data, applications (joint appointment with CS.)
Ananth Shankar: (Harvard, 2017) Arithmetic geometry and number theory.
Paul Terwilliger: (Illinois, 1982) Algebraic combinatorics, representation theory, Lie algebras, quantum groups, special functions.
Botong Wang: (Purdue, 2012) Complex algebraic geometry, algebraic statistics and combinatorics. (Also in the geometry/topology group)
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.
Daniel Corey: (Yale, 2018) Tropical geometry
Yousheng Shi: (Maryland, 2019) Number theory, automorphic forms
Mark Shusterman: (Tel Aviv, 2019) Number theory and group theory
Aleksandra (Ola) Sobieska: (Texas A&M University, 2020) Commutative algebra, combinatorics
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)
Combinatorics Seminar (Mondays at 2:25)
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)
Online Social Chit-Chats (various times)
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
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
I. Martin Isaacs Professor, Ph.D. Harvard University (1964) Research: Group Theory, Algebra
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
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.