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.)

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.

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) Representation theory, with applications to harmonic analysis, signal processing, mathematical physics.

Michael Kemeny: (Bonn, 2015) Algebraic geometry and commutative algebra, in particular the study of moduli and syzygies of algebraic varieties.

Brian Lawrence: (Stanford, 2017) Number theory, arithmetic geometry.

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.)

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

Boya Wen: (Princeton, 2021) Number theory and arithmetic geometry.

Ziquan Yang (Harvard, 2021) Number theory and arithmetic geometry.

Aleksandra (Ola) Sobieska: (Texas A&M University, 2020) Commutative algebra, combinatorics

Joshua Mundinger: (Chicago, 2023) Representation theory, algebraic geometry, arithmetic geometry.

Thomas Yahl (Texas A&M, 2023) Algebraic geometry, applied algebra.

Seminars in algebra

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

Algebra and Algebraic Geometry Seminar (Fridays at 2:30)

Graduate Algebraic Geometry Seminar (Wednesdays at 4:00)

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

Previous conferences in algebra held at UW

Madison Moduli Weekend, September 2020.

ANTS XIII (Algorithmic Number Theory Symposium), July 2018

Arithmetic of Algebraic Curves, April 2018

Singularities in the Midwest V, March 2018

Singularities in the Midwest IV, March 2017

Applied Algebra Days 3, May 2016

Upper midwest commutative algebra colloquium, November 2015

Stratified spaces in geometric and computational topology and physics (Shaneson 70), March 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.

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 Georgia, Washington U., UIUC, Bowdoin, Leiden, 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, Two Sigma, 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

Nigel Boston Professor, Ph.D. Harvard (1987) Research: Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering

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.