The Department of Mathematics is committed to provide a setting that fosters excellence in teaching, learning and research, and that communicates to students the beauty and excitement of mathematics. We seek opportunities for undergraduates, graduate students, faculty, and staff to interact in productive ways. Both the Department and its individual members take their responsibilities seriously, and have produced a system that successfully teaches mathematics to students at all levels.
The department teaches nearly 5000 students each year. The department records over forty majors a year in five different tracks for the major. A wide range of students from many departments take courses from our department each year. Most students at Washington University in St. Louis will visit our Department. The Department of Mathematics teaches more student hours in the Fall semester than any other department in Arts & Sciences, and is consistently among the top five departments for student hours taught in the Spring semester.
Faculty members are hired with an eye both to their teaching and research. The department is roughly divided into four loosely knit and sometimes overlapping research groups which can be generically listed as: algebra, analysis, geometry, and statistics.
Algebra includes commutative algebra, algebraic geometry, group theory, combinatorics, and algebraic K-theory. The algebra group contains Mohan Kumar, David Wright, John Shareshian, Roya Beheshti, Matthew Kerr, Jack Shapiro, Wushi Goldring, and William Chauvenet Lecturer Xuanyu Pan. Mohan Kumar, Roya Beheshti, and Matthew Kerr specialize in algebraic geometry, David Wright in affine algebraic geometry and polynomial automorphisms, Jack Shapiro in K-Theory, and John Shareshian in group theory and combinatorics. A weekly seminar on algebraic geometry meets during the academic year, as does a seminar on combinatorics. See the Events area of our website for all seminars details.
Analysis covers functional analysis, harmonic analysis, and complex variables. The analysis group consists of John McCarthy, Gregory Knese, Brett Wick, Victor Wickerhauser, Ari Stern, Steve Krantz, and Brian Blank, plus Emeriti professors, Richard Rochberg, Ed Wilson, and Guido Weiss. Each has a free-standing research program, but they have a rich web of overlapping interests, discuss mathematics with each other often and have had a few joint papers over the years. This group has seen considerable activity in the area of wavelets with Guido Weiss and Ed Wilson as the principal instigators. Victor Wickerhauser specializes in applied and computational harmonic analysis and works with researchers in other departments. He has a courtesy joint appointment in Biomedical Engineering. Steve Krantz works in the field of several complex variables, primarily on analytical problems, but with many techniques intersecting interests of people in the geometry group. Ari Stern specializes in geometric numerical analysis, particularly applications of differential and symplectic geometry to numerical integration and finite element methods. John McCarthy works on Operator theory and its applications in analysis, especially to several complex variables. He has also collaborated with scientists in a wide range of disciplines, including biology, engineering, medicine and physics. A weekly analysis seminar is offered during the academic year.
Geometry includes differential geometry, topology, and dynamical systems. The group is composed of Quo-Shin Chi, Rachel Roberts, Renato Feres, Xiang Tang, Steve Krantz, Ari Stern, and postdoctoral instructor Songhao Li. We also have several Emeriti professors in this group: Gary Jensen, Ed Wilson, and Lawrence Conlon. Chi and Jensen share a broad interest in the geometry of submanifolds, in which they have published four joint papers. Chi's interests in algebraic geometry have led to his interaction with members of the algebra group. Feres's interests are based in dynamical systems and spread to foliation theory, rigidity theorems, and applications to physics and engineering. Larry Conlon works on the topology and geometry of foliated manifolds and Ed Wilson is the department expert on every aspect of Lie groups and Lie algebras. Rachel Roberts is a topologist working on problems from low dimensional topology. Xiang Tang's research in quantization and noncommutative geometry has broadened significantly the Department's research activity in Geometry. Generally, this group runs several seminars in a semester since their interests are quite wide. A weekly topology & geometry seminar is offered during the academic year.
The statistics group in the mathematics department contains Ed Spitznagel, Nan Lin, Jimin Ding, Todd Kuffner, Jose Figueroa-Lopez, and Postdoctoral Teaching Fellow in Statistics Han Liang Gan. Stanley Sawyer is a Professor Emeritus. Jeff Gill (political science) has a courtesy appointment, and is also an active member of the statistics group. Spitznagel is known across the University community for collaborations in many different fields, especially in the Medical School. Lin's methodological research is in the areas of statistical computing for massive data, Bayesian regularization, bioinformatics, longitudinal and functional data analysis and psychometrics. His applied research involves statistical analysis of data from anesthesiology, genomics and cognition. Ding works in statistical survival analysis and has an ongoing collaboration with the Fred Hutchinson Cancer Research Institute in Seattle. Kuffner works on asymptotic theory, in particular for likelihood methods, as well as the bootstrap, objective Bayes and Bayesian asymptotics. Figueroa-Lopez is an expert on short-time asymptotics for continuous-time stochastic models with jumps, nonparametric inference for Levy-based models, stochastic control & stochastic optimization in jump-diffusion models & hidden Markov-switching models, and applications of these methods to mathematical finance. Gill has done extensive work developing Bayesian hierarchical models and nonparametric Bayesian models, and also has expertise in Markov chain Monte Carlo (MCMC) tools. Gan's research is in probability theory, in particular the approximation of conditional random variables using Stein's method. A statistics seminar as well as a reading group in probability & statistics are offered by the statistics group during the academic year.
Blake Thornton (Room 108A) serves as the department's Associate Director of Undergraduate Studies; Mohan Kumar serves as Director of Graduate Studies.
Faculty members participate each semester in the College's Course Evaluation program to receive student feedback on their teaching and course design. Faculty members propose ideas for new, special-topic courses for majors and other students in the University.
Building on their own research and classroom teaching, faculty provide opportunities for students to work on projects or research of their own. Faculty present ideas to students through lectures, seminars, colloquia, the math club, in course work, and on web pages such as the Faculty Ideas for Undergraduate Projects or Research in the Undergraduate area of our website.
Graduate Teaching Assistants
Our graduate teaching assistants work with students in lower division courses and sometimes provide assistance with more advanced courses. TAs are visited in their classes at least once a year, advised by experienced teachers, and their students offer feedback through e-mail (including an anonymous option) and in an evaluation survey at the end of each semester.
The department has five full-time staff members and one part-time member.
Fiona Vaughn, Mary Ann Stenner, Lori Amundson, and Camille Johnson are housed in the department office in room 100 of Cupples I on the Danforth campus, and headed by Business Manager Fiona Vaughn, who also serves as Department Accountant and Grants Specialist. Their duties are roughly apportioned as follows: Mary Ann Stenner assists with the graduate program and events, Lori Amundson assists with the undergraduate program, reimbursements, and is the textbook coordinator, and Camille Johnson fields department related questions, helps with grants, assists the Department Chair, and is the website contact.
Our Computing Manager is Steven Xiao, whose office is in room 13.