Mathematics, PhD

Chair

Uday Banerjee, 215 Carnegie, 315-443-1472.

Faculty

Uday Banerjee, Pinyuen Chen, Dan Coman, J. Theodore Cox, Steven Diaz, Helen M. Doerr, Jack E. Graver, Philip S. Griffin, Peter D. Horn, Tadeusz Iwaniec, Hyune-Ju Kim, Mark Kleiner, Leonid Kovalev, Loredana Lanzani, Graham J. Leuschke, Adam Lutoborski, Joanna O. Masingila, Terry R. McConnell, Claudia Miller, Jani Onninen, Evgeny Poletsky, Declan Quinn, Lixin Shen, John Ucci, Gregory Verchota, Andrew Vogel, William Voltermann, Stephan Wehrli, William Wylie, Yuan Yuan, Dan Zacharia

The Department of Mathematics has 31 faculty members, with research interests in several areas of mathematics, statistics, and mathematics education, and approximately 55 graduate students. The department is housed in the recently renovated Carnegie Library building on the main campus quadrangle. Programs of study include those for M.S. and Ph.D. degrees in Mathematics, with or without a concentration in Statistics, and for M.S. and Ph.D. degrees in Mathematics Education.

Ph.D. in Mathematics

Doctoral students are expected to have completed the requirements for a master’s degree in mathematics or the equivalent. They then take at least 60 credits of additional work including up to 30 credits of dissertation credit and at least 30 credits of coursework. All students must demonstrate a mastery of English. Students must pass preliminary examinations in analysis and algebra and qualifying examinations in a major area and a minor area chosen (subject to some restrictions), from algebra, analysis, combinatorics, numerical analysis, statistics, and topology. Students who successfully complete the qualifying examination are granted the Master’s of Philosophy (M.Phil.) degree in mathematics. Each Ph.D. student must defend in oral examination a dissertation that demonstrates ability to carry out independent investigation which makes an original contribution to mathematics. Mathematics students may write a Ph.D. dissertation under certain faculty members in computer science. Further information is available from Mark Kleiner, 215 Carnegie Building, or on our web site: math.syr.edu.

Research Areas

The department’s Colloquium series features weekly lectures by mathematicians from all over the United States and abroad in many of the areas of mathematical research represented in the department. Furthermore several of the research groups organize regular research seminars. Colloquia and seminar schedules, along with other information about our programs, courses, and events, can be found at math.syr.edu.

The following research groups are currently represented in the department.

Algebra

Algebraic geometry (moduli spaces of curves, equations defining finite sets of points), commutative algebra (homological algebra, Cohen-Macaulay modules, characteristic p), non-commutative algebra (representations of finite-dimensional algebras, homological algebra, group actions on non-commutative rings, Hopf algebras, enveloping algebras, non-commutative algebraic geometry). Faculty: Diaz, Kleiner, Leuschke, Miller, Quinn, Zacharia.

Analysis

Complex analysis (several complex variables, pluripotential theory, complex dynamics, invariant metrics, holomorphic currents, Kähler geometry, rigidity problems), geometric analysis (PDE on manifolds, geometric flows), harmonic analysis, partial differential equations (linear and nonlinear elliptic PDE, boundary value problems on nonsmooth domains), geometric function theory (quasiconformal mappings, analysis on metric spaces). Faculty: Coman, Iwaniec, Kovalev, Lanzani, Onninen, Poletsky, Verchota, Vogel, Wylie, Yuan.

Applied Mathematics

Numerical analysis (approximate solutions of elliptic PDE, generalized finite element methods and meshless methods), nonlinear variational problems (microstructure in nonlinear elasticity), applied and computational harmonic analysis (wavelets, digital image processing). Faculty: Banerjee, Lutoborski, Shen.

Combinatorics

Combinatorics, graph theory, rigidity theory, symmetries of planar graphs, automorphism groups of graphs. Faculty: Graver.

Geometry/Topology

Low-dimensional topology and knot theory (knot concordance, Heegaard Floer homology, homology theories for knots and links), K-theory (topological K-theory of Eilenberg-Mac Lane spaces, equivariant homotopy theory), Riemannian/Kähler geometry (Ricci curvature and topology, special metrics, geometric flows, rigidity problems). Faculty: Horn, Ucci, Wehrli, Wylie, Yuan.

Math Education

Secondary mathematics education, teacher learning, mathematical modeling, out-of-school mathematics practice, teacher development. Faculty: Doerr, Masingila.

Probability

Interacting particle systems, Brownian motion, random walks, probabilistic methods in mathematical finance, martingales. Faculty: Cox, Griffin, McConnell.

Statistics

Ranking and selection theory (applications in radar signal processing and two-stage procedures for multinomial problems), change-point problems, sequential analysis, longitudinal analysis, neural networks. Faculty: Chen, Kim, Voltermann.

Graduate Awards

Figures for graduate appointments represent 2014-2015 stipends.

Graduate Scholarships:

Support graduate study for students with superior qualifications; provide, in most cases, full tuition for the academic year.

Graduate Assistantships:

Offered to most Graduate Scholarship recipients; no more than an average of 15 hours of work per week; nine months; stipend ranging from $17,244.26 to $21,072.77 in addition to tuition scholarship for 24 credits per year. Additional summer support is generally available.

Syracuse University Graduate Fellowships:

Tax-free stipends ranging from $14,250 to $23,830 for nine months of full-time study; tuition scholarship for 15 credits per semester for a total of 30 credits during the academic year.

Facilities

The mathematics library currently holds over 57,000 volumes, including 34,000 books and over 350 print and electronic journal subscriptions Online databases include MathSciNet, Current Index to Statistics, Jahrbuch Database, MathEduc, ERIC, Scopus, and Web of Science.

In addition to covering a broad range of pure and applied mathematics, the mathematics library contains print and electronic resources in the history of mathematics, mathematics education, and statistics. The following resources are available for student borrowing: TI graphing calculators, geometry kits, and course reserve books.

The computer lab in Carnegie Library, Room 208, has 16 computers, and a color printer with copying and scanning capability. The lab computers provide extensive software for statistical or data analysis, data base management, programming, and graphics. More information on computing services and the software available for students may be found on the ITS website: https://its.syr.edu/computer-labs/index.html.

The Carnegie Library contains over 210,000 volumes in the sciences, including biology, chemistry, engineering and computer science, library and information science, nutrition science and dietetics, public health, physics & astronomy, photography, technical arts, pure and applied mathematics, probability and statistics, mathematics education, and military and naval sciences. The historic Reading Room provides a quiet place for students to study and use library resources.