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Mathematics Department
4111 McHenry
Santa Cruz, CA 95064
Phone: 831.459.2969
Fax: 831.459.3260
Hours: 9am-12; 1-3:30pm
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Graduate Program Overview
Research
The Mathematics Department at UC Santa Cruz is small but dynamic, with an ongoing commitment to both research and teaching. The department has leading research programs in several actively developing areas on the frontiers of pure and applied mathematics, interacting strongly with theoretical physics and mechanics. The extraordinary level of National Science Foundation support received by our faculty reflects the high caliber of the research carried out in the department. The current areas of research include:
- Vertex operator algebras, higher genus conformal field theory, modular forms, quasi-Hopf algebras, infinite-dimensional Lie algebras, mathematical physics.
- Representations of Lie and p-adic groups, applications to number theory, Bessel functions, Rankin-Selberg integrals, Gelfand-Graev models.
- Algebra, group theory, finite groups and their representations, conjectures of Alperin, Dade and Broué, Mackey functors, modular representation theory, fusion systems, blocks of finite groups, bisects, bisect functors, Burnside rings, representations of algebras, ring theory, module theory.
- Algebraic topology, elliptic cohomology, quantum field theory, automorphic forms, string topology, topology of Lie groups, loop spaces.
- Symplectic geometry and topology, Floer homology, Poisson Lie groups.
- Dynamical systems, celestial mechanics, geometric mechanics, bifurcation theory, control theory.
- Fluid and continuum mechanics, the Navier-Stokes equation, long time behavior of solutions of PDEs.
- Geometric integration schemes, numerical methods on manifolds.
Algebraic geometry.
- Differential geometry, nonlinear analysis, harmonic maps, Ginzburg-Landau problem.
- General relativity, Einstein's equations, positive mass conjecture, Teichmuller theory.
- Galois and incidence geometry.
- Algebraic number theory, elliptic curves, L-functions, p-adic L-functions, special values of L-functions, Gross-Stark conjecture, Heegner points.
- Graph theory, expander graphs, prime number distribution
- Functional analysis, random matrix theory, spectral gap, operator theory, Banach algebras, harmonic analysis, Wiener-Hopf factorization, statistical physics.
See faculty web pages for more information.
Seminars and workshops
Summer Schools, Workshops and Conferences Attended by our Graduate Students
The department's strong connections to the international mathematics community enable our students to participate in important mathematical events around the globe, present their results, and make substantial contributions to their fields before graduation. Some recent examples of such events include:
- Summer schools at the Mathematical Sciences Research Institute (MSRI).
The UCSC math department is a sponsoring member of MSRI. As such the department regularly sends graduate students to the summer programs at the Institute, with full financial support.
- Academic exchange programs with UC Berkeley and the University of Jena, Germany.
Qualified graduate students can spend up to a year at UC Berkeley. Recent participants in the Berkeley program are Francisco Molina, Ely Kerman, and Basak Gurel. The exchange program with the University of Jena supports short visits of graduate students and their participation in workshops in representation theory. Recent participants in the Jena program are Adam Glesser, Jen Mogel and Abe Berman.
- Conferences and workshops.
Our graduate students have been active participants in numerous national and international programs and conferences, including:- Workshop on Symplectic Techniques in Conservative Dynamics, Lorentz Center, Leiden,Netherlands, 2012
- Workshop Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry, Mathematisches Forschungsinstitut Oberwolfach, Germany, 2012
- MRC 2012 - Discrete and Computational Geometry, in Snowbird, Utah., 2012
- 2012 Women and Mathematics at IAS (21st Century Geometry), IAS, Princeton, USA
I am a co-organizer of this worksho, May 2012
- IV Latin American Conference on Lie Groups and Geometry to be held in the Center for Research in Mathematics (CIMAT) in Guanajuato, México, 27-31 August 2012
- FRG Workshop and Conference on Characters, Liftings, and Types - Washington DC - Jun 19-22 (Link)
- AMS Short Course: Computing with Elliptic Curves using Sage - Boston, MA - Jan 2012
- Pacific Northwest Geometry Seminar, Stanford, February 2012Conference in Memory of Robert Osserman, Stanford University, April 2012
- Northern California Symplectic Geometry Seminar, UC Berkeley and Stanford University, 2010-2012
- Bay Area Differential Geometry Seminar, Mathematical Sciences Research Institute and Stanford University, 2011-2012
- Fifth International Summer School on Geometry, Mechanics, and Control, Autonomous University of Madrid, Spain, July 2011
- Georgia Topology Conference, University of Georgia, USA 2011
- International Conference as part of a Trimester on Contact and Symplectic Topology, Université de Nantes, Nantes, France,
- XIth GESTA Meeting on New Trends in Symplectic and Contact Geometry, CIEM, Castro Urdiales, Spain, 2011
- Workshop Dynamische Systeme, Mathematisches Forschungsinstitut Oberwolfach, Germany, 2011
- Workshop in Conservative dynamics and symplectic geometry, IMPA, Rio de Janeiro, Brazil, 2011
- 5th Geometry, Mechanics and Control theory summer school in La Cristalera, Spain, 2011
- Workshop on Symplectic and Contact Geometry and Topology: Puzzles and Horizons, MSRI, Berkeley, USA 2010
- Xth GESTA Meeting on Symplectic Geometry with Algebraic Techniques, Instituto Superior Técnico, Lisbon, Portugal 2010
- Workshop on Symplectic Geometry and Transformation Groups, ICMS, Edinbourgh, UK 2010
- Workshop on Symplectic Techniques in Conservative Dynamics, Lorentz Center, Leiden,Netherlands 2010
- Uniqueness of maximal two-distance sets on a sphere, Research into Vertex Operator Algebras, Finite Groups and Combinatorics Dec 2010
- US-China Summer School on Representation Theory at East China Normal University, Shanghai, China July 2010
- Application of Nonlinear PDE - AMS sectional meeting at UCLA Oct. 2010
- Symplectic Techniques in Conservative Dynamics, Leiden, The Netherlands Aug 2010
- Workshop on Algebra Representation Theory, Jena, Germany, 2003
- Special Program on Analysis and Non-linear PDEs, Princeton, NJ, 2003
- Geometria em Lisboa Seminar, Lisbon, Portugal, 2003
- AMS-IMS-SIAM Joint Summer Research Conferences: Integer points in polyhedra, Snowbird, UT, 2003
- UCLA-IPAM Program: Symplectic Geometry and Physics, Los Angeles, CA, 2003
- AMS-SIAM Joint Meeting, Mini-symposium on Geometric Integration, San Diego, CA, 2002
- LMS Durham Symposium on Representations of Finite Groups and Related Algebras, Durham, England, 2002
- Symplectic Geometry Workshop, Oberwolfach, Germany, 2002
- AMS Sectional Meeting: Special Session on Symplectic and Contact Topology, Atlanta, GA, 2002
- Floer Homology and Arnold Conjecture Workshop, Oberwolfach, Germany, 2001
- Symplectic and Contact Geometry Workshop, Leiden, Netherlands, 2001
Fellowships and Grants
The majority of our Ph.D. students are at least partially supported by fellowships, grants or tuition waivers. Some of sources of financial support are:
- Provost's Fellowship (awarded at admission)
- Dean's Fellowship (awarded at admission)
- Doctoral Sabbatical Fellowship (one quarter of support for qualified students nearing completion of their degrees
- Achievement Rewards for College Scientists (ARCS)
- Graduate Assistance in Areas of National Need (GAANN) (up to three years of support for five qualified Ph.D. students; US citizenship required)
Additional programs include Graduate Opportunity Fellowships, Diversity Fellowships, Tuition Fellowships, Regent's Fellowships. Some students are supported by faculty research grants.
Academic Positions Held by Recent Graduates
- Basak Gurel, Ph.D. 2003: Simon's Instructor, SUNY Stony Brook
- Geoffrey Buhl, Ph.D. 2003: Visiting Assistant Professor (NSF Postdoctoral Fellowship), Rutgers University
- Kate Hurley, Ph.D. 2002: Postdoctoral fellow, Penn State University
- John Bruschi, Ph.D. 2002: Lecturer, Cal State Hayward
- Robert Hartmann, Ph.D. 2002: Marie Curie Research Fellow, University of Leicester, UK
- Gail Yamskulna, Ph.D. 2001: Postdoctoral fellow, MSRI; Visiting Assistant Professor, SUNY Binghamton
- Eric Matsui, Ph.D. 2001: Visiting Assistant Professor, University of Ottawa, Canada
- Ely Kerman, Ph.D. 2000: Fields Institute and the University of Toronto (NSERC Postdoctoral Fellowship); Simon's Instructor, SUNY Stony Brook
- Chris Goff, Ph.D. 1999: Postdoctoral fellow, University of Arizona, Tucson; tenure track Assistant Professor at UOP
Our proximity to Silicon Valley and the greater San Francisco Bay Area offers our students an exceptional selection of employment opportunities in high-tech companies. Some of our recent graduates now work in the research and development groups at CADexterity, Microsoft. and other leading software developers.
Related research at UCSC
- Santa Cruz Institute for Particle Physics
- University of California Observatories/Lick Observatory
- Institute of Geophysics and Planetary Physics
- Institute of Marine Sciences
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