GEOMETRY AND TOPOLOGY GROUP
AT THE DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ARIZONA


PEOPLE IN OUR GROUP:
hermann Hermann Flaschka, Ph.D.
MIT, 1970
Wiener Prize, 1995
 philip Philip Foth, Ph.D.
Penn State, 1998

 hu Yi Hu, Ph.D.
MIT, 1991
AMS Centennial Fellowship
 doug Doug Pickrell, Ph.D.
U. Arizona, 1984
Integrable Hamiltonian systems,
Lie theory
and geometry
 Algebraic geometry,
differential geometry,
Lie theory
 Algebraic geometry,
symplectic geometry,
topology
 Lie groups,
representation theory,
quantum field theory

Postdocs:       Nathan Carlson,     Dorin Dumitrascu,     Michael Otto,     Adam Spiegler .

Graduate students:          Arlo Caine,     McKenzie Lamb,     Luis Garcia-Naranjo,     Jefferson Taft.

OUR WEEKLY SEMINAR

In addition to the core course in Geometry-Topology the following graduate courses are offered on a regular basis: Algebraic Geometry; Complex Variables; Algebraic Topology; Global Differential Geometry; Lie Groups and Lie Algebras.

Recent special topic courses:  Introduction to Geometric Invariant Theory and Moduli Spaces; Symplectic and Poisson Geometry; Computational Methods in Algebraic Geometry and Commutative Algebra; Geometric Methods in Differential Equations; Topics in Algebraic Geometry; Group Theory and Physics;  Mechanics, Symmetry, and Bifurcations; An Algebraic Introduction to Combinatorics and Geometry;  Differential Geometry. 

Recent conferences organized:

ANALYSYS ON HOMOGENEOUS SPACES
AMS SESSION ON MODULI SPACES AND INVARIANT THEORY
GEOMETRIC REPRESENTATION THEORY
GEOMETRY AND TOPOLOGY OF QUOTIENTS
CONFERENCE ON LIE THEORY AND GEOMETRY, TUCSON, 1999
SPECIAL AMS SESSION ON INTEGRABLE SYSTEMS AND POISSON GEOMETRY
SPECIAL AMS SESSION ON GEOMETRY AND LIE GROUPS


        Modern Geometry is a rapidly developing field, which vigorously interacts with other disciplines such as physics, analysis, biology, number theory, to name just a few. Such effective cooperation across traditional boundaries allowed geometric and topological branches to flourish and to help solving numerous problems and inspired many applications and techniques.
        In recent years geometers encountered a significant number of groundbreaking results and fascinating applications. From progress in the Poincarè conjecture, geometric representation theory, quantization, to the mirror symmetry, string theory,  applications in optics, biology, quantum computing - the ubiquity of geometry is impossible to overestimate.
        People in our group work in several important directions such as algebraic geometry, differential geometry, symplectic geometry, integrable systems, quantum field theory, topology, representation theory, algebraic analysis, and index theorems. We have our own weekly geometry seminar, where people from within the department and visitors from outside present their latest achievements. We have close contact and collaboration with other groups in our department working in the areas of number theory, geometric analysis, dynamical systems, and mathematical physics.