Graduate Program in Differential Geometry The department has a vigorous graduate program in differential geometry. Faculty Permanent: (tenured and tenure-track) Dan Burns Complex geometry, symplectic geometry. Lizhen Ji Spectral theory of locally symmetric spaces, Selberg trace formula, compactifications of symmetric and locally symmetric spaces John Lott Spectral theory, index theory, collapsing Ralf Spatzier Manifolds of nonpositive curvature, dynamics and group actions Junior faculty and visitors: Joel Fish Symplectic and contact geometry, pseudo-holomorphic curves, and symplectic field theory. Victor Guillemin (Visiting from MIT, Fall, 2007) Symplectic geometry, partial differential equations. Zhou Zhang. Differential equations, Kaehler-Ricci flow, complex Monge-Ampere equations. Thomas Foertsch Metric geometry Tatyana Foth Automorphic forms Alexander Gorodnik Dynamical systems Faculty in related areas include: Mario Bonk Quasiconformal geometry. Dick Canary Hyperbolic 3-manifolds. Xiaojun Chen Algebraic topology, especially string topology. Mattias Jonsson Complex dynamics. Igor Kriz Algebraic topology, in particular stable homotopy theory, and string topology. Peter Scott 3-manifolds and geometric group theory. Yongbin Ruan Symplectic topology, Gromov-Witten theory and geometry related to physics. Juan Souto Low-dimensional topology, Kleinian groups. Alejandro Uribe Microlocal analysis. Courses Each year the department offers two undergraduate courses and five graduate courses in differential geometry. The undergraduate courses, Math 433 Introduction to Differential Geometry Math 531 Transformation Groups in Geometry, are largely taken by undergraduate concentrators in Mathematics, Natural Sciences and Engineering. There is a year-long sequence of introductory graduate courses in differential geometry, Math 537 Differentiable Geometry I Math 635 Differential Geometry II. A topics class, Math 636 Topics in Differential Geometry is offered twice a year. Recent topics include : Symplectic Geometry and Complex Analysis (F03, Burns) Compactifications of Symmetric and Locally Symmetric Spaces (W03, Ji) Ergodic Theory and Dynamics (F02, Spatzier) Symplectic Geometry and Complex Analysis (F01, Burns) Topics in Large-Scale Geometry (W01, Kleiner) Rigidity Phenomena in Geometry, Group Theory and Dynamics (F00, Spatzier) Topics in Nonpositive Curvature (W00, Kleiner) Convergence of Riemannian Manifolds, Minimal Volume and Rigidity (F99, Spatzier) Dynamical Systems and Group Actions (F98, Spatzier) Pseudoholomorphic Curves (W98, Hind) The Atiyah-Singer Index Theorem (F97, Lott) Eigenvalues in Riemannian Geometry (W97, Ji) Rigidity in Geomery, Group Theory and Dynamics (F96, Spatzier) The Geometry of Gauge Theory (W96, Nicolaescu) Manifolds of Negative and Nonpositive Curvature (F95, Spatzier) Complex Geometry (W95, Uribe) Dynamics and Geometry (F94, Spatzier) Seminars The differential geometry seminar is held weekly during the Fall and Winter terms, usually Tuesday afternoons from 3:00 to 4:00. This is an informal forum which welcomes talks on any topic of geometric interest. Participants include mathematics faculty and graduate students. It is listed on the weekly seminars bulletin here. Current Thesis Students (Advisor) Robert Lonigro (Burns), Alvaro Pelayo (Burns), Ben Schmidt (Spatzier) and others. Recent Graduates Jean-Francois Lafont Dissertation:Rigidity Results for Singular Spaces. Advisor, year:Spatzier, 2003. First Position:SUNY-Binghamton. T.J. Hitchman Dissertation:Rigidity Theorems for Large Dynamical Systems with Hyperbolic Behavior. Advisor, year:Spatzier, 2002. First Position:Rice. Craig Sutton Dissertation:Applications of Representation Theory to Dynamics and Spectral Geometry. Advisor, year:Spatzier, 2001. First Position:Dartmouth. Chris Connell Dissertation:Rigidity and Dynamics of Negative Curved Homogeneous Spaces. Advisor, year:Spatzier, 1999. First Position:NSF Postdoc, University of Illinois - Chicago. Jeff Boland Dissertation:The Dynamics and Geometry of Contact Anosov Flows. Advisor, year:Spatzier, 1998. First Position:McMaster University. Maria Walters Dissertation:Geometry and Uniqueness of Some Extreme Subvarieties in Complex Grassmannians. Advisor, year:Burns, 1997. First Position: Ohio Northern University. John Szaro Dissertation:Isotropy of Semisimple Group Actiosn on Manifolds with Geometric Structure. Advisor, year:Spatzier, 1997. First Position:TRW, Denver. Raul Aguilar Dissertation:On Certain Canonical Structures on Tangent Bundles of Riemannian Manifolds. Advisor, year:Burns, 1997. First Position: Loyola University. Tracy Payne Dissertation: Invariant Submanifolds for Homogeneous Flows on Quotients of Semisimple Lie Groups of Noncompact Type. Advisor, year: Spatzier, 1995. First Position: Washington University. Su-Jen Kan Dissertation: The Global Burns-Epstein Invariant and Grauert Tubes. Advisor, year: Burns, 1994. First Position: Academia Sinica, Taipei. Rodrigo Gomez Dissertation: Geodesic Flow on Hilbert Grassmannians. Advisor, year: Burns, 1993. First Position: National Security Agency. Leslie Kay Dissertation: The Kobayashi-Royden Metric for Ellipsoids and Perturbations of the Ball. Advisor, year: Burns, 1991. First Position: Virginia Polytechnic. Jeong Seog Ryu Dissertation: Development Mapping on CR-Manifolds. Advisor, year: Burns, 1991. First Position: Hongik University, Seoul. Man Chun Leung Dissertation: Harmonic Maps Between Asymptotically Hyperbolic Spaces. Advisor, year: Burns, 1991. First Position: National University of Singapore. Zhongyuan Li Dissertation: On Spherical CR Manifolds with Positive Webster Scalar Curvature. Advisor, year: Burns, 1990. First Position: MIT.   Webpage format - Jim Milne