Graduate Program in Topology at the University of Michigan The department has a very active graduate program in topology. Faculty Permanent: (tenured and tenure-track) Dick Canary Low-dimensional topology, Kleinian groups Igor Kriz Algebraic topology, in particular stable homotopy theory Yongbin Ruan Symplectic topology, Gromov-Witten theory and geometry related to physics Peter Scott 3-manifolds and geometric group theory Juan Souto Low-dimensional topology, Kleinian groups Arthur Wasserman Differential topology, in particular transformation groups on manifolds Junior faculty and visitors: Angela Kubena Barnhill Geometric group theory, in particular group actions on CAT(0) spaces Hanna Bennett geometric group theory Bill Breslin Low-dimensional topology and Kleinian groups Jeff Brown symplectic geometry and Gromov-Witten invariants Xiaojun Chen Algebraic topology, particularly string topology Moon Duchin Geometric topology and geometric group theor Yvonne Lai Geometric group theory and hyperbolic geometry Anna Lenzhen Teichmuller theory Lars Louder Geometric group theory, limit groups, low-dimensional topology Todor Milanov Singularity theory, Gromov--Witten invariants, and representations of infinite-dimensional Lie algebras Christopher Mooney Geometric group theory, particularly CAT(0) groups Alexandra Pettet Geometric group theory and low-dimensional topology Enrique Torres-Giese algebraic topology, particularly homotopy theory and group cohomology Faculty in related areas include: Hyman Bass Geometric methods in group theory, representation theory of discrete groups, algebraic K-theory Dan Burns Complex geometry, symplectic geometry Lizhen Ji Spectral theory of locally symmetric spaces, Selberg trace formula, compactifications of symmetric and locally symmetric spaces Jeffrey Lagarias Algorithmic questions in low-dimensional topology, including knot theory, discrete and computational geometry Ralf Spatzier Manifolds of nonpositive curvature, dynamics and group actions Courses Each year the department offers two undergraduate courses and six graduate courses in topology. The undergraduate course, Math 490 Introduction to Topology is largely taken by undergraduate concentrators in Mathematics, Natural Sciences and Engineering. The undergraduate course, Math 590 Introduction to Topology is taken by undergraduate concentrators in Mathematics, Natural Sciences and Engineering and also by graduate students, usually from departments other than the Mathematics Department. There is a 3 semester sequence of introductory graduate courses in topology. Math 591 General and Differential Topology Math 592 Introduction to Algebraic Topology Math 695 Algebraic Topology I A topics class, Math 697 Topics in Topology, is offered twice a year, and occasional topics courses with other numbers are also offered. Recent topics include: Hyperbolic 3-manifolds (W09, Canary) Splittings of groups and manifolds (F08, Scott) Minimal surfaces in 3-manifolds (W08, Souto) Rigidity in Topology, Geometry and Dynamics (F07, Spatzier) 3-Manifolds (F06, Scott) Triangulations of Three-Manifolds and Normal Surface Theory (W06, Jaco) Hyperbolic manifolds (F05, Canary) Splittings of Groups and Manifolds (W05, Scott) Hyperbolic manifolds (W04, Canary) Topology of 3-manifolds (W03, Scott) Characteristic classes (F02, Lott) Hyperbolic 3-manifolds (W02, Minsky) Geometric group theory (F01, Canary) Topology of 3-manifolds (W01, Scott) Deformation theory of hyperbolic manifolds (F00, Canary) Group actions on trees (W00, Bass) New invariants of 3-manifolds (F99, Szabo) Loop Groups and Conformal Field Theory (F99, Kriz) A topics class, Math 696 Topics in Algebraic Topology, is offered once a year. Seminars The topology seminar is held weekly during the Fall and Winter terms. This is an informal forum which welcomes talks on any topic of geometric interest. Participants include mathematics faculty and graduate students. The schedule is here. Current Thesis Students (Advisor) D. Kneezel (Kriz), M. Krawitz (Ruan), R. Lassonde (Scott), M. Lee (Canary), J. Mangahas (Souto), K. Ormsby (Kriz), J. Sahattchieve (Scott), N. White (Souto). Recent Graduates David Constantine Dissertation: Hyperbolic rank-rigidity and compact forms of homogeneous spaces Advisor: Ralf Spatzier, 2009 First Position: University of Chicago Paul Johnson Dissertation: Equivariant Gromov-Witten theory of one-dimensional stacks Advisor: Yongbin Ruan, 2009 First Position: Imperial College, London Cagatay Kutluhan Dissertation: Floer homology and symplectic forms on S1xM3 Advisor: Dan Burns, 2009 First Position: MSRI, Berkeley Aaron Magid Dissertation: Deformation spaces of Kleinian groups are not locally connected Advisor: Dick Canary, 2009 First Position: University of Maryland J. Gomez-Guerra Dissertation: Models of twisted K-theory Advisor: Igor Kriz, 2008 First Position: University of British Columbia Diane Vavrichek Dissertation: Accessibility and JSJ decompositions of groups Advisor: Peter Scott, 2008 First Position: SUNY Binghamton Eric Zupunski Dissertation: A bound on the complexity of the JSJ decomposition in the bounded case Advisor: Peter Scott, 2007 First Position: Ilesanmi Adeboye Dissertation: Volumes of hyperbolic orbifolds Advisor: Dick Canary, 2006 First Position: University of Southern California Tom Fiore Dissertation: Pseudo limits, bi-adjoints, and pseudo algebras: categorical foundations of conformal field theory Advisor: Igor Kriz, 2005 First Position: University of Chicago Craig Westerland Dissertation: Stable splittings of configuration spaces of surfaces and related mapping spaces Advisor: Igor Kriz, 2004 First Position: Institute for Advanced Study, Princeton Elizabeth Klodginski Dissertation: Essential surfaces in fibered 3-manifolds Advisor: Peter Scott, 2003 First Position: UC Davis Peter Storm Dissertation: The barycenter method on singular spaces Advisor: Dick Canary, 2003 First Position: University of Chicago