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 Junior faculty and visitors: Khalid Bou-Rabee Combinatorial group theory, low dimensional topology, residual properties of groups Mark Hagen Geometric group theory, CAT(0) spaces and groups, cube complexes Angela Kubena Geometric group theory Ben Linowitz Arithmetic groups, applications of algebraic number theory to hyperbolic geometry, especially hyperbolic surfaces and 3-manifolds Matthew Stover Arithmetic groups, geometry, and low dimensional topology Daniel Visscher Dynamical systems and differential geometry Weiyi Zhang Symplectic topology and its interactions with complex geometry 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 Gopal Prasad Topology and geometry of homogeneous spaces and locally symmetric spaces Ralf Spatzier Manifolds of nonpositive curvature, dynamics and group actions Alejandro Uribe Spectral theory, symplectic geometry, Chern-Simons theory 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: 3-manifolds (W12, Scott) Mirror symmetry (F11, Ruan) K3 surfaces (W11, Ruan) Spaces of non-positive curvature (F10, Souto) Singularity theory (W10, Ruan) 3-manifolds (F09, Scott) 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) 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) W. Abram (Kriz), E. Clader (Ruan),, N. Priddis (Ruan), Y. Shen (Ruan), M. Shoemaker (Ruan), T. Zhang (Canary). Recent Graduates Robin Lassonde Dissertation: Splittings of non-finitely generated groups Advisor: Peter Scott, 2012 First Position: East Agile Michelle Lee Dissertation: Dynamics on the PSL(2, C)-character variety of certain hyperbolic 3-manifolds Advisor: Dick Canary, 2012 First Position: University of Maryland Jordan Sahattchieve Dissertation: Solutions to two open problems in geometric group theory Advisor: Peter Scott, 2012 First Position: NIna White Dissertation: Bounds on Eigenvalues of the Laplace-Beltrami Operator for Certain Classes of Hyperbolic 3-manifolds Advisor: Juan Souto, 2012 First Position: University of Michigan Daniel Kneezel Dissertation: Verlinde K-theory Advisor: Igor Kriz, 2011 First Position: Johanna Mangahas Dissertation: A Recipe for Short-word Pseudo-Anosovs, and More Advisor: Juan Souto, 2010 First Position: Brown University Kyle Ormsby Dissertation: Computations in Stable Motivic Homotopy Theory Advisor: Igor Kriz, 2010 First Position: Massachusetts Institute of Technology Marc Krawitz Dissertation: FJRW Rings and Landau-Ginzburg Mirror Symmetry Advisor: Yongbin Ruan, 2010 First Position: McKinsey & Co. 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