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: Xiaojun Chen Algebraic topology, in particular string topology Valentina Joukhovitski Algebraic topology, in particular topological modular forms Anna Lenzhen Teichmuller theory Lars Louder Geometric group theory, limit groups, low-dimensional topology Kacey Walker Geometric topology, in particular moduli spaces of quadratic differentials 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 Renzo Cavalieri Gromov-Witten theory and moduli spaces of admissible covers Joel Fish Symplectic and contact geometry, pseudo-holomorphic curves, and symplectic field theory 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 John Lott Spectral theory, index theory, collapsing 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: 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) J. Gomez-Guerra (Kriz), P. Johnson (Ruan), A. Magid (Canary), J. Mangahas (Souto), J. Sahattchieve (Scott), D. Vavrichek (Scott). Recent Graduates 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 Tim Schwider Dissertation: The classification of essential laminations in Dehn surgeries on the figure-eight knot Advisor: Peter Scott, 2001 First Position: Derivatives Strategist at JP Morgan Richard Evans Dissertation: Deformation Spaces of Hyperbolic 3-Manifolds: Strong Convergence and Tameness Advisor: Dick Canary, 2000 First Position: Rice University John Holt Dissertation: The Global Topology of Deformation Spaces of Kleinian Groups Advisor: Dick Canary, 2000 First Position: Harvard University Bryan Johnston Dissertation: The Values of the Milnor Genus on Smooth Irreducible Projective Varieties over the Complex Numbers Advisor: Igor Kriz, 2000 First Position: Michigan State Opera Kendrick Smith Dissertation: The Mod 2 Cohomology of some Classifying Spaces of Compact Lie Groups Advisor: Igor Kriz, 2000 First Position: University of Michigan IT department