# 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:**

- Mark Hagen
- Geometric group theory, CAT(0) spaces and groups, cube complexes

- Angela Kubena
- Geometric group theory

- Ben Linowitz
- Geometry and topology of arithmetic groups
- Dustin Ross
- Moduli spaces, virtual curve counting and connections with mathematical physics

- Moduli spaces, virtual curve counting and connections with mathematical physics
- David Sher
- Spectral theory, analysis on singular spaces

- Daniel Visscher
- Dynamical systems and differential 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

- Algorithmic questions in low-dimensional
topology,
- 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:

- Teichmuller theory and its generalizations (W13, Canary)
- Introduction to Floer Theories (F12, Burns)
- 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 is offered once a year.

- Math 696 Topics in Algebraic Topology,

## 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)**

P. Acosta (Ruan), E. Clader (Ruan), N. Priddis (Ruan), D. Renardy (Canary), A. Schaug (Ruan), R. Silversmith (Ruan), T. Zhang (Canary).

Recent Graduates

**William Abram**- Dissertation: Equivariant Complex Cobordism

- Advisor: Igor Kriz, 2013

- First Position: Hillsdale College

- Dissertation: Equivariant Complex Cobordism
**Yefeng Shen**- Dissertation: Gromov-Witten theory of elliptic orbifold projective lines

- Advisor: Yongbin Ruan, 2013

- First Position: Kavli IPMU

- Dissertation: Gromov-Witten theory of elliptic orbifold projective lines
**Mark Shoemaker**

- Dissertation: Mirror Theorem for the Mirror Quintic

- Advisor: Yongbin Ruan, 2013

- First Position: University of Utah

- Dissertation: Mirror Theorem for the Mirror Quintic
**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

- Dissertation: Stable splittings of configuration
spaces of surfaces and related mapping spaces
**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