Geometry & Topology

Courses

Each year the department offers four undergraduate courses and nine graduate courses in geometry and topology. 

The undergraduate courses,

•   Math 433 Introduction to Differential Geometry

•   Math 490 Introduction to Topology

are largely taken by undergraduate concentrators in Mathematics, Natural Sciences and Engineering.

The undergraduate courses,

•   Math 531 Transformation Groups in Geometry

•   Math 590 Introduction to Topology

are 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 4 semester sequence of introductory graduate courses in geometry and topology.

•   Math 591 Differentiable Manifolds

•   Math 592 Introduction to Algebraic Topology

•   Math 635 Differential Geometry

•   Math 695 Algebraic Topology I

Topics classes,

•   Math 636 Topics in Differential Geometry

•   Math 696 Topics in Algebraic Topology

•   Math 697 Topics in Topology

are offered. Usually, each year Math 636 and 697 are offered twice, and Math 696 is offered once. Occasional topics courses with other numbers are also offered. Recent topics include:

•   Introduction to Rigidity Theory (W17, Spatzier)

•   Quiver Varieties (W17, Ruan)

•   Dynamics and geometry (F16, Spatzier)

•   Equivariant Algebraic Topology (F16, Kriz)

•   Introduction to Riemann Surfaces (F16, Ji)

•   Symplectic Geometry and Integrable Systems (W16, Burns)

•   Teichmuller Space vs Symmetric Space (W16, Ji)

•   Dynamics and geometry (F15, Spatzier)

•   Teichmuller Theory and its Generalizations (F15, Canary)

Seminars

The geometry/topology group has four seminars held weekly during the Fall and Winter terms. These are the Geometry Seminar, Topology Seminar, RTG Seminar and Complex Dynamics Seminar. These are informal forums which welcome talks on any topic of geometric interest. Participants include mathematics faculty and graduate students. The schedules are available by cllicking on the name of the appropriate seminar.  

Current Thesis Students (Advisor)

R. Chen (Kriz), M. Gill (Kriz), M. Greenfield (Ji), D. Irvine (Burns), J. Kilgore (Ji), R. Mi (Ruan), S. Pinella (Spatzier), J. Powell (Koch), P. Satpathy (Ji), Y. Shelah (Koch), S. Siddiqi (Spatzier), R. Webb (Ruan), M. Zhang (Ruan), F. Zhu (Canary).

Below is a list of recent graduates in geometry/topology. For a complete list of all recent graduates in mathematics, click here.

Recent Graduates

•   Dondi Ellis

Dissertation: Motivic Analogues of MO and MSO
Advisor: Igor Kriz, 2017
First Position:

•   Rohini Ramadas

Dissertation: Dynamics on the Moduli Space of Pointed Rational Curves
Advisor: Sarah Koch and David Speyer, 2017
First Position: Harvard University

•   Andrew Schaug

Dissertation: Dualities Arising from Borcea-Voisin Threefolds
Advisor: Yongbin Ruan, 2017
First Position: EY's Financial Advisory Office in New York

•   Robert Silversmith

Dissertation:  Mirror Theorem For Symmetric Products of Projective Space
Advisor: Yongbin Ruan, 2017
First Position: Simons Center in NY

•   David Renardy

Dissertation: Bumping in Deformation Spaces of Hyperbolic 3-manifolds with Compressible Boundary
Advisor: Dick Canary, 2016
First Position: Invincea Labs

•   Pedro Acosta

Dissertation: A General Landau-Ginzburg/Gromov-Witten Correspondence
Advisor: Yongbin Ruan, 2015
First Position: University of Minnesota

•   Russell Ricks

Dissertation: Flat strips, Bowen-Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces
Advisor: Ralf Spatzier, 2015
First Position: Binghamton University

•   Brandon Seward

Dissertation: Krieger's finite generator theorem for ergodic actions of countable groups
Advisor: Ralf Spatzier, 2015
First Position: Hebrew University of Jerusalem

•   Tengren Zhang

Dissertation: Degeneration of Hitchin Representations
Advisor: Dick Canary, 2015
First Position: California Institute of Technology

•   Emily Clader

Dissertation: The Landau-Ginzburg/Calabi-Yau correspondence for certain complete intersections
Advisor: Yongbin Ruan, 2014
First Position: ETH Zurich 

•   Bich (Becky) Hoai

Dissertation: On Symplectic Invariants Associated to Zoll Manifolds
Advisor: Dan Burns, 2014
First Position: Federal Reserve Bank of St. Louis

•   Kin Kwan Leung

Dissertation: omplex Geometric Invariants Associated to Zoll Manifolds
Advisor: Dan Burns, 2014
First Position:  University of Toronto

•   Nathan Priddis

Dissertation: A Landau-Ginzburg/Calabi-Yau correspondence for the mirror quintic
Advisor: Yongbin Ruan, 2014
First Position: Leibniz Universitaet Hannover 

•   Geoffrey Scott

Dissertation:  Torus Actions and Singularities in Symplectic Geometry
Advisor: Dan Burns, 2014
First Position: University of Toronto

•   Andrew Zimmer

Dissertation: Rigidity in Complex Projective Space
Advisor: Ralf Spatzier, 2014
First Position: University of Chicago

•   William Abram

Dissertation: Equivariant Complex Cobordism
Advisor: Igor Kriz, 2013
First Position: Hillsdale College

•   Jeffrey Meyer

 Dissertation: On the Totally Geodesic Commensurability Spectrum of an Arithmetic Locally Symmetric Spaces
Advisor: Ralf Spatzier and Matthew Stover, 2013
First Position: University of Oklahoma

•   Yefeng Shen

Dissertation: Gromov-Witten theory of elliptic orbifold projective lines
Advisor: Yongbin Ruan, 2013
First Position: Kavli IPMU

•   Mark Shoemaker

Dissertation: Mirror Theorem for the Mirror Quintic
Advisor: Yongbin Ruan, 2013
First Position: University of Utah

•   Jordan Watkins

Dissertation: The Rank Rigidity Theorem for Manifolds with No Focal Points
Advisor: Ralf Spatzier, 2013
First Position: