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Summer School in Geometry and Topology 2023

 

A three-week intensive program at Princeton University for 25 advanced undergraduates and first-year graduate students consisting of courses in geometry and topology. The program will focus on invariants related to 3- and 4-dimensional manifolds and to knots within them. These include Floer homological invariants, such as versions of Heegaard Floer homology for both knots and 3-manifolds. The program will also explore the structure of symplectic manifolds, which are crucial for understanding these Floer theoretic invariants. Other topics include surfaces in 4-dimensional manifolds, the hyperbolic geometry of 3-manifolds and knot complements, and other knot invariants such as the colored Jones polynomial. The goal of the program is to introduce these invariants and the basic tools needed to apply them to topological problems.

There will be eight courses. The majority of courses will consist of five-six lectures and TA review sessions. In addition, Weeks 2 and 3 will each include a three-day mini conference to cover recent research in areas related to the courses.

It is expected that participants will attend for the full duration of the three-week program.

Courses:

  • Introduction to Knot Theory and Knot homologies (Zoltan Szabó)
  • Introduction to Heegaard Floer Homology (Peter Ozsváth)
  • Lattice Homology and Bordered Floer Homology (Ian Zemke)
  • Immersed curves and invariants of knots and 3-manifolds (Jonathan Hanselman)
  • Surfaces in 4-manifolds (David Gabai)
  • An introduction to the Volume Conjecture (Andrew Yarmola)
  • Introduction to symplectic geometry (Shira Tanny)
  • Moduli spaces of pseudo-holomorphic curves (John Pardon; to be confirmed)

 

Participants of the 2018 Princeton Summer School in Topology and Geometry

 

Schedule (TBA)

Eligibility:

• Open to currently enrolled undergraduate juniors and seniors and first-year graduate students.

• Must be U.S. citizen or permanent resident. In the past, we have had international students fund themselves, and we will again consider such applications, space permitting.

• Applicants will be considered without regard to race, color, religion, sex, sexual orientation, gender identity or expression, national origin, age, ethnicity, or disability status.

Application Requirements:

Complete and submit the online application, including the following:

• Letter of recommendation from a faculty member well-acquainted with your academic work.

• Unofficial transcript.

• Personal Statement. Please include (1) a description of your most meaningful mathematical experience, and (2) your background in geometry and topology.

What's Provided?

On-campus housing and dining points will be provided for all eligible/admitted participants from Sunday, July 2, 2023 (check-in) through Saturday, July 22, 2023 (check-out). Travel reimbursement allowance will be available.

Application Deadline: March 1, 2023                                              

The program is sponsored by the National Science Foundation Research Training Grant in Geometry and Topology at Princeton.

For more information, please contact Jill LeClair, Program Coordinator, at leclair@princeton.edu.