Leon Takhtajan

Department of Mathematics
Stony Brook University

office: Math Tower 5-111
phone: (631) 632-8287
e-mail: leon.takhtajan@stonybrook.edu

MAT 682 Topics in Differential Geometry: Teichmüller Theory and Character Varieties
Fall 2020


Character varieties appear in many areas of mathematics. Character varieties of surface groups inlclude Teichmüller spaces, spaces of projective structures on surfaces, moduli spaces of flat connections, hoilomorphic vector bundles and Higgs bundles. In context of Hamiltonian action, character varieties are examples of symplectic reduction. In mathematical physics, character varieties appear in the context of Yang-Mills and Chern-Simons theories and are related to many interesting construction.


TuTh 9:45am-11:05am, Math Tower 5-127. There will be a simultaneous Zoom broadcast of chalkboard lectures.


Leon Takhtajan

Office hours: Wed & Th 2:30pm-4:00pm in Math Tower 5-111 and by Zoom personal meeting (by email request).

Course description

The course will cover the basics of Teichmüller theory and character varieties. Specifically, we plan to cover the following topics (if time permits):


There will be no assigned textbooks. Each week a reference will be given on the Blackboard to research papers and monographs related to the material covered.

Information for students with disabilities

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, 128 ECC Building (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website and search Fire Safety and Evacuation and Disabilities.

Academic integrity

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website.

Critical Incident Management

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Last updated August 2020