Leon Takhtajan

Course description

The goal of the seminar is to study hyperbolic (Lobachevskian) geometry, where Euclid’s fifth postulate fails. During the seminar we, following H. Poincaré, will unravel its remarkably rich structure and applications, ranging from the theory of discrete groups and automorphic functions to general relativity.

I will give a few short lectures on a chosen topic and will assign further material for the students to read and to present in class. Corresponding topics and reading material will be regularly posted on the Brightspace.

We will be using the following book

S. Stahl A Gateway to Modern Geometry: The Poincare Half-Plane, Jones & Bartlett Learning, 2007

as well as the elementary

J.W. Anderson, Hyperbolic Geometry, Springer Verlag, 2005

and

J. Lehner, A Short Course in Automorphic Functions, Dover Publications, 2015.

for applications to automorphic functions.

Measurable Learning Outcomes

Upon successful completion of MAT 401 Seminar in Mathematics: Hyperbolic Geometry, a student will:

Be familiar with the contributions of great mathematicians of the past.

Be conversant with the specialized vocabulary of the topic of non-Euclidean geometry.

Be ablie to rigorously prove the main results specific to the topic.

Be able to solve routine problems and quote assumptions and main theorems of the topic.

Appreciate the relationship of the topic to the undergraduate mathematics curriculum and to other areas of mathematics.

Lectures

TuTh 2:00pm-3:20pm in Physics P129.

Instructor

Leon Takhtajan

Office hours: Wednesday, 2:00pm-4:00pm in Math Tower 5-111, and by appointment.

Textbook

There is no formal textbook required to this class. Instead, it is required that to read, on a regular basis, all materials posted in the Brightspace.

Prerequisites

Complex analysis at the level of MAT342 or higher. MAT360 (geometry), MAT362 (differential geometry), MAT364 (topology) are recommended but not required.

Grading Policy

The grades will be based on the class participation, the oral presentations and on solution of selected homework problems.

Student Accessibility Support Center Statement

If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748, or at sasc@stonybrook.edu. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: https://ehs.stonybrook.edu//programs/fire-safety/emergency-evacuation/evacuation-guide-disabilities 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 at http://www.stonybrook.edu/commcms/academic_integrity/index.html.

Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Student Conduct and Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.