Math 410
Elements of Representation Theory

General Information

The information on this page is given tentatively and subject to changes during the term. The seminar is open to anyone with an interest in representation theory. Students taking the course for credit will be graded on their presentation(s) of the topics listed below.

Instructor

Pierre Clare
Office: 130 Jones Hall
Office Hours: by chance and by appointment.

References

• An Introduction to the Representation Theory of Groups, by E. Kowalski (primary reference). GTM, vol. 155
• Linear Representations of Finite Groups, by J.-P. Serre

Schedule

The seminar meets on Wednesdays at 6pm in Jones 302.

Date	Speaker	Topic
8/31	PC	Introduction: group actions and harmonic analysis
9/07	PC Jack Straus	Group actions in the language of categories Group representations: definitions, first examples
9/14	PC Paul Anderson	Intertwining operators Basic operations on representations
9/21	PC Luke Mrini Ben Neifeld & Ryan Pesak	On the regular representation Schur's Lemma Semisimplicity
9/28	Ben Neifeld & Ryan Pesak Tyler Pringle & Jack Straus	Semisimplicity Representations of quotients
10/05	Group work	Induction and restriction
10/12	Paul Anderson	Frobenius Reciprocity
10/19	Group work Ryan Pesak	Functoriality of induction Finite-dimensional representation of $\mathrm{SL}(2,\mathbf{C})$
10/26	Ryan Pesak	Remarks on representations in finite characteristic
11/02	PC Jude Bedessem	Introduction to unitary representations Unitary representations of the torus
11/09	Jude Bedessem	Fourier analysis on the torus
11/16	Luke Mrini	Integration on topological groups
11/30	Leo Murphy & Tyler Pringle Ben Neifeld & Jack Straus	Unitarization Regular and quasi-regular representations
12/07	PC	The Peter-Weyl Theorem

Academic Integrity

The Honor Code applies to all activities related to this course. The Honor System is responsible for resolving any suspected violations of the Honor Code. Do not hesitate to ask the instructor beforehand if you have any questions as to whether some action would be compatible with the Honor Code.

ADA Considerations

Students with disabilities who will be taking this course and may need disability-related accommodations are encouraged to make an appointment to see their instructor as soon as possible.

William & Mary accommodates students with disabilities in accordance with federal laws and university policy. Any student who feels they may need an accommodation based on the impact of a learning, psychiatric, physical, or chronic health diagnosis should contact Student Accessibility Services staff at 757-221-2512 or at sas@wm.edu to determine if accommodations are warranted and to obtain an official letter of accommodation. For more information, please visit www.wm.edu/sas.

ADA Considerations

Students with disabilities who will be taking this course and may need disability-related accommodations are encouraged to make an appointment to see their instructor as soon as possible.

William & Mary accommodates students with disabilities in accordance with federal laws and university policy. Any student who feels they may need an accommodation based on the impact of a learning, psychiatric, physical, or chronic health diagnosis should contact Student Accessibility Services staff at 757-221-2512 or at sas@wm.edu to determine if accommodations are warranted and to obtain an official letter of accommodation. For more information, please visit www.wm.edu/sas.

Mental and Physical Well-Being

William & Mary recognizes that students juggle different responsibilities and can face challenges that make learning difficult. There are many resources available at W&M to help students navigate emotional/psychological, physical/medical, material/accessibility concerns. Asking for help is a sign of courage and strength. If you or someone you know is experiencing any of these challenges, we encourage you to reach out to the following offices:

• For psychological/emotional stress, please consider reaching out to the W&M Counseling Center; (757) 221-3620, 240 Gooch Dr., 2nd floor. Services are free and confidential.
• For physical/medical concerns, please consider reaching out to the W&M Health Center; (757) 221-4386, 240 Gooch Drive.
• For additional support or resources, please contact the Dean of Students by submitting a Care Report online or by calling 757-221-2510, or by emailing deanofstudents@wm.edu.

For a list of many other resources available to students, see Health and Wellness Resources for Students.

As your professor, I also encourage you to reach out to me if you are facing challenges inside or outside the classroom; I will guide you to ​appropriate resources on campus.