General Information

See the course syllabus.

Instructor

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


References


Schedule

The seminar meets on Mondays at 3:30pm in Jones 131.


DateSpeakerTopic
09/03PCLie groups and infinitesimal transformations
09/10Cooper SpinelliLie algebras, examples, ideals
09/17PC
Brennan Dolson
Algebraic background, representations
Adjoint representation, Killing form
09/24Honora Overby
Cooper Spinelli
Torger Olson
Derived series, characteristic ideals
Solvable Lie algebras
Nilpotent Lie algebras
10/01Torger Olson
Henry Hannon
Nilpotent Lie algebras
Lie's Theorem
10/08Alexander MichelEngel's Theorem
10/15Fall Break
10/22Ben BechtoldCartan's criteria for solvability and semisimplicity
10/29PCSemisimple Lie algebras, spectral loose ends
11/05Mark AgriosCartan subalgebras
11/12Torger OlsonRoot space decomposition
11/19Torger Olson
Honora Overby
Self-centralizing property of Cartan subalgebras
Root space decomposition for $\mathfrak{sl}(3,\mathbb{C})$
11/26PC
Torger Olson
Picturing roots of $\mathfrak{sl}(3,\mathbb{C})$
Abstract root systems
12/03PCDynkin diagrams and the classification of semisimple Lie algebras

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.