18.704 (Seminar in Algebra and Number Theory) Schedule

February 2. Symmetry (David Vogan).

February 4. Groups and actions (David Vogan).

February 7. Fields (Matt Garcia).

February 9. Adjoining roots (Gary Sivek).

February 11. Finite fields (John Rogers); Groups of order 8 (Eitan Reich).

February 14. Symmetry groups of regular solids (David Vogan).

February 16. The symmetric group (Harold Cooper).

February 18. The finite general linear group (Gabe Cunningham); Projective space (David Glasser).

February 22. Grassman varieties (David Vogan).

February 23. Simple groups (Gen Hanlon and Rachel Lee).

February 25. Regular solids in higher dimensions (Gary Sivek); Iwasawa's theorem (Gen Hanlon and Rachel Lee).

February 28. Introduction to bilinear forms (Eitan Reich).

March 2. Quaternions (Daniel Briggs).

March 4. Hyperbolic planes and Witt's cancellation theorem for symmetric forms (Yelena Yasinnik).

March 7. Counting subspaces by row reduction (Yaim Cooper); classification of quadratic forms over finite fields (David Glasser).

March 9. Generators for the symplectic group (text, 21-24) (Yaim Cooper).

March 11. Sylow theorems for GL_n(F_q) (Gabe Cunningham).

March 14. Order of the finite symplectic group (text, 25-29) (David Vogan).

March 16. Generators for the orthogonal group (text, 45-49) (Katherine Dalis); recursion formula for #G(k,n)(F_q) (Nicholas Lucero).

March 18. PGL(2) over small fields (John Rogers); the Rubik's cube group (Jenna Hanlon).

March 28. Generators for the orthogonal group continued (text, 45-49) (Katherine Dalis); normal subgroups for the orthogonal group (Yelena Yasinnik).

March 30. Normal subgroups for the orthogonal group continued (Yelena Yasinnik); orders of finite orthogonal groups (Gabe Cunningham).

April 1. Hermitian forms (text, 85-89) (Harold Cooper).

April 4. Generators for symplectic groups (Yaim Cooper).

April 6. Simplicity of PGL(n,F_q) (text, chapter 1) (David Glasser).

April 8. Generators for unitary groups (Yaim Cooper).

April 11. Maximal parabolic subgroups in GL(n) and Sp(2n) (David Vogan).

April 13. Simplicity of PSp(2n,F_q) (text, chapter 3) (Gary Sivek).

April 15. Clifford algebras (text, chapter 8) (John Rogers).

April 20. Maximal parabolic subgroups in O(n) (Oleg Shamovsky). MEETING RESCHEDULED TO 4/21 at 7:00 p.m. in 4-145.

April 22. Counting points in O(n)/maximal parabolic (Katherine Dalis). Counting points in Sp(2n)/maximal parabolic. (medium - Jenna Hanlon).

April 25. Classical linear groups are manifolds (long - Matt Garcia).

April 27. General parabolic subgroups of Sp(2n) (Oleg Shamovsky).

April 29. Sylow subgroups of Sp(2n,F_q) (long - Rachel Lee).

May 2. Some special elements of orthogonal groups (Katherine Dalis).

May 4. General parabolic subgroups of GL(n) (short - Matt Garcia). Conjugacy classes in GL(2,F_q) (short - Harold Cooper).

May 6. Clifford algebra for a hyperbolic plane (text, page 72) (short - Jenna Hanlon). Filtered algebras, graded algebras, and Clifford algebras (short - Yaim Cooper).

May 9. Clifford algebras redux (long - Eitan Reich). An application of Clifford algebras (short - John Rogers).

May 11. Nicholas Lucero, topic TBA. Orthogonal geometry (medium, Oleg Shamovsky).

Return to 18.704 home page