Spring 2015 MATH 249 001 LEC

Algebraic Combinatorics
Schedule: 
SectionDays/TimeLocationInstructorCCN
001 LECMWF 2-3P 2 EVANSHAIMAN, M54422
Units/CreditFinal Exam GroupEnrollment
4NONELimit:28 Enrolled:17 Waitlist:0 Avail Seats:11 [on 03/22/15]
Additional Information: 

Prerequisites: 250A or consent of instructor.

Syllabus: (I) Enumeration, generating functions and exponential structures, (II) Posets and lattices, (III) Geometric combinatorics, (IV) Symmetric functions, Young tableaux, and connections with representation theory. Further study of applications of the core material and/or additional topics, chosen by instructor.

Of the above core syllabus topics, I plan to emphasize (I) and (IV).  I will introduce species, which provide a nice unifying framework for ordinary and exponential generating functions and a connection with symmetric funcitons and representation theory of the symmetric group.  I will also try to find time for an introduction to  q and q,t-analogs in combinatorial symmetric function theory, and their connection with Hall-Littlewood and Macdonald pollynomials and the geometry of flag varieties and Hilbert schemes.  This is an area in which there are both beautiful recent results, and many important research problems still open.

Office: 855 Evans Hall

Office Hours: Wed 11-12:30 or by appointment

Required Text: Stanley, Enumerative Combinatorics Vols 1 and 2

Grading and Homework: Grading based on homework assigned periodically

Course Webpage: math.berkeley.edu/~mhaiman/math249-spring15/