SMS scnews item created by Zhou Zhang at Wed 27 Feb 2013 0021
Type: Seminar
Modified: Wed 27 Feb 2013 0022
Distribution: World
Expiry: 27 Mar 2013
Calendar1: 8 Mar 2013 1430-1530
CalLoc1: Chemistry Lecture Theatre 2
CalTitle1: SYD- UNSW Joint Colloquium: Scott -- The Legacy of the Wall and Guralnick Conjectures
Auth: zhangou@60.225.181.121 (zhouz) in SMS-WASM

# SYD-UNSW Joint Colloquium: Scott -- The Legacy of the Wall and Guralnick Conjectures

Speaker: Prof. Leonard Scott (Virginia)

http://pi.math.virginia.edu/~lls2l/

Time: Friday, March 8, 2:30--3:30PM

Room: Chemistry Lecture Theatre 2, the University of Sydney

Lunch plan: we meet near Level 2 entrance to Carslaw Building
around 1PM. The lunch would be at Law Annex Cafe with reservation
at 1:10PM.

-----------------------------------------------

Title: The Legacy of the Wall and Guralnick Conjectures

Abstract: In 1961 G.E. Wall conjectured that the number of
maximal subgroups of a finite group is less than the order
of the group.

The conjecture holds for all finite solvable groups (proved
by Wall himself in his original paper) and holds for almost
all finite simple groups, possibly all of them (proved by
Liebeck, Pyber and Shalev in 2007). it is now known to be
false in general, at least as originally stated, with
infinitely many negative composite group examples found
through a combination of computational and theoretical
techniques. (I cite in particular computer calculations
of Frank Luebeck, as partly inspired and later confirmed
by calculations of my undergraduate student, Tim Sprowl,
with theoretical input from myself and Bob Guralnick.)
Somewhat surprisingly, the Wall  conjecture, through a
related 1986 conjecture of Bob Guralnick, has had a
tremendous impact on the development of cohomology theory
of finite and algebraic groups, with many positive results
proved regarding first 1-cohomology with irreducible
coefficients and, most recently, higher degree cohomology.
The negative examples that have been now found arise from
combining deep considerations in algebraic group theory
(such as rational and generic cohomology theory,  cohomology
theory related to the Lusztig conjecture,  and the Lusztig
conjecture itself) with computer calculations of Kazhdan-Lusztig
polynomials.  I will discuss all of these things, and, as
time permits, a new algorithm my student and I have developed
for calculating individual Kazhdan-Lusztig polynomials (which
might have been guessed ahead of time to be especially
interesting), or more accurately, individual Kazhdan-Lusztig
basis elements in a Hecke algebra, with minimal input from
lower degree calculations.

-----------------------------------------------

Joint Colloquium web site:

http://www.maths.usyd.edu.au/u/SemConf/JointColloquium/index.html


If you are registered you may mark the scnews item as read.
School members may try to .