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X-WR-CALDESC:Montana State University Social Calendar Brief Feed
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BEGIN:VEVENT
UID:20191210T043907CET-5852vvVXhK@ical.php
DTSTAMP:20191210T031207Z
CLASS:PUBLIC
DESCRIPTION:Over the past 35 years\, knot theory has witnessed an explosion
of powerful new invariants such as the colored Jones polynomial and the H
OMFLY-PT polynomial. The origin of many of these invariants can be unified
using quantum groups. One of the fundamental problems in modern knot theo
ry is to relate these quantum knot invariants to the topology of a knot co
mplement and the AJ-conjecture gives one possible connection. In this two
part series of lectures\, we will endeavor to understand the statement of
the AJ-conjecture\, its current states of affairs\, and attempt to pinpoin
t the main difficulties in its resolution.\nIn part 1\, we will discuss th
e 'A' in the AJ-conjecture\, which refers to the A-polynomial of a knot. T
he A-polynomial is defined using representations from the fundamental grou
p of a knot complement to SL(2\, C) and has seen broad applications in 3-m
anifold topology. To understand its connection to topology\, we will descr
ibe representation/character varieties and schemes and Culler-Shalen theor
y\, which uses the algebraic geometry of a character varieties to build sp
ecial surfaces in 3-manifolds.\nThese lectures will be expository in natur
e and should be well suited to introduce graduate students to the topics d
escribed above.
DTSTART:20180910T160000
DTEND:20180910T160000
LOCATION:Wilson Hall\, 1-144
SUMMARY:Math Seminar with Charles Katerba (MSU) 'On the AJ-conjecture\, Par
t 1'
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