Department of

Mathematics

Seminar Calendar
for events the day of Friday, November 7, 2014.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2014          November 2014          December 2014
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4                      1       1  2  3  4  5  6
5  6  7  8  9 10 11    2  3  4  5  6  7  8    7  8  9 10 11 12 13
12 13 14 15 16 17 18    9 10 11 12 13 14 15   14 15 16 17 18 19 20
19 20 21 22 23 24 25   16 17 18 19 20 21 22   21 22 23 24 25 26 27
26 27 28 29 30 31      23 24 25 26 27 28 29   28 29 30 31
30


Friday, November 7, 2014

4:00 pm in 345 Altgeld Hall,Friday, November 7, 2014

The Counting Types Method of Proving NIP

Allen Gehret (UIUC)

Abstract: First I will define the stability function $g_T(\kappa):=\sup_{M\models T, |M|=\kappa}|S^1(M)|$ for a complete theory $T$ (where $S^1(M)$ is the Stone Space of 1-types with parameters from $M$). Next, I will recall some dividing lines associated to $g_T$. Then, I will give a proof that for a NIP (=Not the Independence Property) theory $T$, we have $g_T(\kappa)\leq ded(\kappa)^{\aleph_0}$, whereas $g_T(\kappa) = 2^{\kappa}$ in the IP (not NIP) case. ($ded(\kappa)$ is roughly the maximum number of Dedekind cuts a linear order of size $\kappa$ can have). Finally, I will mention how some set-theoretic black magic shows that NIPness can always be detected from the function $g_T(\kappa)$. I will use this last thing in my proof of NIP for $T_{\log}$ in a future talk.

4:00 pm in 243 Altgeld Hall,Friday, November 7, 2014

Everything is connected: the Reshetikhin-Turaev story

Josh Wen (UIUC Math)

Abstract: In the 80's, Jones discovered his knot polynomial, Drinfeld and Jimbo constructed interesting braided monoidal categories via quantum groups, and Atiyah gave a first approximation of what a topological quantum field theory should be. The following decade saw these three notions combined in the construction of Reshetikhin-Turaev invariants of links, which via Dehn surgery yield quantum 3-manifold invariants. As the list of ingredients suggests, this story involves a rich interplay of algebra, low-dimensional topology, and physics(?), and I will take on the formidable task of introducing the characters at play as well as staging the drama.