Department of

Mathematics


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

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                        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.