Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 11, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, November 11, 2016

3:00 pm in 241 Altgeld Hall,Friday, November 11, 2016

#### Quantum Kostka and the rank one problem for ${\mathfrak sl}_{2m}$

###### Natalie Hobson   [email] (University of Georgia)

Abstract: In this talk we will define and explore an infinite family of vector bundles, known as vector bundles of conformal blocks, on the moduli space $M_{0,n}$ of marked curves. These bundles arise from data associated to a simple Lie algebra. We will show a correspondence (in certain cases) of the rank of these bundles with coefficients in the cohomology of the Grassmannian. This correspondence allows us to use a formula for computing "quantum Kostka" numbers and explicitly characterize families of bundles of rank one by enumerating Young tableau. We will show these results and illuminate the methods involved.

4:00 pm in 345 Altgeld Hall,Friday, November 11, 2016

#### Colorful introduction to OCA

###### Iván Ongay Valverde (U of Wisconsin-Madison Math)

Abstract: During the 80's, some specific combinatorial/topological consequences of PFA (Proper Forcing Axiom) concerning topological spaces and colorings were isolated. As Justin Moore showed in the early 2000s, these Coloring Axioms turn out to be a very powerful tool (they decide the size of the continuum to be $\aleph_2$). In this talk, we will not mention any PFA and, instead, will focus on what the colors do to the set theory universe if you assume these axioms in addition to ZFC.

4:00 pm in 241 Altgeld Hall,Friday, November 11, 2016

#### A primary obstruction to an ideal hairy ball

###### Ningchuan Zhang (UIUC Math)

Abstract: The hairy ball theorem can be stated as there’s no non-vanishing vector field on the 2-sphere. A primary obstruction to this is the Euler number, which is 2 in this case. Let’s consider the inverse problem: Given an oriented vector bundle over a smooth manifold with vanishing Euler class, does there exist a nowhere vanishing vector field? To answer this question, I’ll introduce the obstruction theory of fiber bundles. We’ll see that the primary obstruction to extending a section is actually a local cohomology class, which, in good cases, coincides with certain characteristic class of the vector bundle.