Department of

# Mathematics

Seminar Calendar
for events the day of Monday, December 1, 2014.

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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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Monday, December 1, 2014

3:00 pm in 341 Altgeld Hall,Monday, December 1, 2014

#### The dynamics of the minimal set of Kuperberg's plug

###### Ana Rechtman (Université de Strasbourg)

Abstract: In 1993 K. Kuperberg constructed examples of C∞ and real analytic flows without periodic orbits on any closed 3-manifold. These examples continue to be the only known examples with such properties. A plug is a manifold with boundary of the type D2 x [0, 1] endowed with a flow that enters through D2 x{0}, exits through D2 x{1} and is parallel to the rest of the boundary. Moreover, it has the particularity that there are orbits that enter the plug and never exit, that is there are trapped orbits. The closure of a trapped orbit limits to a compact invariant set contained entirely within the interior of the plug. This compact invariant set contains a minimal. The first construction of a plug without periodic orbits was done by P. Schweitzer. This plug is constructed from the minimal set that is the Denjoy flow on the torus, implying that the flow of the plug is only C1 . Kuperberg's construction is completely different in nature. I will present a study of the minimal set, its dynamics and topology. (Joint work with Steven Hurder (University of Illinois at Chicago).)

4:00 pm in 173 Altgeld Hall,Monday, December 1, 2014

#### Internships in Government and Industry

Abstract: Informal discussion with Mathematics PhD students who did internships last summer in government and industry. Are you interested in how they found the position, what they found challenging about the internship, and what career options it opened up? Then come along and join the discussion! International and U.S. graduate students in Mathematics are welcome. - Prof. Richard Laugesen (DGS)

4:00 pm in 243 Altgeld Hall,Monday, December 1, 2014

#### Where do TQFTs come from?

###### Matej Penciak (UIUC Math)

Abstract: In this talk I will try to motivate the modern $\infty$-categorical definition of TQFTs from considerations in physics relating to path integrals appearing in quantum field theorie

5:00 pm in 145 Altgeld Hall,Monday, December 1, 2014

#### Grothendieck's theorem following Pisier-Shlyakhtenko

###### Li Gao (UIUC)

Abstract: We will finish Li Gao's talk, and if time permits see some application of cb-entropy to quantum group channels