Department of

# Mathematics

Seminar Calendar
for events the day of Monday, May 5, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      April 2014              May 2014              June 2014
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1  2  3  4  5                1  2  3    1  2  3  4  5  6  7
6  7  8  9 10 11 12    4  5  6  7  8  9 10    8  9 10 11 12 13 14
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Monday, May 5, 2014

3:00 pm in 145 Altgeld Hall,Monday, May 5, 2014

#### Symplectic toric manifolds as centered reductions of products of weighted projective spaces

###### Milena Pabiniak (Instituto Superior Técnico)

Abstract: We prove that every symplectic toric orbifold is a "centered" symplectic reduction of a Cartesian product of weighted projective spaces. Reduction is centered if the level set contains central Lagrangian torus fiber of the product of weighted projective spaces. In that case one can deduce certain information about non-displaceable sets or existence of quasimorphisms. For example, a theorem of Abreu and Macarini shows that if the level set of the reduction passes through a non-displaceable set then the image of this set in the reduced space is also non-displaceable. Using this theorem and our result we reprove that every symplectic toric orbifold contains a non-displaceable fiber and identify this fiber. Joint work with Aleksandra Marinkovic.

4:00 pm in 245 Altgeld Hall,Monday, May 5, 2014

#### Special Math 499 lecture today

###### (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Note the special day, time and lecture of Math 499 this week. Please attend the Coble Memorial Lecture.

4:00 pm in 314 Altgeld Hall,Monday, May 5, 2014

#### The virtual Haken conjecture

###### Ian Agol (University of California, Berkeley)

Abstract: Waldhausen conjectured in 1968 that every aspherical 3-manifold has a finite-sheeted cover which is Haken (contains an embedded essential surface). Thurston conjectured that hyperbolic 3-manifolds have a finite-sheeted cover which fibers over the circle. The first lecture will be an overview of 3-manifold topology in order to explain the meaning of Waldhausen's virtual Haken conjecture and Thurston's virtual fibering conjecture, and how they relate to other problems in 3-manifold theory. The second lecture will give some background on geometric group theory, including the topics of hyperbolic groups and CAT(0) cube complexes after Gromov, and explain how the above conjectures may be reduced to a conjecture of Dani Wise in geometric group theory. The third lecture will discuss the proof of Wise's conjecture, that cubulated hyperbolic groups are virtually special, and some discussion of a new proof of Wise's Malnormal Special Quotient Theorem. Part of these results are joint work with Daniel Groves and Jason Manning.

A reception will be held in 239 Altgeld Hall immediately following this lecture.

5:00 pm in 241 Altgeld,Monday, May 5, 2014