Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, May 7, 2014.

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events for the
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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
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Wednesday, May 7, 2014

4:00 pm in 245 Altgeld Hall,Wednesday, May 7, 2014

#### There be no Math 499 lecture today.

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

Abstract: There be no Math 499 lecture today. Students are welcome to attend the Coble Memorial Lectures, May 5-7, 2014.

4:00 pm in 245 Altgeld Hall,Wednesday, May 7, 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.