Department of

Mathematics

Seminar Calendar
for events the day of Tuesday, May 6, 2014.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, May 6, 2014

1:00 pm in 347 Altgeld Hall ,Tuesday, May 6, 2014

Geometric theory of garden hoses, or string theory in your backyard

Vakhtang Putkaradze   [email] (University of Alberta, Mathematics)

Abstract: A garden hose inevitably wiggles and twists when water is rushing through it. We derive a fully three-dimensional, geometrically exact theory for this phenomenon. The theory also incorporates the change of the cross-section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We analyze the linear stability, and show that the change of cross-section plays an important role. We derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions. Time permitting, we shall also discuss the effects of the boundary conditions and experimental results. Partially supported by NSERC and the University of Alberta.

2:00 pm in 241 Altgeld Hall,Tuesday, May 6, 2014

Generic singularity of maximal spectral types (part 2)

Anush Tserunyan (UIUC Math)

Abstract: We will continue reading through "Generic spectral properties of measure-preserving maps and applications" by Del Junco and Lemanczyk.

2:00 pm in Altgeld Hall 347,Tuesday, May 6, 2014

Probability on quantum groups and generalized circular elements

Michael Brannan (UIUC Math)

Abstract: It is a well known fact that as N tends to infinity, the standard coordinate functions over the N by N orthogonal group O_N converge in distribution with respect to the Haar measure (after an appropriate scaling) to a standard i.i.d. Gaussian family. In this talk, I will discuss some analogous probabilistic convergence results that occur for free orthogonal quantum groups. In the quantum group setting, we will see that Voiculescu's free independence appears as the large rank limiting structure, and freely independent generalized circular elements appear as the limiting variables. (Generalized circular elements play the role of complex Gaussian random variables in free probability theory). This talk is based on joint work with Kay Kirkpatrick. No knowledge of quantum groups will be assumed.

3:00 pm in 243 Altgeld Hall,Tuesday, May 6, 2014

Combinatorics and topology of toric maps

Mircea Mustata (University of Michigan)

Abstract: Toric varieties are algebraic varieties endowed with a nice" action of an algebraic torus. A remarkable feature is that their geometry can be fully described in terms of combinatorics of fans and polytopes. I will discuss some results concerning the topology of the fibers of toric maps and a combinatorial invariant that comes out of these considerations. This is based on joint work in progress with Marc de Cataldo and Luca Migliorini.

3:00 pm in 241 Altgeld Hall,Tuesday, May 6, 2014

On the applications of counting independent sets in hypergraphs

Jozsef Balogh   [email] (U. of Szeged & UIUC)

Abstract: Recently, Balogh-Morris-Samotij and Saxton-Thomason developed a method of counting independent sets in hypergraphs. I show some recent applications of the method: - First I prove a conjecture of Kohayakawa-Kreuter-Osthus on the `random Sperner’ problem. - Then I prove a conjecture of Erdos on extremal graph theory. - And finally I give a sketch of the proof of a Cameron-Erdos conjecture on the number of maximal sum-free subsets of integers. These results are partly joint with Hu, Liu, Mycroft, Petrickova, Sharifzadeh, and Treglown.

4:00 pm in 245 Altgeld Hall,Tuesday, May 6, 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.