Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 21, 2013.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2013          October 2013          November 2013
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7          1  2  3  4  5                   1  2
8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
15 16 17 18 19 20 21   13 14 15 16 17 18 19   10 11 12 13 14 15 16
22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
29 30                  27 28 29 30 31         24 25 26 27 28 29 30



Monday, October 21, 2013

10:00 am in 145 Altgeld Hall,Monday, October 21, 2013

#### On the Topological Dynamics Arising from a Contact Form

###### Peter Spaeth (Pennsylvania State University Math)

Abstract: Stefan Müller and Yong-Geun Oh introduced the Hamiltonian metric on the group of Hamiltonian isotopies of a symplectic manifold, and with it defined the groups of topological Hamiltonian isotopies and homeomorphisms. With Augustin Banyaga we introduced the contact metric on the space of strictly contact isotopies of a contact manifold, and defined the groups of topological strictly contact isotopies and homeomorphisms in a similar manner. In the talk I will explain how the one to one correspondence between smooth strictly contact isotopies and generating contact Hamiltonian functions extends to their topological counterparts when the contact form is regular. I will also prove that the group of diffeomorphisms that preserve a contact form is rigid in the sense of Eliashberg-Gromov. This last result is joint with Müller.

1:30 pm in 345 Altgeld Hall,Monday, October 21, 2013

#### Hex-meshing Things with Topology

###### Jeff Erickson   [email] (UIUC CS)

Abstract: A topological quadrilateral mesh $Q$ of a connected surface in $\mathbb{R}^3$ can be extended to a topological hexahedral mesh of the interior domain $M$ if and only if $Q$ has an even number of quadrilaterals and no odd cycle in $Q$ bounds a surface inside $M$. Moreover, if such a mesh exists, the required number of hexahedra is within a constant factor of the minimum number of tetrahedra in a triangulation of $M$ that respects $Q$. Finally, if $Q$ is given as a polyhedron in $\mathbb{R}^3$ with quadrilateral facets, a topological hexahedral mesh of the polyhedron can be constructed in polynomial time if such a mesh exists. All our results extend to domains with disconnected boundaries. Our results naturally generalize results of Thurston, Mitchell, and Eppstein for genus-zero and bipartite meshes, for which the odd-cycle criterion is trivial. A preliminary version of this paper was presented at the 29th Annual Symposium on Computational Geometry. The full version (in submission) is available at http://www.cs.uiuc.edu/~jeffe/pubs/hexmesh.html

5:00 pm in 241 Altgeld,Monday, October 21, 2013