Department of

Mathematics


Seminar Calendar
for events the day of Monday, September 23, 2013.

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Monday, September 23, 2013

10:00 am in 145 Altgeld Hall,Monday, September 23, 2013

Hamiltonian and contact dynamics, part II: applications

Stefan Mueller (UIUC Math)

Abstract: After recalling the precise definition of a topological Hamiltonian dynamical system, I will sketch the proof of the 1-1 correspondence between topological Hamiltonian isotopies and topological Hamiltonian functions. I also show that this result has non-empty content by constructing a non-smooth topological Hamiltonian dynamical system (with support in a Darboux chart). We then shift gears and focus on two sample applications to 1) hydrodynamics (topological character of the helicity invariant, which measures the average asymptotic linking number of the flow lines of a divergence-free vector field) and to 2) Riemannian geometry (C^0-rigidity of the geodesic flows associated to a sequence of weakly uniformly converging Riemannian metrics).

1:30 pm in 345 Altgeld Hall,Monday, September 23, 2013

Covering with Excess One

Han Wang (UIUC Math)

Abstract: We consider in this talk the topology of the space of coverings on grid domains. The space has the following constraint: while all the covering agents can move freely (we allow overlapping) on the domain, their union must cover the whole domain. A minimal number $N$ of the covering agents is required for a successful covering of the domain. We demonstrate the topological structure of this space on grid domains in 2D and 3D with $N+1$ coverings, the topology of the space has the homotopy type of 1-dimensional complex, regardless of the domain shape. We also present the Euler characteristic formulae which connect the topology of the space with that of the domain itself.

5:00 pm in 241 Altgeld,Monday, September 23, 2013

Uniqueness of group measure space decomposition for Popa's HT factors (after Adrian Ioana): Part III

Bogdan Udrea (UIUC Math)

Abstract: We continue to discuss Ioana's results on the HT factors of Popa.