Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, November 3, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, November 3, 2016

12:00 pm in 243 Altgeld Hall,Thursday, November 3, 2016

#### The isometric embedding problem for length metric spaces.

###### Barry Minemyer (Ohio State)

Abstract: In the 1950's John Nash famously proved that every Riemannian manifold admits an isometric embedding into Euclidean space. In this talk I will explain Nash's results and discuss adaptations of his isometric embedding theorem(s) to other types of spaces. These spaces include various types of manifolds, polyhedra, and more generally length metric spaces. This talk will mostly be a "state of the art" survey on what is known about the isometric embedding problem for the spaces listed above.

12:30 pm in 464 Loomis Laboratory,Thursday, November 3, 2016

#### Entanglement growth in quantum quenches

###### Mark Mezai (Princeton Physics)

Abstract: A global quench is an interesting setting where we can study thermalization of subsystems in a pure state. We investigate the spread of entanglement following a global quench in free field theory, holography, spin chains, and toy models. We find that the results in free scalar field theory are exactly reproduced by the model of free streaming quasiparticles, but strongly interacting chaotic systems spread entanglement more effectively. Based on recent insight into many-body quantum chaos, we propose two inequalities on the entropy, and suggest that the true evolution of the entropy is well approximated by saturating the combined bounds. A model based on the chaotic growth of operators saturates the combined bounds, and is a promising candidate to replace the quasiparticle model for chaotic systems.

2:00 pm in 243 Altgeld Hall,Thursday, November 3, 2016

#### Uniqueness in higher dimensional Beltrami Systems and the Hilbert-Smith conjecture

###### Gaven Martin (Massey University, New Zealand)

4:00 pm in 245 Altgeld Hall,Thursday, November 3, 2016

#### Siegel's problem on small volume lattices

###### Gaven Martin, AMS-NZMS Maclaurin Lecturer (Massey University, New Zealand)

Abstract: We outline in very general terms the history and the proof of the identification of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3 Coxeter group extended by the involution preserving the symmetry of this diagram. This gives us the smallest regular tessellation of hyperbolic 3-space. This solves (in three dimensions) the problem posed by Siegel in 1945 (Siegel solved this problem in two dimensions by deriving the Signature formula identifying the (2,3,7)-triangle group as having minimal co-area). There are strong connections with arithmetic hyperbolic geometry in the proof and the result has applications in the maximal symmetry groups of hyperbolic 3-manifolds (in much the same way that Hurwitz 84g-84 theorem and Siegel's result do).