Department of

# Mathematics

Seminar Calendar
for events the day of Monday, December 11, 2017.

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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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Monday, December 11, 2017

3:00 pm in 243 Altgeld Hall,Monday, December 11, 2017

#### Post-Lie algebroids and Lie algebra actions

###### Ari Stern (Washington University in St. Louis)

Abstract: A fundamental problem in numerical analysis is the approximation of flows of vector fields on manifolds. For vector fields in Euclidean space (i.e., systems of ODEs), Butcher gave a brilliant characterization of Runge-Kutta methods in terms of the algebra and combinatorics of rooted trees. Subsequent work related this to the fact that vector fields on Euclidean space form a "pre-Lie algebra". More recently, this work has been extended to "post-Lie algebroids": vector bundles whose sections form a "post-Lie algebra" with respect to a connection. We give a complete characterization of post-Lie algebroids in terms of local Lie algebra actions. As a corollary, we get a "no-go theorem" limiting the cases to which this class of numerical methods can be applied. (Joint work with Hans Munthe-Kaas and Olivier Verdier.)

5:00 pm in 445 Altgeld Hall,Monday, December 11, 2017

#### presentations

###### uiuc students (UIUC)

Abstract: Several talks will be presented on Stinespring's dilation theorem, Bell inequalities, Teleportation and superdense coding, Grothendieck's inequality and nonlocality, and recovery.