Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, March 29, 2018.

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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, March 29, 2018

3:00 pm in 243 Altgeld Hall,Thursday, March 29, 2018

#### An algorithm for volumes of polytopes with applications to social choice

###### Winfried Bruns (Universität Osnabrück)

Abstract: We discuss a fast algorithm for the computation of the volume of rational polytopes with few (nonsimplicial) facets. It is based on a natural recursive approach, originally suggested by Lasserre, that uses descent in the face lattice. For efficient computations in high dimensions it needs a sophisticated implementation that has now been realized in Normaliz. Probabilities in social choice that are based on the Impartial Anonymous Culture can often be interpreted as volumes of rational polytopes. For 4 candidates these polytopes have dimension 24, and the computation is a challenge. Before the new algorithm had been implemented, Normaliz had to use triangulations. Descent in the face lattice makes all these computations very easy and gives access to many more that hitherto had been inaccessible.

4:00 pm in 245 Altgeld Hall,Thursday, March 29, 2018

#### Swarming by Nature and by Design

###### Andrea Bertozzi (UCLA)

Abstract: The cohesive movement of a biological population is a commonly observed natural phenomenon. With the advent of platforms of unmanned vehicles, such phenomena have attracted a renewed interest from the engineering community. This talk will cover a survey of models ranging from aggregation models in nonlinear partial differential equations to control algorithms and robotic testbed experiments. We will show how pairwise potential models are used to study biological movement and how to develop a systematic theory of such models. We also discuss how to use "designer potentials" to orchestrate cooperative movement in specific patterns, many of which may not be observed in nature but could be desirable for artificial swarms. Finally we conclude with some recent related work on emotional contagion in crowds and on design of algorithms for crop pollination.