Department of

# Mathematics

Seminar Calendar
for events the day of Friday, February 8, 2019.

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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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Friday, February 8, 2019

4:00 pm in 245 Altgeld Hall,Friday, February 8, 2019

#### Can you be both central and vacant? A study of a small pond network

###### Prof. Zoi Rapti   [email] (UIUC Math)

Abstract: We will introduce a simple one-dimensional ordinary differential equation (Levin's equation) and concepts from network theory to analyze occupancy patterns in a small network of freshwater ponds. We will investigate various factors that determine whether a pond can be vacant or occupied by our organism (Daphnia pulex aka waterflea), which is prevalent in ponds and lakes of the Midwest. No knowledge of differential equations or network theory will be assumed: all background will be introduced in the talk.

4:00 pm in 345 Altgeld Hall,Friday, February 8, 2019

#### "The complexity of topological group isomorphism" by A. Kechris, A. Nies, and K. Tent (Part 1)

###### Anush Tserunyan (UIUC)

Abstract: This will be the introductory talk of the series on the paper in the title [arXiv link], which deals with the classification of some natural classes of non-Archimedean groups (= closed subgroups of S) up to topological group isomorphism. It gives a general criterion for a class of non-Archimedean groups to show that the topological group isomorphism on it is Borel-classifiable by countable structures. This criterion is satisfied by the classes of profinite groups, locally compact non-Archimedean groups, and oligomorphic groups.

4:00 pm in 145 Altgeld Hall,Friday, February 8, 2019

#### Hamiltonian Lie algebroids

###### Luka Zwaan (UIUC)

Abstract: Hamiltonian Lie algebroids were introduced quite recently by Blohmann and Weinstein, resulting from their work in general relativity. They are a generalisation of the usual notion of a Hamiltonian action of a Lie algebra on a presymplectic manifold to arbitrary Lie algebroids. In this talk, I will quickly recall this usual notion, and then discuss several ways Blohmann and Weinstein tried to generalise it. In the end, the most convenient method makes use of a choice of connection on the Lie algebroid.