A reminder: this is today.
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On 2023-05-01 20:09, Mykhaylo Tyomkyn wrote:
Dear all,
This Thursday, 4 May, we will have TWO noon lectures. The first lecture will be given by Peter Hinow, at the usual time 12:20. Afterwards, we will have a second lecture, given by Ioannis Eleftheriadis, starting at 13:10. Please find the talk abstracts below.
Misha Tyomkyn.
Ergodicity and loss of capacity for a random family of concave maps Peter Hinow University of Wisconsin - Milwaukee May 4, 2023, 12:20 in S6
Abstract Random fluctuations of an environment are common in ecological and economical settings. We consider a family of concave quadratic polynomials on the unit interval that model a self-limiting growth behavior. The maps are parametrized by an independent, identically distributed random parameter. What in the deterministic setting would be a single fixed point is now replaced by an invariant measure, which is a fixed point of the Perron-Frobenius operator. In select cases, we show the existence of a unique invariant ergodic measure of the resulting random dynamical system. Moreover, there is an attenuation of the mean of the state variable compared to the constant environment with the averaged parameter. This is joint work with Ami Radunskaya (Pomona College, Pomona, CA).
Towards a characterisation of universal categories of relational structures Ioannis Eleftheriadis University of Cambridge May 4, 2023, 13:10 in S6
Abstract Answering a conjecture of Konig, Frucht first established that every finite group is isomorphic to the automorphism group of a finite graph. Since then, there has been a series of results regarding the representation of groups in various finite and infinite structures. These culminated in the work of Isbel, who initiated the study of algebraically universal categories, i.e. those that fully embed every category of universal algebras. In this talk, I'll discuss recent work that establishes a partial characterisation of algebraically universal categories of relational structures, given in terms of a sparsity notion known as nowhere density and its model-theoretic consequences. This extends a result of Nesetril-Ossona de Mendez on categories of finite graphs to the context of categories of relational structures of unbounded size.
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