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Wednesday, 6 August 2025 - 11:00 to 14:00 <br />
Place: seminar room, 3rd floor, front building, IM
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Speaker: Dragan Mašulović, University of Novi Sad<br />
Title: Projective KPT and automorphism groups of profinite structures
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Abstract <br />
<p>The Kechris-Pestov-Todorčević correspondence (or KPT-correspondence, for short) is a remarkable connection between model theory, combinatorics and topological dynamics first published in 2005. For a locally finite countable homogeneous first-order structure F the KPT-correspondence establishes a relationship between combinatorial properties of Age(F), the class of finite substructures of F, and dynamical properties of Aut(F) in the following sense: Aut(F) is extremely amenable if and only if Age(F) has the embedding Ramsey property. In cases where Aut(F) is not extremely amenable KPT-correspondence provides a technique for computing its universal minimal flow.</p><p><br></p><p> The starting point of this talk is the observation that Andy Zucker's 2016 proof of a very natural generalization of the KPT-correspondence is surprisingly categorical in nature. We will describe the categorical essence of Zucker's proof, present its categorical dual, and then combine it with recent results on the existence of small dual Ramsey degrees for some classes of algebras and relational structures, allowing us to infer the metrizability of the universal minimal flow of certain profinite algebras and relational structures.</p><p><br></p><p>Organized under the auspices of the <a href="https://www.math.cas.cz/index.php/events/seminar/15"> Seminar on Reckoning</a>.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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