Buongiorno, vi inoltro l'annuncio del OWPS di domani. Saluti Alessandra

---------- Forwarded message --------- Da: One World Probability ow.probability@gmail.com Date: mer 24 feb 2021 alle ore 12:25 Subject: [owps] One World Probability Seminar Thursday February 25, 2021 To: owps@lists.bath.ac.uk

Tomorrow's speakers in the One World Probability Seminar are (Note: all times are in UTC. *Due to time changes, you should check what that translates to in your location*) ------------------------------------------------

(14:00-15:00 UTC) Speaker: Fredrik Viklund (KTH) Title: Interplay between Dirichlet and Loewner energies: cutting-welding operations and foliations by Weil-Petersson quasicircles - Part 1 Abstract: The Loewner energy is a Mobius invariant deterministic quantity attached to Jordan curves in the plane. One way in which it arises is as a large deviations rate function for the Schramm-Loewner evolution with small parameter. A curve has finite Loewner Energy if and only if it is a Weil-Petersson quasicircle, a class of curves that in the last decades has received significant attention by both physicists and mathematicians, but only very recently by probabilists. The Loewner-Kufarev energy is a dual quantity attached to certain continuous families of Jordan curves, which arises in the context of large deviations of SLEs with large parameter.

We will survey recent joint works (and beyond) that describe the interplay between these energies (and the Weil-Petersson quasicircles) with the usual Dirichlet energy on the plane. The results are closely related to recent ideas and developments in Random Conformal Geometry but proofs are purely analytic.

In the first talk, we begin by presenting background material and a survey of properties and characterisations of Weil-Petersson quasicircles. We then discuss interactions between Weil-Petersson quasicircles with ambient Dirichlet class functions via cutting and conformal welding operations as well as interpretations in terms of "flow-lines". At the end we will present a "dictionary" that relates these statements with ideas in Random Conformal Geometry.

(15:00-16:00 UTC) Speaker: Yilin Wang (MIT) Title: Interplay between Dirichlet and Loewner energies: cutting-welding operations and foliations by Weil-Petersson quasicircles - Part 2 Abstract: The main topic of the second talk is the Loewner-Kufarev energy and corresponding families of Weil-Petersson quasicircles. We will indicate how to associate to such a foliation a (geometric) "winding function" on the plane whose Dirichlet energy equals the (analytic) Loewner-Kufarev energy. This duality entails several interesting results: for example, the Loewner-Kufarev Energy is in fact reversible and we obtain a new characterisation of Weil-Petersson quasicircles. We will end by discussing further implications and open problems.

*Main references:*F. Viklund, Y. Wang: Interplay between Loewner and Dirichlet energies via conformal welding and flow-lines, Geom. Funct. Anal. (GAFA) 30 289–321 (2020) F. Viklund, Y. Wang: The Loewner-Kufarev Energy and Foliations by Weil-Petersson Quasicircles, arXiv:2012.05771 (2020)

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The zoom link will appear the day before on the OWPS website: https://www.owprobability.org/one-world-probability-seminar https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.owprobability.org%2Fone-world-probability-seminar&data=04%7C01%7Cowps%40lists.bath.ac.uk%7C99fe32b5533e4434c7d208d8d8b687f2%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637497626468857599%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=7a9pGpqwovlxc9JpK5psm6uROFdX1nF%2FaatsqgTUhaU%3D&reserved=0

It can also be directly accessed through the link below: https://uniroma1.zoom.us/j/89460596402?pwd=QmZ5N25waCs5NVl5QkJGdWxQTFpDdz09 https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Funiroma1.zoom.us%2Fj%2F89460596402%3Fpwd%3DQmZ5N25waCs5NVl5QkJGdWxQTFpDdz09&data=04%7C01%7Cowps%40lists.bath.ac.uk%7C99fe32b5533e4434c7d208d8d8b687f2%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637497626468867557%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=D1tPag8QvxbB3ZDD%2F3CvnZy%2FNm1qbbZxCiubC%2BxNtGQ%3D&reserved=0 Meeting-ID: 894 6059 6402 Passcode: 307302

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We hope to see you all tomorrow! One World Probability Team