[ABE-L] IM-UFRJ - próximo seminário (online) de probabilidade - 12/04

[Maria Eulalia Vares]

*Probability Webinar -   IM-UFRJ *



Dear colleagues,

Our next online seminar will be held on Monday, *April 12*, from *3 p.m. to
4 p.m*. (Rio de Janeiro local time)

The GoogleMeet link for the seminar is  https://meet.google.com/uew-ehhn-kby




Speaker:   *Yuval Peres **(**Kent State University**)*

Title: *Gravitational allocation of uniform points on the sphere*

Abstract: Given uniform points on the surface of a two-dimensional sphere,
how can we partition the sphere fairly among them? "Fairly" means that each
region has the same area. It turns out that if the given points apply a
two-dimensional gravity force to the rest of the sphere, then the basins of
attraction for the resulting gradient flow yield such a partition-with
exactly equal areas, no matter how the points are distributed. This is
related to work of Nazarov-Sodin-Volberg on Gaussian analytic
functions. (See the cover of the AMS Notices at
http://www.ams.org/publications/journals/notices/201705/rnoti-cvr1.pdf.) Our
main result is that this partition minimizes, up to a bounded factor, the
average distance between points in the same cell. I will also present an
application to almost optimal matching on the sphere, connecting to a
classical result of Ajtai, Komlos and Tusnady (Combinatorica 1984).

Joint work with Nina Holden and Alex Zhai.



All the talks are held in English.

The videos of the online seminars held in 2020 are available at
http://www.dme.ufrj.br/?page_id=2885

For the 2021 series, a few days after each meeting the video should be
available at http://www.dme.ufrj.br/?page_id=3027



Thanks for circulating this information.

Sincerely,
Organizers: Guilherme Ost and Maria Eulalia Vares

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