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SUMMARY:Topology Seminar: Dessins d'enfants and the generalized Hurwitz nu
 mbers
DTSTART:20171114T151500
DTEND:20171114T161500
DTSTAMP:20260920T164830Z
UID:9eac7454fb2ff47b8f6514d7682a71cc724b6ab9467b1f555713558f
CATEGORIES:Conferences - Seminars
DESCRIPTION:George Shabat (Moscow State University)\nA multi-graph\, embed
 ded into a closed connected oriented surface\, is called  a 'dessin d'enf
 ant' if its complement is homeomorphic to a disjoint union of cells. The (
 appropriately defined) category of dessins d'enfants turned out to be equi
 valent to the category of 'Belyi pairs' that belongs to arithmetic geometr
 y\; a first part of the talk will be devoted to the foundations of this th
 eory.\n\nThen the certain problems of enumeration of dessins (and their ge
 neralizations) will be introduced. The particular cases of these problems\
 , e.g.\, recursions for the so-called 'Hurwitz numbers'\, were studied int
 ensively during the last decades\; the corresponding recent results will b
 e mentioned. However\, the general case is currently out of reach\, and du
 ring the second part of the talk a certain project\, based on the above ca
 tegory equivalence\, will be presented. Hopefully\, realization of this pr
 oject will promote the understanding of general case.
LOCATION:ELE 111 https://plan.epfl.ch/?room=ELE111
STATUS:CONFIRMED
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