BEGIN:VCALENDAR
VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VTIMEZONE
TZID:Europe/Vienna
BEGIN:DAYLIGHT
DTSTART:20180325T030000
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=3
TZNAME:CEST
END:DAYLIGHT
BEGIN:STANDARD
DTSTART:20171029T020000
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=10
TZNAME:CET
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTAMP:20260406T092221Z
UID:5936c170405c5030110904@ist.ac.at
DTSTART:20180118T130000
DTEND:20180118T150000
DESCRIPTION:Speaker: Alexander Minets\nhosted by Tamas Hausel\nAbstract: Gi
 ven a (hereditary) finitary abelian category $\\mathcal C$\, one can assoc
 iate to it the Hall algebra $H_\\mathcal C$\, which encodes the combinator
 ial information about extensions between objects in $\\mathcal C$. When $\
 \mathcal C$ is the category of finite-dimensional representations of a qui
 ver over a finite field\, these algebras are rather well understood and pr
 ovide a useful viewpoint on quantum groups. Much less is known when $\\mat
 hcal C=\\operatornameCohX$ is the category of coherent sheaves over a smoo
 th projective curve $X$\, even though they seem to encode interesting geom
 etric and arithmetic data associated to curves\, such as the number of cus
 pidal functions. In particular\, there is no comprehensive representation 
 theory of such algebras.My talk will consist of two parts. The first hour 
 will primarily serve as a motivation for the second part\, and will be ded
 icated to an overview of the classical theory of Hall algebras. We will re
 call their relation to quantum groups as evidenced by Ringel's theorem\, a
 nd some structural results in the case when $\\mathcal C=\\operatornameCoh
 X$. In the second hour\, I will shift the gears somewhat and introduce the
  cohomological version of Hall algebras (so-called CoHAs). I will then dis
 cuss some recent results providing an action of CoHA of Higgs torsion shea
 ves on homology groups of certain moduli spaces. These moduli spaces are h
 eavily inspired by Nakajima quiver varieties\, and are closely related to 
 Hilbert schemes of points and moduli of sheaves on $T^*X$. If time permits
 \, I will speculate about possible analogs of these CoHAs for an arbitrary
  smooth surface $S$ and/or extension of these results to Higgs bundles.
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
 TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Alexander Minets: Cohomological Hall algebras of Higgs torsion shea
 ves and moduli of stable triples
URL:https://talks-calendar.ista.ac.at/events/993
END:VEVENT
END:VCALENDAR