BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//UM//UM*Events//EN
CALSCALE:GREGORIAN
BEGIN:VTIMEZONE
TZID:America/Detroit
TZURL:http://tzurl.org/zoneinfo/America/Detroit
X-LIC-LOCATION:America/Detroit
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20070311T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20071104T020000
RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTAMP:20260316T104615
DTSTART;TZID=America/Detroit:20260414T160000
DTEND;TZID=America/Detroit:20260414T170000
SUMMARY:Lecture / Discussion:Colloquium: Total positivity: combinatorics\, geometry\, and representation theory
DESCRIPTION:An invertible matrix is called totally positive if all of its minors are positive. Over the past several decades\, this classical notion has evolved into a rich and far-reaching theory. In a foundational 1994 work\, Lusztig extended total positivity to arbitrary split real reductive groups and their flag varieties\, uncovering remarkable connections with combinatorics\, geometry\, and representation theory. Since then\, total positivity has emerged in a wide range of contexts\, from cluster algebras and higher Teichmüller theory to the geometry\nunderlying the amplituhedron.\n\nIn this talk\, I will give an overview of the basic theory of total positivity and describe some recent developments. I will explain how the subject is intertwined with combinatorial structures such as Bruhat order and shellable posets\, with representation theory through Lusztig's canonical basis\, and with topology through the study of regular CW complexes and with an unexpected appearance of the Poincaré econjecture. I will also discuss recent progress on the conjectures of Björner\, of Fomin-Zelevinsky\, as well as further conjectures of Postnikov\, Galashin-Karp-Lam\, and Williams. This talk is based on my joint works with Huanchen Bao and with Kaitao Xie.
UID:144881-21896089@events.umich.edu
URL:https://events.umich.edu/event/144881
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:
CONTACT:
END:VEVENT
END:VCALENDAR