BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CMSA - ECPv6.17.1//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:CMSA
X-ORIGINAL-URL:https://cmsa.fas.harvard.edu
X-WR-CALDESC:Events for CMSA
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:America/New_York
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20200308T070000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20201101T060000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20210314T070000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20211107T060000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20220313T070000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20221106T060000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211021T184400
DTEND;TZID=America/New_York:20211021T204400
DTSTAMP:20240301T104328Z
CREATED:20240214T082555Z
LAST-MODIFIED:20240301T104328Z
UID:10002587-1634841840-1634849040@cmsa.fas.harvard.edu
SUMMARY:10/21/2021 Interdisciplinary Science Seminar
DESCRIPTION:Title: Mathematical resolution of the Liouville conformal field theory. \nAbstract: The Liouville conformal field theory is a well-known beautiful quantum field theory in physics describing random surfaces. Only recently a mathematical approach based on a well-defined path integral to this theory has been proposed using probability by David\, Kupiainen\, Rhodes\, Vargas. \nMany works since the ’80s in theoretical physics (starting with Belavin-Polyakov-Zamolodchikov) tell us that conformal field theories in dimension 2 are in general « Integrable »\, the correlations functions are solutions of PDEs and can in principle be computed explicitely by using algebraic tools (vertex operator algebras\, representations of Virasoro algebras\, the theory of conformal blocks). However\, for Liouville Theory this was not done at the mathematical level by algebraic methods. \nI’ll explain how to combine probabilistic\, analytic and geometric tools to give explicit (although complicated) expressions for all the correlation functions on all Riemann surfaces in terms of certain holomorphic functions of the moduli parameters called conformal blocks\, and of the structure constant (3-point function on the sphere). This gives a concrete mathematical proof of the so-called conformal bootstrap and of Segal’s gluing axioms for this CFT. The idea is to break the path integral on a closed surface into path integrals on pairs of pants and reduce all correlation functions to the 3-point correlation function on the Riemann sphere $S^2$. This amounts in particular to prove a spectral resolution of a certain operator acting on $L^2(H^{-s}(S^1))$ where $H^{-s}(S^1)$ is the Sobolev space of order -s<0 equipped with a Gaussian measure\, which is viewed as the space of fields\, and to construct a certain representation of the Virasoro algebra into unbounded operators acting on this Hilbert space. \nThis is joint work with A. Kupiainen\, R. Rhodes and V. Vargas.
URL:https://cmsa.fas.harvard.edu/event/10-21-2021-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
END:VEVENT
END:VCALENDAR