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Уважаемые коллеги,
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В пятницу 19 февраля в 11:30 состоится коллоквиум, на котором
будут заслушан доклад:<br>
<br>
Antti Kupiainen (University of Helsinki)<br>
<font size="+1"><b>Probabilistic Liouville Theory</b></font><br>
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<div class="abstract tex">
A. Polyakov introduced Liouville Conformal Field theory (LCFT)
in 1981 as a way to put a natural measure on the set of
Riemannian metrics over a two dimensional
manifold. Ever since, the work of Polyakov has echoed in various
branches of physics
and mathematics, ranging from string theory to probability
theory and geometry.
In the context of 2D quantum gravity models, LCFT is related
through the work of Knizhnik, Polyakov and Zamolodchikov to the
scaling limit of Random Planar Maps and through the
Alday-Gaiotto- Tachikava correspondence LCFT is conjecturally
related to certain 4D Yang-Mills theories. Through the work of
Dorn,Otto, Zamolodchikov and Zamolodchikov and Teschner LCFT was
argued to be to a certain extent integrable.
<br>
I will review a probabilistic construction of LCFT developed
together with David,
Rhodes and Vargas and recent proofs concerning the integrability
of LCFT.
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References:
<br>
Francois David, Antti Kupiainen, Remi Rhodes, Vincent Vargas,
Liouville quantum
gravity on the Riemann sphere, Commun. Math. Phys. 342 (3),
869-907 (2016)
<br>
Antti Kupiainen, Remi Rhodes, Vincent Vargas, The DOZZ formula
from the path integral, Journal of High Energy Physics May 2018,
2018:94
<br>
Antti Kupiainen, Remi Rhodes, Vincent Vargas, Integrability of
Liouville Theory:
Proof of the DOZZ Formula, Annals of Mathematics 191, 81-166,
(2020)
<br>
Colin Guillarmou, Antti Kupiainen, Remi Rhodes, Vincent Vargas,
Conformal bootstrap in Liouville Theory, arXiv:2005.11530
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Доклад будет сопровождаться онлайн-трансляцией в Zoom. ID и
пароль те же, что и для предыдущих трансляций:<a
class="moz-txt-link-freetext"
href="https://zoom.us/j/93947383544?pwd=QnU4VGVuYVBlSlJSeHBkTlp4QW9HZz09"
moz-do-not-send="true"><br>
</a><a class="moz-txt-link-freetext"
href="https://zoom.us/j/96899364518?pwd=MzBsR2lYT0lYL2x2b1oyNU9LeWlWUT09"
moz-do-not-send="true">https://zoom.us/j/96899364518?pwd=MzBsR2lYT0lYL2x2b1oyNU9LeWlWUT09</a><br>
Meeting ID: 968 9936 4518<br>
Пароль: 250319<br>
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