The YangMills measure on surfaces and the master field on the plane
Speaker 
Speaker: Antoine Dahlqvist (University of Sussex)


When 
Jan 30, 2024
from 04:00 PM to 05:00 PM 
Where  Online via Zoom 
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As a Euclidean quantum field theories, the YangMills measure can be formally understood as a probability measure, like the Wiener measure, on a very large probability space. Making rigorous mathematical sense of this formal point of view is a challenging problem, that is most often open, in particular for the YangMills measure with a nonabelian structure group and a four dimensional spacetime. Nonetheless, for a two dimensional spacetime, this problem has been solved recently in different ways, leading to a welldefined notion of YangMills measure, as a specific law of a random holonomy field. We will recall a construction due to T. Lévy and discuss its large N limit. We will present partial results and a conjecture, based on joint works with T. Lemoine, according to which, in negative Euler characteristics, the topology of spacetime do not impact the master field.
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