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DTSTART:20210328T030000
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DTSTAMP:20210921T021646Z
UID:1604589300@ist.ac.at
DTSTART:20201105T161500
DTEND:20201105T171500
DESCRIPTION:Speaker: Melchior Wirth\nhosted by Jan Maas\nAbstract: (Quantum
) Markov semigroups play a role in a variety of fields such as operator al
gebras\, classical and quantum probability\, differential geometry and ope
n quantum systems. As they model dissipative time evolutions\, they tend t
o converge to an equilibrium state in the long-time limit. One central que
stion is to quantify this return to equilibrium. If one uses the entropy a
s a measure of the deviation from the equilibrium state\, this question is
closely related to logarithmic Sobolev inequalities. In the classical cas
e\, Bakry-Émery theory or optimal transport methods allow to deduce such
logarithmic Sobolev inequalities from lower bounds on the Ricci curvature.
In this talk I will review a notion of lower Ricci curvature bounds via a
gradient estimate that allows to transfer the optimal transport approach
to the quantum setting. I will discuss some of its stability properties an
d show how to obtain lower Ricci curvature bounds for a couple of examples
such as quantum tori\, free group factors and q-Gaussian algebras. (This
talk is based on joint work with Haonan Zhang.)
LOCATION:Online via Zoom\, IST Austria
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Gradient estimates for quantum Markov semigroups and return to equi
librium
URL:https://talks-calendar.app.ist.ac.at/events/2886
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