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SUMMARY:Energy solutions and generators of singular SPDEs
DTSTART:20230404T150000
DTEND:20230404T155000
DTSTAMP:20260501T000708Z
UID:c994b8dad81208ea4c55608aad553718fb8e64771497575e0f968f7a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Nicolas Perkowski (Free University)\n\nAbstract:\nEnergy solut
 ions provide probabilistic solution theories for singular SPDEs with tract
 able (quasi-)invariant measures\, with the prototypical example being the 
 stochastic Burgers/KPZ equation with its white noise invariant measure. En
 ergy solutions were introduced by Gonçalves and Jara and later Gubinelli 
 and they are based on methods from hydrodynamic limits such as replacement
  lemmas and martingale estimates. More recently\, we used operator theory 
 and functional analysis to construct and control infinitesimal generators 
 in this setting\, which yields (weak) well-posedness of energy solutions. 
 Compared to pathwise approaches like regularity structures\, this requires
  only relatively soft estimates and the method applies to some scaling (su
 per-)critical equations. I will start with the guiding example of a diffus
 ion in a singular divergence-free vector field\, where we can understand t
 he main ideas of energy solutions without many technicalities and we can a
 lready see some (super-)critical problems. Then I will present an abstract
  construction of infinitesimal generators\, semigroups\, and energy soluti
 ons. Finally we study applications to singular SPDEs. This is joint work w
 ith Lukas Gräfner.\n\n 
LOCATION:GA 3 34 https://plan.epfl.ch/?room==GA%203%2034
STATUS:CONFIRMED
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