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BEGIN:VEVENT
SUMMARY:Lorenzo Zambotti (Sorbonne Université)
DTSTART:20210531T080000Z
DTEND:20210531T090000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/1
DESCRIPTION:Title: Weighted norms and a priori estimates for rough paths\nby Lorenzo
Zambotti (Sorbonne Université) as part of Stochastic PDEs and their frie
nds\n\n\nAbstract\nWe introduce weighted norms on controlled paths and pro
ve some a priori estimates for solutions to rough differential equations.
This method seems particularly effective to handle equations with Lipschit
z but unbounded non-linearities. Joint work with F. Caravenna and M. Gubin
elli.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Holden (ETH Zurich)
DTSTART:20210601T080000Z
DTEND:20210601T090000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/2
DESCRIPTION:Title: Integrability of the Schramm-Loewner evolution via conformal welding
of random surfaces\nby Nina Holden (ETH Zurich) as part of Stochastic
PDEs and their friends\n\n\nAbstract\nThe Schramm-Loewner evolution is a o
ne-parameter family of random fractal curves which describe the scaling li
mit of statistical physics models. We derive an explicit formula for the m
oments of the derivative of a particular uniformizing conformal map associ
ated with an SLE. The problems is hard to approach via classical Ito calcu
lus methods\, and our proof relies instead on conformal welding of Liouvil
le quantum gravity surfaces along with integrability results from Liouvill
e conformal field theory. Joint work with Morris Ang and Xin Sun.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Crisan (Imperial College London)
DTSTART:20210601T090000Z
DTEND:20210601T100000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/3
DESCRIPTION:Title: Well-posedness Properties for a Stochastic Rotating Shallow Water Mod
el\nby Dan Crisan (Imperial College London) as part of Stochastic PDEs
and their friends\n\n\nAbstract\nThe rotating shallow water (RSW) equatio
ns describe the evolution of a compressible rotating fluid below a free su
rface. The typical vertical length scale is assumed to be much smaller tha
n the horizontal one\, hence the shallow aspect. The RSW equations are a s
implification of the primitive equations which are the equations of choice
for modelling atmospheric and oceanic dynamics. In this talk\, I will pre
sent some well-posedness properties of a viscous rotating shallow water sy
stem. The system is stochastically perturbed in such a way that two key pr
operties of its deterministic counterpart are preserved. First\, it retain
s the characterisation of its dynamics as the critical path of a variation
al problem. In this case\, the corresponding action function is stochastic
ally perturbed. Secondly\, it satisfies the classical Kelvin circulation t
heorem. The introduction of stochasticity replaces the effects of the unre
solved scales. The stochastic RSW equations are shown to admit a unique ma
ximal strong solution in a suitably chosen Sobolev space which depends con
tinuously on the initial datum. The maximal stopping time up to which the
solution exist is shown to be strictly positive and\, for sufficiently sma
ll initial datum\, the solution is shown global in time with positive prob
ability. This is joint work with Dr Oana Lang (Imperial College London).\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Powell (Durham University)
DTSTART:20210602T080000Z
DTEND:20210602T090000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/4
DESCRIPTION:Title: Brownian half-plane excursions\, CLE4 and critical Liouville quantum
gravity\nby Ellen Powell (Durham University) as part of Stochastic PDE
s and their friends\n\n\nAbstract\nI will discuss a coupling between a Bro
wnian excursion in the upper half plane and an exploration of nested CLE$_
4$ loops in the unit disk. In this coupling\, the CLE$_4$ is drawn on top
of an independent “critical Liouville quantum gravity surface” known a
s a quantum disk. This is based on a forthcoming joint work with Juhan Aru
\, Nina Holden and Xin Sun\, and describes the analogue of Duplantier-Mill
er-Sheffield’s “mating-of-trees correspondence” in the critical regi
me ($\\kappa=4$).\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Krylov (University of Minnesota)
DTSTART:20210602T140000Z
DTEND:20210602T150000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/5
DESCRIPTION:Title: On diffusion processes with drift in a Morrey class containing Ld+2\nby Nicolai Krylov (University of Minnesota) as part of Stochastic PDEs
and their friends\n\n\nAbstract\nWe present new conditions on the drift o
f the Morrey type with mixed norms allowing us to obtain Aleksandrov type
estimates of potentials of time inhomogeneous diffusion processes in space
s with mixed norms.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gigliola Staffilani (MIT)
DTSTART:20210601T140000Z
DTEND:20210601T150000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/6
DESCRIPTION:Title: On almost sure well-posedness for certain dispersive PDE\nby Gigl
iola Staffilani (MIT) as part of Stochastic PDEs and their friends\n\n\nAb
stract\nIn this talk we summarize some of the many almost sure well-posedn
ess results proved in recent years for dispersive equations. This study go
es back to the work of Bourgain on invariant Gibbs measures and continued
with the applications and evolution of his original ideas to address the q
uestion of local and global well-posedness for equations that are in a sen
se “supercritical”. If time permits we will also present some results
for stochastic NLS equations\, a direction of research started by de Bouar
d and Debussche.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajay Chandra (Imperial College London)
DTSTART:20210531T090000Z
DTEND:20210531T100000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/7
DESCRIPTION:Title: Stochastic Quantization of Yang Mills\nby Ajay Chandra (Imperial
College London) as part of Stochastic PDEs and their friends\n\n\nAbstract
\nI will result some recent work along with work in progress on the constr
uction of a stochastic dynamic and a corresponding state space that in pri
nciple should have the Yang Mills Euclidean quantum field theory as its in
variant measure. This is joint work with Ilya Chevyrev\, Martin Hairer\, a
nd Hao Shen.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Perkowski (FU Berlin)
DTSTART:20210602T090000Z
DTEND:20210602T100000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/8
DESCRIPTION:Title: Martingale problems for some singular SPDEs\nby Nicolas Perkowski
(FU Berlin) as part of Stochastic PDEs and their friends\n\n\nAbstract\nM
ost techniques for solving singular SPDEs\, such as regularity structures\
, are based on pathwise calculus. It would be interesting to study singula
r SPDEs from a more probabilistic perspective\, for example via the martin
gale problem. In general that is a too difficult problem at the moment\, b
ut there are some equations for which we can do this. I will explain the i
deas on the example of the conservative stochastic Burgers equation and in
dicate how to extend the results to a larger class of equations that share
a similar structure. A novelty of this approach is that it allows to prov
e (weak) well-posedness for some scaling critical singular SPDEs. Based on
works with Massimiliano Gubinelli and Lukas Gräfner.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davar Khoshnevisan (University of Utah)
DTSTART:20210531T140000Z
DTEND:20210531T150000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/9
DESCRIPTION:Title: Phase Analysis of a Family of Stochastic Reaction-Diffusion Equations
\nby Davar Khoshnevisan (University of Utah) as part of Stochastic PDE
s and their friends\n\n\nAbstract\nWe consider a wide family of reaction-d
iffusion equations that are forced with multiplicative space-time white no
ise\, and show that if the level of the noise is sufficiently high then th
e resulting SPDE has a unique invariant measure. By contrast\, we prove al
so that when the level of the noise is sufficiently low\, then there are i
nfinitely many invariant measures. In that case\, we prove that the collec
tion of all invariant measures is a line segment\; that is\, there are two
extreme points. Time permitting\, we will say a few thing about the two e
xtremal invariant measures as well in the low-noise case. The phase pictur
e that is described here was predicted in an earlier work of Zimmerman et
al (2000).\n\nThis is based on joint work with Carl Mueller (University of
Rochester\, USA)\, Kunwoo Kim (POSTECH\, S Korea)\, and Shang-Yuan Shiu (
National Central University\, Taiwan).\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Mattingly (Duke)
DTSTART:20210602T120000Z
DTEND:20210602T130000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/10
DESCRIPTION:Title: The Gaussian Structure of the Stochastically Forced Burgers Equation
and related problems\nby Jonathan Mattingly (Duke) as part of Stochas
tic PDEs and their friends\n\n\nAbstract\nI will explain some recent resul
ts which show that the law of the stochastic burgers equation at a fixed t
ime t is absolutely continuous with respect to the natural Gaussian measur
e on the spatial domain. The results will apply to forcing just up to the
point where the roughness of the forcing corresponds to the classical KPZ
equation in the Burgers setting. As one approaches this level of roughness
\, the equations must be understood in as a Singular SPDEs (in the sense o
f Hairer ). As such the construction helps illuminate the structure of the
equation and makes clear in what sense we might call these equations “t
ruly” elliptic in this infinite dimensional setting. I will also make co
mments connecting back to previous results on the 2D Naiver Stokes equatio
n. This work is joint with Marco Romito and Langxuan Su and builds on work
with Andrea Watkins Hairston.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Khanin (University of Toronto)
DTSTART:20210531T120000Z
DTEND:20210531T130000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/11
DESCRIPTION:Title: On Stationary Solutions to the Stochastic Heat Equation\nby Kons
tantin Khanin (University of Toronto) as part of Stochastic PDEs and their
friends\n\n\nAbstract\nI plan to discuss the problem of uniqueness of glo
bal solutions to the random Hamilton-Jacobi equation. I will formulate sev
eral conjectures and present results supporting them. Then I will discuss
a new uniqueness result for the Stochastic Heat equation in the regime of
weak disorder.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Quastel (University of Toronto)
DTSTART:20210531T130000Z
DTEND:20210531T140000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/12
DESCRIPTION:Title: The KPZ fixed point: Part I\nby Jeremy Quastel (University of To
ronto) as part of Stochastic PDEs and their friends\n\n\nAbstract\nThe 1-d
KPZ universality class contains random interface growth models as well as
random polymer free energies and driven diffusive systems. Various exact
asymptotic distributions have been computed over the last two decades\, so
me of them coming from random matrix theory. These are special cases of th
e strong coupling fixed point\, which turns out to be a completely integra
ble Markov process: its transition probabilities are described by classica
l integrable PDE’s.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rémi Rhodes (Université Aix-Marseille)
DTSTART:20210601T070000Z
DTEND:20210601T080000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/13
DESCRIPTION:Title: Gluing random surfaces: conformal bootstrap in Liouville theory via
Segal’s axioms\nby Rémi Rhodes (Université Aix-Marseille) as part
of Stochastic PDEs and their friends\n\n\nAbstract\nThe law of Markov proc
esses indexed by time (the real line) take a simple form when expressed in
terms of the action of the associated semigroup. The generalization of th
is question to the case when the process is indexed by higher dimensional
manifolds is more intricate and this question is particularly relevant in
the study of quantum field theories. A general proposal was formalized by
G. Segal in the eighties in this direction. Yet\, concrete examples of QFT
s where the Segal axioms are indeed valid are extremely limited (beyond tr
ivial cases). We treat here the case of a specific Conformal Field Theory
(CFT)\, called the Liouville theory which is a probabilistic model of 2D r
andom surfaces. The outcome is the validity of the conformal bootstrap\, i
.e. a bridge between probability and representation theory: correlation fu
nctions are expressed in terms of (universal) holomorphic functions of the
moduli parameters of the Riemann surface\, called conformal blocks which
have a strong representation theoretical content\, and the structure const
ants of the CFT\, here the DOZZ formula. Conformal bootstrap was conjectur
ed in physics in the eighties to be the universal structure of CFTs and Li
ouville theory is perhaps the first non trivial example where it can be sh
own to hold mathematically. This talk will be introductory to these topics
.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Remenik (Universidad de Chile)
DTSTART:20210601T130000Z
DTEND:20210601T140000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/14
DESCRIPTION:Title: The KPZ fixed point: Part II\nby Daniel Remenik (Universidad de
Chile) as part of Stochastic PDEs and their friends\n\n\nAbstract\nThe KPZ
fixed point\, the universal limit of all models in the KPZ universality c
lass\, is obtained as the scaling limit of the totally asymmetric simple e
xclusion process (TASEP). The main ingredient in the construction is an ex
plicit formula for the distribution of TASEP in terms of the Fredholm dete
rminant of a kernel which involves certain random walk hitting times. The
formula has a natural scaling limit which defines the KPZ fixed point and
can be used to show that its transition probabilities are integrable.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bakhtin (NYU)
DTSTART:20210601T150000Z
DTEND:20210601T160000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/15
DESCRIPTION:Title: Dynamic polymers: invariant measures and ordering by noise\nby Y
uri Bakhtin (NYU) as part of Stochastic PDEs and their friends\n\n\nAbstra
ct\nGibbs measures describing directed polymers in random potential are ti
ghtly related to the stochastic Burgers/KPZ/heat equations. One of the bas
ic questions is: do the local interactions of the polymer chain with the r
andom environment and with itself define the macroscopic state uniquely fo
r these models? We establish and explore the connection of this problem wi
th ergodic properties of an infinite-dimensional stochastic gradient flow.
Joint work with Hong-Bin Chen and Liying Li.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Mytnik (Technion)
DTSTART:20210602T070000Z
DTEND:20210602T080000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/16
DESCRIPTION:Title: On the speed of a front for stochastic reaction-diffusion equations
with non-Lipschitz drift\nby Leonid Mytnik (Technion) as part of Stoch
astic PDEs and their friends\n\n\nAbstract\nWe study the asymptotic speed
of a random front for solutions to stochastic reaction-diffusion equations
with non-Lipschitz drift and Wright-Fisher noise proportional to $\\sigma
$. Under some conditions on the drift\, we show the existence of the speed
of the front and derive its asymptotics depending on $\\sigma$. \n\nThis
talk is based on joint works with C. Mueller\, L. Ryzhik\, C. Barnes and Z
. Sun.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armen Shirikyan (Cergy Paris Université)
DTSTART:20210531T070000Z
DTEND:20210531T080000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/17
DESCRIPTION:Title: Mixing for PDEs with degenerate noise: an overview and open problems
\nby Armen Shirikyan (Cergy Paris Université) as part of Stochastic P
DEs and their friends\n\n\nAbstract\nWe discuss some results about uniquen
ess and stability of a stationary measure for randomly forced PDEs arising
in fluid dynamics. Two different scenarios expressed in terms of controll
ability properties of the associated deterministic problem will be present
ed. We show\, in particular\, how they influence the choice of admissible
random forces. We also formulate some open problems in the field.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Cerrai (University of Maryland)
DTSTART:20210602T130000Z
DTEND:20210602T140000Z
DTSTAMP:20260404T094652Z
UID:SPDEs/18
DESCRIPTION:Title: On the small mass limit for infinite-dimensional systems with state-
dependent damping\nby Sandra Cerrai (University of Maryland) as part o
f Stochastic PDEs and their friends\n\n\nAbstract\nI will present a series
of results on the asymptotic behavior\, with respect to the small mass\,
of infinite-dimensional stochastic systems described by a damped waves equ
ation perturbed by a Gaussian noise. I will consider in particular the cas
e when the friction coefficient depends on the position of the particles a
nd I will show how things change drastically\, compared to what happens in
the case of constant friction.\n
LOCATION:https://stable.researchseminars.org/talk/SPDEs/18/
END:VEVENT
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