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BEGIN:VEVENT
SUMMARY:Lorenzo Zambotti (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20210531T080000Z
DTEND;VALUE=DATE-TIME:20210531T090000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/1
DESCRIPTION:Title: We
ighted norms and a priori estimates for rough paths\nby Lorenzo Zambot
ti (Sorbonne Université) as part of Stochastic PDEs and their friends\n\n
\nAbstract\nWe introduce weighted norms on controlled paths and prove some
a priori estimates for solutions to rough differential equations. This me
thod seems particularly effective to handle equations with Lipschitz but u
nbounded non-linearities. Joint work with F. Caravenna and M. Gubinelli.\n
LOCATION:https://researchseminars.org/talk/SPDEs/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Holden (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20210601T080000Z
DTEND;VALUE=DATE-TIME:20210601T090000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/2
DESCRIPTION:Title: In
tegrability of the Schramm-Loewner evolution via conformal welding of rand
om surfaces\nby Nina Holden (ETH Zurich) as part of Stochastic PDEs an
d their friends\n\n\nAbstract\nThe Schramm-Loewner evolution is a one-para
meter family of random fractal curves which describe the scaling limit of
statistical physics models. We derive an explicit formula for the moments
of the derivative of a particular uniformizing conformal map associated wi
th an SLE. The problems is hard to approach via classical Ito calculus met
hods\, and our proof relies instead on conformal welding of Liouville quan
tum gravity surfaces along with integrability results from Liouville confo
rmal field theory. Joint work with Morris Ang and Xin Sun.\n
LOCATION:https://researchseminars.org/talk/SPDEs/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Crisan (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210601T090000Z
DTEND;VALUE=DATE-TIME:20210601T100000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/3
DESCRIPTION:Title: We
ll-posedness Properties for a Stochastic Rotating Shallow Water Model\
nby Dan Crisan (Imperial College London) as part of Stochastic PDEs and th
eir friends\n\n\nAbstract\nThe rotating shallow water (RSW) equations desc
ribe the evolution of a compressible rotating fluid below a free surface.
The typical vertical length scale is assumed to be much smaller than the h
orizontal one\, hence the shallow aspect. The RSW equations are a simplifi
cation of the primitive equations which are the equations of choice for mo
delling atmospheric and oceanic dynamics. In this talk\, I will present so
me well-posedness properties of a viscous rotating shallow water system. T
he system is stochastically perturbed in such a way that two key propertie
s of its deterministic counterpart are preserved. First\, it retains the c
haracterisation of its dynamics as the critical path of a variational prob
lem. In this case\, the corresponding action function is stochastically pe
rturbed. Secondly\, it satisfies the classical Kelvin circulation theorem.
The introduction of stochasticity replaces the effects of the unresolved
scales. The stochastic RSW equations are shown to admit a unique maximal s
trong solution in a suitably chosen Sobolev space which depends continuous
ly on the initial datum. The maximal stopping time up to which the solutio
n exist is shown to be strictly positive and\, for sufficiently small init
ial datum\, the solution is shown global in time with positive probability
. This is joint work with Dr Oana Lang (Imperial College London).\n
LOCATION:https://researchseminars.org/talk/SPDEs/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Powell (Durham University)
DTSTART;VALUE=DATE-TIME:20210602T080000Z
DTEND;VALUE=DATE-TIME:20210602T090000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/4
DESCRIPTION:Title: Br
ownian half-plane excursions\, CLE4 and critical Liouville quantum gravity
\nby Ellen Powell (Durham University) as part of Stochastic PDEs and t
heir friends\n\n\nAbstract\nI will discuss a coupling between a Brownian e
xcursion in the upper half plane and an exploration of nested CLE$_4$ loop
s in the unit disk. In this coupling\, the CLE$_4$ is drawn on top of an i
ndependent “critical Liouville quantum gravity surface” known as a qua
ntum disk. This is based on a forthcoming joint work with Juhan Aru\, Nina
Holden and Xin Sun\, and describes the analogue of Duplantier-Miller-Shef
field’s “mating-of-trees correspondence” in the critical regime ($\\
kappa=4$).\n
LOCATION:https://researchseminars.org/talk/SPDEs/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Krylov (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20210602T140000Z
DTEND;VALUE=DATE-TIME:20210602T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
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 th
eir friends\n\n\nAbstract\nWe present new conditions on the drift of the M
orrey type with mixed norms allowing us to obtain Aleksandrov type estimat
es of potentials of time inhomogeneous diffusion processes in spaces with
mixed norms.\n
LOCATION:https://researchseminars.org/talk/SPDEs/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gigliola Staffilani (MIT)
DTSTART;VALUE=DATE-TIME:20210601T140000Z
DTEND;VALUE=DATE-TIME:20210601T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/6
DESCRIPTION:Title: On
almost sure well-posedness for certain dispersive PDE\nby Gigliola St
affilani (MIT) as part of Stochastic PDEs and their friends\n\n\nAbstract\
nIn this talk we summarize some of the many almost sure well-posedness res
ults proved in recent years for dispersive equations. This study goes back
to the work of Bourgain on invariant Gibbs measures and continued with th
e applications and evolution of his original ideas to address the question
of local and global well-posedness for equations that are in a sense “s
upercritical”. If time permits we will also present some results for sto
chastic NLS equations\, a direction of research started by de Bouard and D
ebussche.\n
LOCATION:https://researchseminars.org/talk/SPDEs/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajay Chandra (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210531T090000Z
DTEND;VALUE=DATE-TIME:20210531T100000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/7
DESCRIPTION:Title: St
ochastic Quantization of Yang Mills\nby Ajay Chandra (Imperial College
London) as part of Stochastic PDEs and their friends\n\n\nAbstract\nI wil
l result some recent work along with work in progress on the construction
of a stochastic dynamic and a corresponding state space that in principle
should have the Yang Mills Euclidean quantum field theory as its invariant
measure. This is joint work with Ilya Chevyrev\, Martin Hairer\, and Hao
Shen.\n
LOCATION:https://researchseminars.org/talk/SPDEs/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Perkowski (FU Berlin)
DTSTART;VALUE=DATE-TIME:20210602T090000Z
DTEND;VALUE=DATE-TIME:20210602T100000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/8
DESCRIPTION:Title: Ma
rtingale problems for some singular SPDEs\nby Nicolas Perkowski (FU Be
rlin) as part of Stochastic PDEs and their friends\n\n\nAbstract\nMost tec
hniques for solving singular SPDEs\, such as regularity structures\, are b
ased on pathwise calculus. It would be interesting to study singular SPDEs
from a more probabilistic perspective\, for example via the martingale pr
oblem. In general that is a too difficult problem at the moment\, but ther
e are some equations for which we can do this. I will explain the ideas on
the example of the conservative stochastic Burgers equation and indicate
how to extend the results to a larger class of equations that share a simi
lar structure. A novelty of this approach is that it allows to prove (weak
) well-posedness for some scaling critical singular SPDEs. Based on works
with Massimiliano Gubinelli and Lukas Gräfner.\n
LOCATION:https://researchseminars.org/talk/SPDEs/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davar Khoshnevisan (University of Utah)
DTSTART;VALUE=DATE-TIME:20210531T140000Z
DTEND;VALUE=DATE-TIME:20210531T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/9
DESCRIPTION:Title: Ph
ase Analysis of a Family of Stochastic Reaction-Diffusion Equations\nb
y Davar Khoshnevisan (University of Utah) as part of Stochastic PDEs and t
heir friends\n\n\nAbstract\nWe consider a wide family of reaction-diffusio
n equations that are forced with multiplicative space-time white noise\, a
nd show that if the level of the noise is sufficiently high then the resul
ting SPDE has a unique invariant measure. By contrast\, we prove also that
when the level of the noise is sufficiently low\, then there are infinite
ly many invariant measures. In that case\, we prove that the collection of
all invariant measures is a line segment\; that is\, there are two extrem
e points. Time permitting\, we will say a few thing about the two extremal
invariant measures as well in the low-noise case. The phase picture that
is described here was predicted in an earlier work of Zimmerman et al (200
0).\n\nThis is based on joint work with Carl Mueller (University of Roches
ter\, USA)\, Kunwoo Kim (POSTECH\, S Korea)\, and Shang-Yuan Shiu (Nationa
l Central University\, Taiwan).\n
LOCATION:https://researchseminars.org/talk/SPDEs/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Mattingly (Duke)
DTSTART;VALUE=DATE-TIME:20210602T120000Z
DTEND;VALUE=DATE-TIME:20210602T130000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/10
DESCRIPTION:Title: T
he Gaussian Structure of the Stochastically Forced Burgers Equation and re
lated problems\nby Jonathan Mattingly (Duke) as part of Stochastic PDE
s and their friends\n\n\nAbstract\nI will explain some recent results whic
h show that the law of the stochastic burgers equation at a fixed time t i
s absolutely continuous with respect to the natural Gaussian measure on th
e spatial domain. The results will apply to forcing just up to the point w
here the roughness of the forcing corresponds to the classical KPZ equatio
n in the Burgers setting. As one approaches this level of roughness\, the
equations must be understood in as a Singular SPDEs (in the sense of Haire
r ). As such the construction helps illuminate the structure of the equati
on and makes clear in what sense we might call these equations “truly”
elliptic in this infinite dimensional setting. I will also make comments
connecting back to previous results on the 2D Naiver Stokes equation. This
work is joint with Marco Romito and Langxuan Su and builds on work with A
ndrea Watkins Hairston.\n
LOCATION:https://researchseminars.org/talk/SPDEs/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Khanin (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210531T120000Z
DTEND;VALUE=DATE-TIME:20210531T130000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/11
DESCRIPTION:Title: O
n Stationary Solutions to the Stochastic Heat Equation\nby Konstantin
Khanin (University of Toronto) as part of Stochastic PDEs and their friend
s\n\n\nAbstract\nI plan to discuss the problem of uniqueness of global sol
utions to the random Hamilton-Jacobi equation. I will formulate several co
njectures and present results supporting them. Then I will discuss a new u
niqueness result for the Stochastic Heat equation in the regime of weak di
sorder.\n
LOCATION:https://researchseminars.org/talk/SPDEs/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Quastel (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210531T130000Z
DTEND;VALUE=DATE-TIME:20210531T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/12
DESCRIPTION:Title: T
he KPZ fixed point: Part I\nby Jeremy Quastel (University of Toronto)
as part of Stochastic PDEs and their friends\n\n\nAbstract\nThe 1-d KPZ un
iversality class contains random interface growth models as well as random
polymer free energies and driven diffusive systems. Various exact asympto
tic distributions have been computed over the last two decades\, some of t
hem coming from random matrix theory. These are special cases of the stron
g coupling fixed point\, which turns out to be a completely integrable Mar
kov process: its transition probabilities are described by classical integ
rable PDE’s.\n
LOCATION:https://researchseminars.org/talk/SPDEs/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rémi Rhodes (Université Aix-Marseille)
DTSTART;VALUE=DATE-TIME:20210601T070000Z
DTEND;VALUE=DATE-TIME:20210601T080000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/13
DESCRIPTION:Title: G
luing random surfaces: conformal bootstrap in Liouville theory via Segal
’s axioms\nby Rémi Rhodes (Université Aix-Marseille) as part of St
ochastic PDEs and their friends\n\n\nAbstract\nThe law of Markov processes
indexed by time (the real line) take a simple form when expressed in term
s of the action of the associated semigroup. The generalization of this qu
estion to the case when the process is indexed by higher dimensional manif
olds is more intricate and this question is particularly relevant in the s
tudy of quantum field theories. A general proposal was formalized by G. Se
gal in the eighties in this direction. Yet\, concrete examples of QFTs whe
re the Segal axioms are indeed valid are extremely limited (beyond trivial
cases). We treat here the case of a specific Conformal Field Theory (CFT)
\, called the Liouville theory which is a probabilistic model of 2D random
surfaces. The outcome is the validity of the conformal bootstrap\, i.e. a
bridge between probability and representation theory: correlation functio
ns are expressed in terms of (universal) holomorphic functions of the modu
li parameters of the Riemann surface\, called conformal blocks which have
a strong representation theoretical content\, and the structure constants
of the CFT\, here the DOZZ formula. Conformal bootstrap was conjectured in
physics in the eighties to be the universal structure of CFTs and Liouvil
le theory is perhaps the first non trivial example where it can be shown t
o hold mathematically. This talk will be introductory to these topics.\n
LOCATION:https://researchseminars.org/talk/SPDEs/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Remenik (Universidad de Chile)
DTSTART;VALUE=DATE-TIME:20210601T130000Z
DTEND;VALUE=DATE-TIME:20210601T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/14
DESCRIPTION:Title: T
he 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 class\,
is obtained as the scaling limit of the totally asymmetric simple exclusio
n process (TASEP). The main ingredient in the construction is an explicit
formula for the distribution of TASEP in terms of the Fredholm determinant
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://researchseminars.org/talk/SPDEs/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bakhtin (NYU)
DTSTART;VALUE=DATE-TIME:20210601T150000Z
DTEND;VALUE=DATE-TIME:20210601T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/15
DESCRIPTION:Title: D
ynamic polymers: invariant measures and ordering by noise\nby Yuri Bak
htin (NYU) as part of Stochastic PDEs and their friends\n\n\nAbstract\nGib
bs measures describing directed polymers in random potential are tightly r
elated to the stochastic Burgers/KPZ/heat equations. One of the basic ques
tions is: do the local interactions of the polymer chain with the random e
nvironment and with itself define the macroscopic state uniquely for these
models? We establish and explore the connection of this problem with ergo
dic properties of an infinite-dimensional stochastic gradient flow. Joint
work with Hong-Bin Chen and Liying Li.\n
LOCATION:https://researchseminars.org/talk/SPDEs/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Mytnik (Technion)
DTSTART;VALUE=DATE-TIME:20210602T070000Z
DTEND;VALUE=DATE-TIME:20210602T080000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/16
DESCRIPTION:Title: O
n the speed of a front for stochastic reaction-diffusion equations with no
n-Lipschitz drift\nby Leonid Mytnik (Technion) as part of Stochastic P
DEs and their friends\n\n\nAbstract\nWe study the asymptotic speed of a ra
ndom front for solutions to stochastic reaction-diffusion equations with n
on-Lipschitz drift and Wright-Fisher noise proportional to $\\sigma$. Unde
r 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://researchseminars.org/talk/SPDEs/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armen Shirikyan (Cergy Paris Université)
DTSTART;VALUE=DATE-TIME:20210531T070000Z
DTEND;VALUE=DATE-TIME:20210531T080000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/17
DESCRIPTION:Title: M
ixing for PDEs with degenerate noise: an overview and open problems\nb
y Armen Shirikyan (Cergy Paris Université) as part of Stochastic PDEs and
their friends\n\n\nAbstract\nWe discuss some results about uniqueness and
stability of a stationary measure for randomly forced PDEs arising in flu
id dynamics. Two different scenarios expressed in terms of controllability
properties of the associated deterministic problem will be presented. 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://researchseminars.org/talk/SPDEs/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Cerrai (University of Maryland)
DTSTART;VALUE=DATE-TIME:20210602T130000Z
DTEND;VALUE=DATE-TIME:20210602T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T185825Z
UID:SPDEs/18
DESCRIPTION:Title: O
n the small mass limit for infinite-dimensional systems with state-depende
nt damping\nby Sandra Cerrai (University of Maryland) as part of Stoch
astic PDEs and their friends\n\n\nAbstract\nI will present a series of res
ults on the asymptotic behavior\, with respect to the small mass\, of infi
nite-dimensional stochastic systems described by a damped waves equation p
erturbed by a Gaussian noise. I will consider in particular the case when
the friction coefficient depends on the position of the particles and I wi
ll show how things change drastically\, compared to what happens in the ca
se of constant friction.\n
LOCATION:https://researchseminars.org/talk/SPDEs/18/
END:VEVENT
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