BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Antoine Lejay (Nancy)
DTSTART;VALUE=DATE-TIME:20210616T070000Z
DTEND;VALUE=DATE-TIME:20210616T083000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/1
DESCRIPTION:Title: C
onstruction of Flows through the Non-Linear Sewing Lemma I\nby Antoine
Lejay (Nancy) as part of Young Researchers between Geometry and Stochasti
c Analysis 2021\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/YRbGSA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jürgen Angst (Rennes)
DTSTART;VALUE=DATE-TIME:20210616T084500Z
DTEND;VALUE=DATE-TIME:20210616T093000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/2
DESCRIPTION:Title: O
n the nodal volume associated with random linear combinations of Laplace e
igenfunctions\nby Jürgen Angst (Rennes) as part of Young Researchers
between Geometry and Stochastic Analysis 2021\n\n\nAbstract\nWe will study
the high energy asymptotic behavior of the nodal volume associated with r
andom linear combinations of Laplace eigenfunctions in various geometric c
ontexts. In particular\, we will show the almost sure and expected asympto
tics are in some way universal\, i.e. they do not depend on the base manif
old\, nor on the particular choice of random coefficients. The talk will b
e based on joined works with G. Poly and L. Gass.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Juillet (Strasbourg)
DTSTART;VALUE=DATE-TIME:20210616T093000Z
DTEND;VALUE=DATE-TIME:20210616T101500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/3
DESCRIPTION:Title: M
etric hexachordal theorems on probability spaces\nby Nicolas Juillet (
Strasbourg) as part of Young Researchers between Geometry and Stochastic A
nalysis 2021\n\n\nAbstract\nWe present probabilistic and geometric extensi
ons to Babbit's hexachordal theorem. This result coming from the mathemati
cal theory of Music is initially a combinatorical observation that concern
s the groups of six notes in $\\mathbb{Z}/12\\mathbb{Z}$. Joint work with
Moreno Andreata and Corentin Guichaoua.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xue-Mei Li (Imperial)
DTSTART;VALUE=DATE-TIME:20210616T120000Z
DTEND;VALUE=DATE-TIME:20210616T133000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/5
DESCRIPTION:Title: S
econd order Sub-elliptic operators and its intrinsic geometry\nby Xue-
Mei Li (Imperial) as part of Young Researchers between Geometry and Stocha
stic Analysis 2021\n\n\nAbstract\nI shall discuss the intrinsic geometry
of a family of vector fields with constant rank\,\nand its application in
understanding sub-elliptic diffusions. I intend to follow closely the book
of `On the geometry of diffusion operators and stochastic flows'.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klas Modin (Chalmers)
DTSTART;VALUE=DATE-TIME:20210617T070000Z
DTEND;VALUE=DATE-TIME:20210617T083000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/6
DESCRIPTION:Title: I
ntroduction to geometric hydrodynamics I\nby Klas Modin (Chalmers) as
part of Young Researchers between Geometry and Stochastic Analysis 2021\n\
n\nAbstract\nThe aim of the lectures is to explain Arnold’s discovery fr
om 1966 that solutions to Euler’s equations for the motion of an incompr
essible fluid correspond to geodesics on the infinite-dimensional Riemanni
an manifold of volume preserving diffeomorphisms. In many ways\, this disc
overy is the foundation for the field of geometric hydrodynamics\, which t
oday encompasses much more than just Euler’s equations\, with deep conne
ctions to many other fields such as optimal transport\, shape analysis\, a
nd information theory.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Djurdjevac (FU Berlin)
DTSTART;VALUE=DATE-TIME:20210617T084500Z
DTEND;VALUE=DATE-TIME:20210617T093000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/7
DESCRIPTION:Title: R
epresentation of Gaussian random fields on spheres\nby Ana Djurdjevac
(FU Berlin) as part of Young Researchers between Geometry and Stochastic A
nalysis 2021\n\n\nAbstract\nMotivated by biological application\, such as
cell-biology\, partial differential equations on curved (moving) domains h
ave become a flourishing mathematical field. Moreover\, including uncertai
nty into these models is natural due to the lack of precise initial data o
r randomness of the processes itself. One of the basic questions in these
models is how to represent random field on a curved domain?\n\nIn this pre
sentation we will first give a brief insight into different possibilities
of representing isotropic Gaussian random fields defined on a flat domain
and their importance. In particular\, we will recall the standard Karhunen
-Loeve expansions. Next\, we will consider Gaussian random fields on a sph
ere. The main goal of the talk will be to present the construction of a mu
ltilevel expansions of isotropic Gaussian random fields on a sphere with i
ndependent Gaussian coefficients and localized basis functions (modified s
pherical needlets). In the last part we show numerical illustrations and a
n application to random elliptic\n\nPDEs on a sphere. This is a joint work
with Markus Bachmayr.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Avi Mayorcas (Oxford)
DTSTART;VALUE=DATE-TIME:20210617T093000Z
DTEND;VALUE=DATE-TIME:20210617T101500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/8
DESCRIPTION:Title: D
istribution dependent SDEs driven by additive continuous and fractional Br
ownian noise\nby Avi Mayorcas (Oxford) as part of Young Researchers be
tween Geometry and Stochastic Analysis 2021\n\n\nAbstract\nDistribution de
pendent SDEs (or McKean—Vlasov equations) are important from both the po
int of view of mathematical analysis and applications\; in the case of Bro
wnian noise they are closely related to nonlinear parabolic PDEs.\n\nIn th
is talk I will present some recent joint work with L. Galeati & F. Harang\
, in which we prove a variety of well-posedness results for McKean—Vlaso
v equations driven by either additive continuous or fractional Brownian no
ise. In the former case we extend some of the recent results by Coghi\, De
uschel\, Friz & Maurelli to non-Lipschitz drifts\, establishing separate c
riteria for existence and uniqueness and providing a small extension of kn
own propagation of chaos results. However\, since our results in this case
also apply for zero noise they do cannot make use of any regularisation e
ffects\; in contrast\, for McKean—Vlasov equations driven by fBm we exte
nd the results of Catellier & Gubinelli for SDEs driven by fBm to the dist
ribution dependent setting. We are able to treat McKean—Vlasov equations
with singular drifts provided the dynamics are driven by an additive fBm
of suitably low Hurst parameter.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Lejay (Nancy)
DTSTART;VALUE=DATE-TIME:20210617T111500Z
DTEND;VALUE=DATE-TIME:20210617T120000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/9
DESCRIPTION:Title: C
onstruction of Flows through the Non-Linear Sewing Lemma II\nby Antoin
e Lejay (Nancy) as part of Young Researchers between Geometry and Stochast
ic Analysis 2021\n\n\nAbstract\nThe theory of rough paths is now a vivid f
ield of research at the intersection of many domains such as analysis (sto
chastic and classical)\, algebra\, geometry\, data science and so on. Its
first objective was to construct integrals and differential equations driv
en by irregular signal\, before expanding in many directions.\n\nThe vario
us interpretations of this theory all rely on variants of the so-called se
wing lemma. In this talk\, we consider how to construct directly flows fro
m numerical schemes using a "non-linear sewing lemma”\, and present some
of the main properties that can be reached. We put them in parallel with
some results in the theory of ordinary differential equations and show how
they are expanded.\n\nA second part will be devoted to the relationship b
etween such flows and other objects already existing in the theory of roug
h paths.\n\nFrom a joint work with A. Brault.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annika Lang (Gothenburg)
DTSTART;VALUE=DATE-TIME:20210617T120000Z
DTEND;VALUE=DATE-TIME:20210617T124500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/10
DESCRIPTION:Title:
Connecting random fields on manifolds and stochastic partial differential
equations in simulations\nby Annika Lang (Gothenburg) as part of Young
Researchers between Geometry and Stochastic Analysis 2021\n\n\nAbstract\n
Random fields on manifolds can be used as building blocks for solutions to
stochastic partial differential equations or they can be described by sto
chastic partial differential equations. In this talk I present recent deve
lopments in numerical approximations of random fields and solutions to sto
chastic partial differential equations on manifolds and connect the two. M
ore specifically\, we look at the stochastic wave equation on the sphere a
nd approximations of Gaussian random fields on manifolds using suitable fi
nite element methods. Throughout the talk\, theory and convergence analysi
s are combined with numerical examples and simulations.\n\nThis talk is ba
sed on joint work with David Cohen\, Erik Jansson\, Mihály Kovács\, and
Mike Pereira\n
LOCATION:https://researchseminars.org/talk/YRbGSA/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Habermann (Warwick)
DTSTART;VALUE=DATE-TIME:20210617T130000Z
DTEND;VALUE=DATE-TIME:20210617T134500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/11
DESCRIPTION:Title:
Stochastic processes on surfaces in three-dimensional contact sub-Riemanni
an manifolds\nby Karen Habermann (Warwick) as part of Young Researcher
s between Geometry and Stochastic Analysis 2021\n\n\nAbstract\nWe are conc
erned with stochastic processes on surfaces in three-dimensional contact s
ub-Riemannian manifolds. By considering the Riemannian approximations to t
he sub-Riemannian manifold which make use of the Reeb vector field\, we ob
tain a second order partial differential operator on the surface arising a
s the limit of Laplace-Beltrami operators. The stochastic process associat
ed with the limiting operator moves along the characteristic foliation ind
uced on the surface by the contact distribution. We show that for this sto
chastic process elliptic characteristic points are inaccessible\, while hy
perbolic characteristic points are accessible from the separatrices. We il
lustrate the results with examples and we identify canonical surfaces in t
he Heisenberg group\, and in $\\mathsf{SU}(2)$ and $\\mathsf{SL}(2\,\\math
bb{R})$ equipped with the standard sub-Riemannian contact structures as mo
del cases for this setting. This is joint work with Davide Barilari\, Ugo
Boscain and Daniele Cannarsa.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Sommer (Copenhagen)
DTSTART;VALUE=DATE-TIME:20210617T134500Z
DTEND;VALUE=DATE-TIME:20210617T143000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/12
DESCRIPTION:Title:
Sub-Riemannian geometry in probabilistic geometric statistics\nby Stef
an Sommer (Copenhagen) as part of Young Researchers between Geometry and S
tochastic Analysis 2021\n\n\nAbstract\nGeometric statistics\, the statisti
cal analysis of manifold and Lie group valued data\, can be approached fro
m a probabilistic viewpoint where families of parametric probability distr
ibutions are fitted to data.\n\nThis likelihood-based approach gives one w
ay to generalize Euclidean statistical procedures to the non-linear manifo
ld context. Stochastic processes here play an important role in providing
geometrically natural ways of defining probability distributions. In the t
alk\, I will discuss such constructions and how they lead to new geometric
evolution equations for the most probable paths to observed data. In part
icular\, we will see how such paths for an anisotropically scaled Brownian
motion arise as geodesics of a sub-Riemannian metric on the frame bundle
of the manifold.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xue-Mei Li (Imperial)
DTSTART;VALUE=DATE-TIME:20210618T070000Z
DTEND;VALUE=DATE-TIME:20210618T074500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/13
DESCRIPTION:Title:
Second order Sub-elliptic operators and its intrinsic geometry: Recent Pro
gress and problems\nby Xue-Mei Li (Imperial) as part of Young Research
ers between Geometry and Stochastic Analysis 2021\n\n\nAbstract\nI will di
scuss some recent progress and problems with diffusion models.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klas Modin (Chalmers)
DTSTART;VALUE=DATE-TIME:20210618T074500Z
DTEND;VALUE=DATE-TIME:20210618T083000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/14
DESCRIPTION:Title:
Introduction to geometric hydrodynamics II\nby Klas Modin (Chalmers) a
s part of Young Researchers between Geometry and Stochastic Analysis 2021\
n\n\nAbstract\nThe aim of the lectures is to explain Arnold’s discovery
from 1966 that solutions to Euler’s equations for the motion of an incom
pressible fluid correspond to geodesics on the infinite-dimensional Rieman
nian manifold of volume preserving diffeomorphisms. In many ways\, this di
scovery is the foundation for the field of geometric hydrodynamics\, which
today encompasses much more than just Euler’s equations\, with deep con
nections to many other fields such as optimal transport\, shape analysis\,
and information theory.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Lerario (Trieste)
DTSTART;VALUE=DATE-TIME:20210618T084500Z
DTEND;VALUE=DATE-TIME:20210618T093000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/15
DESCRIPTION:Title:
What is... Random Algebraic Geometry?\nby Antonio Lerario (Trieste) as
part of Young Researchers between Geometry and Stochastic Analysis 2021\n
\n\nAbstract\nIn this seminar I will discuss a modern point of view on Rea
l Algebraic Geometry\, which introduces ideas from Probability for approac
hing classical problems. The main idea of this approach is the shift from
the notion of "generic"\, from classical Algebraic Geometry\, to the notio
n of "random". This change of perspective brings many interesting subjects
into the picture: convex geometry\, measure theory\, representation theor
y\, asymptotic analysis...\n
LOCATION:https://researchseminars.org/talk/YRbGSA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Z. Munthe-Kaas (Bergen)
DTSTART;VALUE=DATE-TIME:20210618T093000Z
DTEND;VALUE=DATE-TIME:20210618T101500Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/16
DESCRIPTION:Title:
Canonical Integration on Symmetric Spaces\nby Hans Z. Munthe-Kaas (Ber
gen) as part of Young Researchers between Geometry and Stochastic Analysis
2021\n\n\nAbstract\nSymmetric spaces are fundamental in differential geom
etry and harmonic analysis. Examples n-spheres and Grassmann manifolds\, t
he space of positive definite symmetric matrices\, Lie groups with a symme
tric product\, and elliptic and hyperbolic spaces with constant sectional
curvatures.\n\nSymmetric spaces are characterised by having an isometric s
ymmetry in each point\, giving rise to a symmetric product structure on th
e manifold. \n\nWe give an introduction to symmetric products and Lie trip
le systems\, which describe their tangent spaces. \n\nA new geometric nume
rical integration algorithm for differential equations evolving on symmetr
ic spaces is discussed. The integrator is constructed from canonical opera
tions on the symmetric space\, its Lie triple system (LTS)\, and the expon
ential from the LTS to the symmetric space.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:PhD Session (Prize for best talk)
DTSTART;VALUE=DATE-TIME:20210618T120000Z
DTEND;VALUE=DATE-TIME:20210618T140000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/18
DESCRIPTION:Title:
Talks by M. Ghani \, E. Jansson\, H. Kremp\, S. Kuzgun\, M. Mertin\, X. Z
hao\nby PhD Session (Prize for best talk) as part of Young Researchers
between Geometry and Stochastic Analysis 2021\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/YRbGSA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Michael Leahy (Imperial)
DTSTART;VALUE=DATE-TIME:20210616T134500Z
DTEND;VALUE=DATE-TIME:20210616T143000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115343Z
UID:YRbGSA/19
DESCRIPTION:Title:
The incompressible Euler system with rough path advection\nby James Mi
chael Leahy (Imperial) as part of Young Researchers between Geometry and S
tochastic Analysis 2021\n\n\nAbstract\nThe incompressible Euler’s equati
ons are a mathematical model of an incompressible inviscid fluid. We will
discuss some aspects of a perturbation of the Euler system by a rough-in-t
ime\, divergence-free\, Lie-advecting vector field. We are inspired by the
problem of parametrizing unmodelled phenomena and representing sources of
uncertainty in mathematical fluid dynamics. We will begin by presenting a
geometric fluid dynamics inspired variational principle for the equations
and the corresponding Kelvin balance law. Then we will give sufficient co
nditions on the data to obtain i) local well-posedness of the system in an
y dimension in $L^2$-Sobolev spaces and ii) a Beale-Kato-Majda (BKM) blow-
up criterion in terms of the $L_t^1L^\\infty_x$-norm of the vorticity. The
$L^p$-norms of the vorticity are conserved in two dimensions\, which yiel
ds global well-posedness and a Wong-Zakai approximation theorem for the st
ochastic version of the equation in two dimensions. \n\nThis talk is based
on joint work with Dan Crisan\, Darryl Holm and Torstein Nilssen.\n
LOCATION:https://researchseminars.org/talk/YRbGSA/19/
END:VEVENT
END:VCALENDAR