BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Antoine Lejay (Nancy) DTSTART:20210616T070000Z DTEND:20210616T083000Z DTSTAMP:20260422T212929Z 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:20210616T084500Z DTEND:20210616T093000Z DTSTAMP:20260422T212929Z 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:20210616T093000Z DTEND:20210616T101500Z DTSTAMP:20260422T212929Z 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:20210616T120000Z DTEND:20210616T133000Z DTSTAMP:20260422T212929Z 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:20210617T070000Z DTEND:20210617T083000Z DTSTAMP:20260422T212929Z 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:20210617T084500Z DTEND:20210617T093000Z DTSTAMP:20260422T212929Z 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:20210617T093000Z DTEND:20210617T101500Z DTSTAMP:20260422T212929Z 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:20210617T111500Z DTEND:20210617T120000Z DTSTAMP:20260422T212929Z 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:20210617T120000Z DTEND:20210617T124500Z DTSTAMP:20260422T212929Z 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:20210617T130000Z DTEND:20210617T134500Z DTSTAMP:20260422T212929Z 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:20210617T134500Z DTEND:20210617T143000Z DTSTAMP:20260422T212929Z 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:20210618T070000Z DTEND:20210618T074500Z DTSTAMP:20260422T212929Z 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:20210618T074500Z DTEND:20210618T083000Z DTSTAMP:20260422T212929Z 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:20210618T084500Z DTEND:20210618T093000Z DTSTAMP:20260422T212929Z 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:20210618T093000Z DTEND:20210618T101500Z DTSTAMP:20260422T212929Z 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:20210618T120000Z DTEND:20210618T140000Z DTSTAMP:20260422T212929Z 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:20210616T134500Z DTEND:20210616T143000Z DTSTAMP:20260422T212929Z 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