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:20260404T094504Z UID:YRbGSA/1 DESCRIPTION:Title: Construction of Flows through the Non-Linear Sewing Lemma I\nby Antoine Lejay (Nancy) as part of Young Researchers between Geometry and St ochastic Analysis 2021\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jürgen Angst (Rennes) DTSTART:20210616T084500Z DTEND:20210616T093000Z DTSTAMP:20260404T094504Z UID:YRbGSA/2 DESCRIPTION:Title: On the nodal volume associated with random linear combinations of La place eigenfunctions\nby Jürgen Angst (Rennes) as part of Young Resea rchers between Geometry and Stochastic Analysis 2021\n\n\nAbstract\nWe wil l study the high energy asymptotic behavior of the nodal volume associated with random linear combinations of Laplace eigenfunctions in various geom etric contexts. In particular\, we will show the almost sure and expected asymptotics are in some way universal\, i.e. they do not depend on the bas e manifold\, nor on the particular choice of random coefficients. The talk will be based on joined works with G. Poly and L. Gass.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Juillet (Strasbourg) DTSTART:20210616T093000Z DTEND:20210616T101500Z DTSTAMP:20260404T094504Z UID:YRbGSA/3 DESCRIPTION:Title: Metric hexachordal theorems on probability spaces\nby Nicolas Ju illet (Strasbourg) as part of Young Researchers between Geometry and Stoch astic Analysis 2021\n\n\nAbstract\nWe present probabilistic and geometric extensions to Babbit's hexachordal theorem. This result coming from the ma thematical theory of Music is initially a combinatorical observation that concerns the groups of six notes in $\\mathbb{Z}/12\\mathbb{Z}$. Joint wor k with Moreno Andreata and Corentin Guichaoua.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Xue-Mei Li (Imperial) DTSTART:20210616T120000Z DTEND:20210616T133000Z DTSTAMP:20260404T094504Z UID:YRbGSA/5 DESCRIPTION:Title: Second order Sub-elliptic operators and its intrinsic geometry\n by Xue-Mei Li (Imperial) as part of Young Researchers between Geometry and Stochastic Analysis 2021\n\n\nAbstract\nI shall discuss the intrinsic ge ometry of a family of vector fields with constant rank\,\nand its applicat ion in understanding sub-elliptic diffusions. I intend to follow closely t he book of `On the geometry of diffusion operators and stochastic flows'.\ n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Klas Modin (Chalmers) DTSTART:20210617T070000Z DTEND:20210617T083000Z DTSTAMP:20260404T094504Z UID:YRbGSA/6 DESCRIPTION:Title: Introduction to geometric hydrodynamics I\nby Klas Modin (Chalme rs) as part of Young Researchers between Geometry and Stochastic Analysis 2021\n\n\nAbstract\nThe aim of the lectures is to explain Arnold’s disco very from 1966 that solutions to Euler’s equations for the motion of an incompressible fluid correspond to geodesics on the infinite-dimensional R iemannian manifold of volume preserving diffeomorphisms. In many ways\, th is discovery is the foundation for the field of geometric hydrodynamics\, which today encompasses much more than just Euler’s equations\, with dee p connections to many other fields such as optimal transport\, shape analy sis\, and information theory.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Djurdjevac (FU Berlin) DTSTART:20210617T084500Z DTEND:20210617T093000Z DTSTAMP:20260404T094504Z UID:YRbGSA/7 DESCRIPTION:Title: Representation of Gaussian random fields on spheres\nby Ana Djur djevac (FU Berlin) as part of Young Researchers between Geometry and Stoch astic Analysis 2021\n\n\nAbstract\nMotivated by biological application\, s uch as cell-biology\, partial differential equations on curved (moving) do mains have become a flourishing mathematical field. Moreover\, including u ncertainty into these models is natural due to the lack of precise initial data or 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 t his presentation we will first give a brief insight into different possibi lities of representing isotropic Gaussian random fields defined on a flat domain and their importance. In particular\, we will recall the standard K arhunen-Loeve expansions. Next\, we will consider Gaussian random fields o n a sphere. The main goal of the talk will be to present the construction of a multilevel expansions of isotropic Gaussian random fields on a sphere with independent Gaussian coefficients and localized basis functions (mod ified spherical needlets). In the last part we show numerical illustration s and an application to random elliptic\n\nPDEs on a sphere. This is a joi nt work with Markus Bachmayr.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Avi Mayorcas (Oxford) DTSTART:20210617T093000Z DTEND:20210617T101500Z DTSTAMP:20260404T094504Z UID:YRbGSA/8 DESCRIPTION:Title: Distribution dependent SDEs driven by additive continuous and fracti onal Brownian noise\nby Avi Mayorcas (Oxford) as part of Young Researc hers between Geometry and Stochastic Analysis 2021\n\n\nAbstract\nDistribu tion dependent SDEs (or McKean—Vlasov equations) are important from both the point of view of mathematical analysis and applications\; in the case of Brownian noise they are closely related to nonlinear parabolic PDEs.\n \nIn this 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 —Vlasov equations driven by either additive continuous or fractional Bro wnian noise. In the former case we extend some of the recent results by Co ghi\, Deuschel\, Friz & Maurelli to non-Lipschitz drifts\, establishing se parate criteria for existence and uniqueness and providing a small extensi on of known propagation of chaos results. However\, since our results in t his case also apply for zero noise they do cannot make use of any regulari sation effects\; in contrast\, for McKean—Vlasov equations driven by fBm we extend the results of Catellier & Gubinelli for SDEs driven by fBm to the distribution dependent setting. We are able to treat McKean—Vlasov e quations with singular drifts provided the dynamics are driven by an addit ive fBm of suitably low Hurst parameter.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Antoine Lejay (Nancy) DTSTART:20210617T111500Z DTEND:20210617T120000Z DTSTAMP:20260404T094504Z UID:YRbGSA/9 DESCRIPTION:Title: Construction of Flows through the Non-Linear Sewing Lemma II\nby Antoine Lejay (Nancy) as part of Young Researchers between Geometry and S tochastic Analysis 2021\n\n\nAbstract\nThe theory of rough paths is now a vivid field of research at the intersection of many domains such as analys is (stochastic and classical)\, algebra\, geometry\, data science and so o n. Its first objective was to construct integrals and differential equatio ns driven by irregular signal\, before expanding in many directions.\n\nTh e various interpretations of this theory all rely on variants of the so-ca lled sewing lemma. In this talk\, we consider how to construct directly fl ows from numerical schemes using a "non-linear sewing lemma”\, and prese nt some of the main properties that can be reached. We put them in paralle l with some results in the theory of ordinary differential equations and s how how they are expanded.\n\nA second part will be devoted to the relatio nship between such flows and other objects already existing in the theory of rough paths.\n\nFrom a joint work with A. Brault.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Annika Lang (Gothenburg) DTSTART:20210617T120000Z DTEND:20210617T124500Z DTSTAMP:20260404T094504Z UID:YRbGSA/10 DESCRIPTION:Title: Connecting random fields on manifolds and stochastic partial differ ential equations in simulations\nby Annika Lang (Gothenburg) as part o f Young Researchers between Geometry and Stochastic Analysis 2021\n\n\nAbs tract\nRandom fields on manifolds can be used as building blocks for solut ions to stochastic partial differential equations or they can be described by stochastic partial differential equations. In this talk I present rece nt developments in numerical approximations of random fields and solutions to stochastic partial differential equations on manifolds and connect the two. More specifically\, we look at the stochastic wave equation on the s phere and approximations of Gaussian random fields on manifolds using suit able finite element methods. Throughout the talk\, theory and convergence analysis are combined with numerical examples and simulations.\n\nThis tal k is based on joint work with David Cohen\, Erik Jansson\, Mihály Kovács \, and Mike Pereira\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Karen Habermann (Warwick) DTSTART:20210617T130000Z DTEND:20210617T134500Z DTSTAMP:20260404T094504Z UID:YRbGSA/11 DESCRIPTION:Title: Stochastic processes on surfaces in three-dimensional contact sub-R iemannian manifolds\nby Karen Habermann (Warwick) as part of Young Res earchers between Geometry and Stochastic Analysis 2021\n\n\nAbstract\nWe a re concerned with stochastic processes on surfaces in three-dimensional co ntact sub-Riemannian manifolds. By considering the Riemannian approximatio ns to the sub-Riemannian manifold which make use of the Reeb vector field\ , we obtain a second order partial differential operator on the surface ar ising as the limit of Laplace-Beltrami operators. The stochastic process a ssociated with the limiting operator moves along the characteristic foliat ion induced on the surface by the contact distribution. We show that for t his stochastic process elliptic characteristic points are inaccessible\, w hile hyperbolic characteristic points are accessible from the separatrices . We illustrate the results with examples and we identify canonical surfac es in the Heisenberg group\, and in $\\mathsf{SU}(2)$ and $\\mathsf{SL}(2\ ,\\mathbb{R})$ equipped with the standard sub-Riemannian contact structure s as model cases for this setting. This is joint work with Davide Barilari \, Ugo Boscain and Daniele Cannarsa.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Sommer (Copenhagen) DTSTART:20210617T134500Z DTEND:20210617T143000Z DTSTAMP:20260404T094504Z UID:YRbGSA/12 DESCRIPTION:Title: Sub-Riemannian geometry in probabilistic geometric statistics\n by Stefan Sommer (Copenhagen) as part of Young Researchers between Geometr y and Stochastic Analysis 2021\n\n\nAbstract\nGeometric statistics\, the s tatistical analysis of manifold and Lie group valued data\, can be approac hed from a probabilistic viewpoint where families of parametric probabilit y distributions are fitted to data.\n\nThis likelihood-based approach give s one way to generalize Euclidean statistical procedures to the non-linear manifold context. Stochastic processes here play an important role in pro viding geometrically natural ways of defining probability distributions. I n the talk\, I will discuss such constructions and how they lead to new ge ometric evolution equations for the most probable paths to observed data. In particular\, we will see how such paths for an anisotropically scaled B rownian motion arise as geodesics of a sub-Riemannian metric on the frame bundle of the manifold.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Xue-Mei Li (Imperial) DTSTART:20210618T070000Z DTEND:20210618T074500Z DTSTAMP:20260404T094504Z UID:YRbGSA/13 DESCRIPTION:Title: Second order Sub-elliptic operators and its intrinsic geometry: Rec ent Progress and problems\nby Xue-Mei Li (Imperial) as part of Young R esearchers between Geometry and Stochastic Analysis 2021\n\n\nAbstract\nI will discuss some recent progress and problems with diffusion models.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Klas Modin (Chalmers) DTSTART:20210618T074500Z DTEND:20210618T083000Z DTSTAMP:20260404T094504Z UID:YRbGSA/14 DESCRIPTION:Title: Introduction to geometric hydrodynamics II\nby Klas Modin (Chal mers) as part of Young Researchers between Geometry and Stochastic Analysi s 2021\n\n\nAbstract\nThe aim of the lectures is to explain Arnold’s dis covery from 1966 that solutions to Euler’s equations for the motion of a n incompressible fluid correspond to geodesics on the infinite-dimensional Riemannian manifold of volume preserving diffeomorphisms. In many ways\, this discovery is the foundation for the field of geometric hydrodynamics\ , which today encompasses much more than just Euler’s equations\, with d eep connections to many other fields such as optimal transport\, shape ana lysis\, and information theory.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Lerario (Trieste) DTSTART:20210618T084500Z DTEND:20210618T093000Z DTSTAMP:20260404T094504Z UID:YRbGSA/15 DESCRIPTION:Title: What is... Random Algebraic Geometry?\nby Antonio Lerario (Trie ste) 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 Real Algebraic Geometry\, which introduces ideas from Probability for approaching classical problems. The main idea of this approach is the shif t from the notion of "generic"\, from classical Algebraic Geometry\, to th e notion of "random". This change of perspective brings many interesting s ubjects into the picture: convex geometry\, measure theory\, representatio n theory\, asymptotic analysis...\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Hans Z. Munthe-Kaas (Bergen) DTSTART:20210618T093000Z DTEND:20210618T101500Z DTSTAMP:20260404T094504Z UID:YRbGSA/16 DESCRIPTION:Title: Canonical Integration on Symmetric Spaces\nby Hans Z. Munthe-Ka as (Bergen) as part of Young Researchers between Geometry and Stochastic A nalysis 2021\n\n\nAbstract\nSymmetric spaces are fundamental in differenti al geometry and harmonic analysis. Examples n-spheres and Grassmann manifo lds\, the space of positive definite symmetric matrices\, Lie groups with a symmetric product\, and elliptic and hyperbolic spaces with constant sec tional curvatures.\n\nSymmetric spaces are characterised by having an isom etric symmetry in each point\, giving rise to a symmetric product structur e on the manifold. \n\nWe give an introduction to symmetric products and L ie triple systems\, which describe their tangent spaces. \n\nA new geometr ic numerical integration algorithm for differential equations evolving on symmetric spaces is discussed. The integrator is constructed from canonica l operations on the symmetric space\, its Lie triple system (LTS)\, and th e exponential from the LTS to the symmetric space.\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/16/ END:VEVENT BEGIN:VEVENT SUMMARY:PhD Session (Prize for best talk) DTSTART:20210618T120000Z DTEND:20210618T140000Z DTSTAMP:20260404T094504Z UID:YRbGSA/18 DESCRIPTION:Title: Talks by M. Ghani \, E. Jansson\, H. Kremp\, S. Kuzgun\, M. Mertin\ , X. Zhao\nby PhD Session (Prize for best talk) as part of Young Rese archers between Geometry and Stochastic Analysis 2021\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/18/ END:VEVENT BEGIN:VEVENT SUMMARY:James Michael Leahy (Imperial) DTSTART:20210616T134500Z DTEND:20210616T143000Z DTSTAMP:20260404T094504Z UID:YRbGSA/19 DESCRIPTION:Title: The incompressible Euler system with rough path advection\nby J ames Michael Leahy (Imperial) as part of Young Researchers between Geometr y and Stochastic Analysis 2021\n\n\nAbstract\nThe incompressible Euler’s equations are a mathematical model of an incompressible inviscid fluid. W e will discuss some aspects of a perturbation of the Euler system by a rou gh-in-time\, divergence-free\, Lie-advecting vector field. We are inspired by the problem of parametrizing unmodelled phenomena and representing sou rces of uncertainty in mathematical fluid dynamics. We will begin by prese nting a geometric fluid dynamics inspired variational principle for the eq uations and the corresponding Kelvin balance law. Then we will give suffic ient conditions on the data to obtain i) local well-posedness of the syste m in any 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 vortici ty. The $L^p$-norms of the vorticity are conserved in two dimensions\, whi ch yields global well-posedness and a Wong-Zakai approximation theorem for the stochastic version of the equation in two dimensions. \n\nThis talk i s based on joint work with Dan Crisan\, Darryl Holm and Torstein Nilssen.\ n LOCATION:https://stable.researchseminars.org/talk/YRbGSA/19/ END:VEVENT END:VCALENDAR