BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Peter Hydon (University of Kent) DTSTART:20211122T160000Z DTEND:20211122T164500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/1 DESCRIPTION:Title: Moving frames for partial difference equations\nby Peter H ydon (University of Kent) as part of BIRS workshop:Moving Frames and their Modern Applications\n\n\nAbstract\nThis talk describes difference moving frames\, which are discrete moving frames that incorporate the natural pro longation structure generated by the group of translations on $\\mathbb{Z} ^N$. They can be modified to cope with finite domains. Difference moving f rames produce group-invariant reductions of partial difference equations. In particular\, they yield invariant formulations of Euler-Lagrange differ ence equations and an equivariant version of Noether's Theorem. We discuss these\, with application to a Toda-type system that stems from the cross- ratio and discrete potential KdV equations.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Hans Munthe-Kaas (University of Bergen Norway) DTSTART:20211122T164500Z DTEND:20211122T173000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/2 DESCRIPTION:Title: Connection Algebras\nby Hans Munthe-Kaas (University of Be rgen Norway) as part of BIRS workshop:Moving Frames and their Modern Appli cations\n\n\nAbstract\nAn affine connection defines a product on the vecto r fields of a manifold\, and more generally on sections of a vector bundle . We study algebras defined by connections. The structure and combinatori cs of the algebra is important for understanding series developments of fl ows on the manifold. \n\nInvariant connections\, where the geometric pictu re was developed by Nomizu 1954\, are interesting also on the algebraic si de. In particular euclidean geometries yield flat and torsion free connect ions which give rise to pre-Lie algebras\, which is the foundation of Butc her-seres\, Branched Rough Path Theory and the Connes-Kreimer Hopf algebra . Lie groups and Klein geometries have natural flat connections with paral lel torsion which yield post-Lie algebras\, Lie-Butcher series\, the MKW H opf algebra and Planarly Branched Rough Paths. Symmetric spaces have torsi on free connections with parallel curvature. We call the algebras Lie-Admi ssible-Triple-Algebras\, but these are not properly understood yet\, and a rough path theory has not yet been developed in this case. \n\nRecent wor k in progress show that post-Lie algebras play a crucial role in the under standing of more general connections\, in particular the Levi—Civita con nection on a general Riemannian manifold. \n\nThe talk will give an overvi ew of the area\, as well as going into the most recent results. I would li ke to spark discussions on relations between \nConnection Algebras and Mov ing Frames.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Ruddy (University of San Francisco) DTSTART:20211122T180000Z DTEND:20211122T184500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/3 DESCRIPTION:Title: The moving frame method for iterated integrals: orthogonal inv ariants\nby Michael Ruddy (University of San Francisco) as part of BIR S workshop:Moving Frames and their Modern Applications\n\n\nAbstract\nCurv es in Euclidean space enjoy a natural action of the orthogonal group on it s ambient space. We apply the Fels-Olver moving frame method paired with t he log-signature transform to construct a set of integral invariants for c urves in $\\mathbb{R}^d$ under rigid motions and to compare curves up to r igid motions (and tree-like extensions). In particular we show that one ca n construct a set of invariants that characterize the equivalence class of the truncated iterated-integrals signature under orthogonal transformatio ns.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Gloria Mari-Beffa (Pseudo difference operators and discrete W_n al gebras) DTSTART:20211122T200000Z DTEND:20211122T204500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/4 DESCRIPTION:Title: Pseudo difference operators and discrete W_n algebras\nby Gloria Mari-Beffa (Pseudo difference operators and discrete W_n algebras) as part of BIRS workshop:Moving Frames and their Modern Applications\n\n\n Abstract\nIn this talk I will summarize work with Anna Calini and Jing-Pin g Wang on the discretization of $W_n$ algebras. I will then introduce the discrete analogue of the algebra of differential and pseudo-differential o perators\, and I will show that two natural Poisson brackets defined on th is algebra coincides with the brackets that were used to integrate discret e systems associated to the $W_n$ algebras. This is ongoing work with Anto n Isozimov.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Mireille Boutin (Purdue University) DTSTART:20211122T204500Z DTEND:20211122T213000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/5 DESCRIPTION:Title: How to recognize an unlabeled point configuration from noisy m easurements\nby Mireille Boutin (Purdue University) as part of BIRS wo rkshop:Moving Frames and their Modern Applications\n\n\nAbstract\nGiven is an (unknown) point configuration in ${\\mathbb R}^d$. We obtain noisy mea surements of the points\, and would like to characterize the shape of the point configuration. More specifically\, let $\\rho(x)$ be a probability d ensity function from which the noisy point measurements are obtained. We w ould like to characterize the orbit $\\{ \\rho(g\\cdot x) | g\\in E(d) \\ } $\, where $E(d)$ denotes the Euclidean group acting on ${\\mathbb R}^d$. I will consider the case where $\\rho(x)$ is a mixture of Gaussians\, rew rite the problem as an algebraic question\, and provide a solution.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Linyu Peng (Keio University) DTSTART:20211122T220000Z DTEND:20211122T224500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/6 DESCRIPTION:Title: Symmetries and Noether’s conservation laws of semi-discrete equations\nby Linyu Peng (Keio University) as part of BIRS workshop:Mo ving Frames and their Modern Applications\n\n\nAbstract\nSemi-discrete equ ations not only can be semi-discretisations of partial differential equa- tions or semi-continuum limits of partial difference equations\, but also arise as mechanical and physical systems themselves\, e.g.\, the Toda latt ice and interconnected systems in mechanics. Symmetries are fundamentally important properties that help us to under- stand the solvability/integrab ility of equations. In this talk\, we will introduce a general treatment f or computing continuous symmetries of semi-discrete equations through the linearized symmetry condition and extend Noether’s two theorems. Worked examples will be provided. This is joint work with Peter Hydon (University of Kent).\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Debra Lewis (University of California - Santa Cruz) DTSTART:20211122T224500Z DTEND:20211122T230500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/7 DESCRIPTION:Title: Geometry in the service of equity: moving frames in learning a nalytics\nby Debra Lewis (University of California - Santa Cruz) as pa rt of BIRS workshop:Moving Frames and their Modern Applications\n\n\nAbstr act\nInnovations in pedagogy and placement can increase the equity of STEM instruction\, but identification of a robust portfolio of outcome measure ments that are easily interpreted by stakeholders can be challenging. Elem entary geometry can facilitate communication between analysts and administ rators without suppression of potentially crucial information for the sake of simplicity. Moving frames provide a versatile\, powerful tool for deco mposing multidimensional outcome data into full cohort trends and deviatio ns of outcomes for sub-cohorts of interest from those trends. If gains in one measure are accompanied by losses in other measures (e.g. average cour se grades in the first STEM course following a preparatory math course inc rease because all but the highest scoring students in the prep course imme diately leave STEM)\, characterizing those changes using linear transforma tions of outcome vectors can potentially reveal patterns that are difficul t to recognize in tables of scalar data.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Oleg Morozov (AGH University of Science and Technology) DTSTART:20211123T160000Z DTEND:20211123T164500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/8 DESCRIPTION:Title: Lax representations via moving frames\nby Oleg Morozov (AG H University of Science and Technology) as part of BIRS workshop:Moving Fr ames and their Modern Applications\n\n\nAbstract\nLax representations of n onlinear PDEs are widely recognized as the key feature of integrable syste ms. Different phenomena thereof\, such as bi-Hamiltonian structures\, recu rsion operators\, nonlocal symmetries\, etc.\, can be derived from the Lax representations.  Therefore the problem to determine whether a given PD E admits a Lax representation is of great importance.  In this talk\, I will discuss how the structure theory of Lie pseudogroups in combination w ith the theory of infinite-dimensional Lie algebras can be applied to tack le this problem. Considerations will be based on the moving frame techniqu e.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Artur Sergyeyev (Silesian University in Opava) DTSTART:20211123T164500Z DTEND:20211123T173000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/9 DESCRIPTION:Title: Multidimensional integrability via contact geometry\nby Ar tur Sergyeyev (Silesian University in Opava) as part of BIRS workshop:Movi ng Frames and their Modern Applications\n\n\nAbstract\nWe give an explicit effective construction for a large new\nclass of partial differential sys tems in four independent variables\nthat are integrable in the sense of so liton theory\, thus showing inter\nalia that there is significantly more o f such systems than it appeared\nbefore. This is achieved by employing con tact vector fields in\ndimension three in the construction of associated L ax pairs\; please\nsee A. Sergyeyev\, Lett. Math. Phys. 108 (2018)\, no. 2 \, 359-376\n(arXiv:1401.2122) for further details.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Ivey (College of Charleston) DTSTART:20211123T180000Z DTEND:20211123T184500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/10 DESCRIPTION:Title: Darboux-integrable elliptic systems and their extensions: Pro blems and prospects\nby Thomas Ivey (College of Charleston) as part of BIRS workshop:Moving Frames and their Modern Applications\n\n\nAbstract\n In a 2009 paper\, Anderson\, Fels and Vassiliou showed that\, for a class of \nDarboux-integrable (DI) hyperbolic systems\, a canonical integrable e xtension exists which is constructed using the action of the Vessiot group \, and which splits as the product of two simpler differential systems. M oreover\, each solution of the DI system arises as a `superposition' of a pair of solutions to the simpler systems.\n\nIn this preliminary report on joint work with Mark Fels\, we outline a conjectural picture for the cons truction of a canonical integrable extension for elliptic DI systems. In general\, the extension does not split\, but in several examples the exten sion is contact-equivalent to a prolongation of the Cauchy-Riemann equatio ns\, leading to solution formulas in terms of holomorphic functions. If t ime permits\, we will discuss an application of these ideas to the isometr ic embedding problem for certain surfaces of revolution.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Fels (Utah State University) DTSTART:20211123T200000Z DTEND:20211123T204500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/11 DESCRIPTION:Title: Equations of Lie type and Darboux integrability\nby Mark Fels (Utah State University) as part of BIRS workshop:Moving Frames and th eir Modern Applications\n\n\nAbstract\nEquations of Lie type are fundament al in the theory of moving frames and these equations \nhave an interestin g and rich history. Equations of Lie type appear in the equations for the reconstruction problem for curves with prescribed differential invariants . By studying equations of Lie type\, E. Vessiot discovered a generalizat ion of these equations which remarkably turn out to underlie the integrati on process for partial differential equations that can be integrated by th e method of Darboux. I will explain this relationship and demonstrate it with examples.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Roman Smirnov (Dalhousie University) DTSTART:20211123T204500Z DTEND:20211123T213000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/12 DESCRIPTION:Title: Applications of the method of moving frames to the theory of orthogonal separation of variables\nby Roman Smirnov (Dalhousie Univer sity) as part of BIRS workshop:Moving Frames and their Modern Applications \n\n\nAbstract\nWe will review the main applications of the method of movi ng frames to the theory of orthogonal separation of variables in pseudo-Ri emannian spaces of constant curvature. In this context\, the method of mov ing frames arises as an indispensable tool in the study of algebraic and g eometric properties of Killing tensors (symmetry operators)  that determi ne the orthogonal separation of variables in problems of classical (quantu m) mechanics.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis The (UiT The Arctic University of Norway) DTSTART:20211123T220000Z DTEND:20211123T224500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/13 DESCRIPTION:Title: A Cartan-theoretic classification of multiply-transitive (2\, 3\,5)-distributions\nby Dennis The (UiT The Arctic University of Norwa y) as part of BIRS workshop:Moving Frames and their Modern Applications\n\ n\nAbstract\nGeneric rank 2 distributions on 5-manifolds\, i.e. (2\,3\,5)- distributions\, are interesting geometric structures arising in the study of non-holonomic kinematical systems (e.g. two 2-spheres rolling on each o ther without twisting or slipping)\, underdetermined ODE of Monge type\, c onformal 5-manifolds with special holonomy\, etc. The origins of their stu dy date to Élie Cartan's "5-variables" paper of 1910\, where he gave a to ur-de-force application of his method of equivalence. In particular\, he obtained a canonical coframing\, discovered a fundamental (tensorial) curv ature quantity (the Cartan quartic)\, and gave a (almost complete) local c lassification of structures that are multiply-transitive\, i.e. (locally) homogeneous with isotropy of positive dimension. In my talk\, I'll revisi t this homogeneous classification and present it from a modern Cartan-geom etric perspective.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Sehun Chun (Yonsei University) DTSTART:20211123T224500Z DTEND:20211123T233000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/14 DESCRIPTION:Title: Moving frames for the numerical solution of PDEs and beyond i n applications to Meteorology\, Cardiology\, and Neuroscience\nby Sehu n Chun (Yonsei University) as part of BIRS workshop:Moving Frames and thei r Modern Applications\n\n\nAbstract\nFirst introduced as orthonormal basis vectors in the numerical solution of PDEs on curved surfaces\, moving fra me algorithms have been proved competitively accurate and stable for vario us PDEs\, particularly with high-order discretization schemes. The PDEs in clude conservational laws\, diffusion equations\, shallow water equations\ , and Maxwell’s equations. High-order discretization schemes mean contin uous/discontinuous Galerkin method or spectral/hp methods. The most striki ng feature of moving frames is that moving frames simplifies the type of m edium in PDEs. A simple representation of anisotropy by the adjusted lengt h of the frames in diffusion equations or a general representation of rota tion surfaces by moving frames provides significant advantages in numerica l algorithms. Beyond the spatial representation of complex domain\, moving frames aligned along with wave propagation yields connection and Riemann curvature tensor to help to identify and predict the flow pattern. One app lication of such an algorithm is to analyze the cardiac electric flow wher e a large amount of a specific component of the Riemann curvature tensor i mplies conduction block and consequently the possibility of reentry and fi brillation. Another application is to construct a numerical algorithm to s imulate neural spike propagation along with a spreading neural fiber bundl e in the brain’s white matter to reveal the geometric structure of the b rain connectivity. The most recent research also applies moving frames to a field of ‘time’ to achieve the spacetime analysis of time-dependent propagation in the heart and brain. All these moving frames applications d emonstrate the beautiful simplicity of moving frames in the complex propag ation phenomena in complex domains. However\, a question still hangs in th e air about its restrictions and real-world interpretation of connection a nd curvature.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Evelyne Hubert (INRIA Sophia Antipolis France) DTSTART:20211124T160000Z DTEND:20211124T164500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/15 DESCRIPTION:Title: Algebraic moving frame and beyond\nby Evelyne Hubert (INR IA Sophia Antipolis France) as part of BIRS workshop:Moving Frames and the ir Modern Applications\n\n\nAbstract\nIn this talk I wish to review variat ions on the constructions of rational invariants and the key role of secti ons therein. \n\nThe moving frame  by Fels & Olver (1999) provided a meth od to compute local invariants. In practice it relies on 1/ making explici t the solution of the application of the implicit function theorem 2/ figh ting through symbolic expressions involving radicals. For a fully algorith mic approach [Hubert Kogan FoCM 2007] recasted the problem in algebraic te rms and offered a construction of local invariant as algebraic functions g iven by the Gröbner basis of their defining ideal. On the way we proved t hat we could also compute a generating set of rational invariants [Hubert Kogan JSC 2007]\, which are global invariants.\n\nThe general construction gave the intuition to refined constructions for specific group actions\, relevant in applications and offering further connections.  Such is the c ase of scalings\, with a new take on the Buckingham-Pi theorem\,  [Hubert Labahn FoCM 2013] and the action of the orthogonal group on homogeneous p olynomials in in 3D [Görlach Hubert Papadopoulo FoCM 2019] with a computa tional take on the  slices  of Seshadri (1962).\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Orn Arnaldsson (University of Iceland) DTSTART:20211124T164500Z DTEND:20211124T173000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/16 DESCRIPTION:Title: The equivariant moving frame for Lie pseudo-groups and Cartan 's equivalence method\nby Orn Arnaldsson (University of Iceland) as pa rt of BIRS workshop:Moving Frames and their Modern Applications\n\n\nAbstr act\nUnderpinning the equivariant moving frame is a basic theorem on congr uence of submanifolds in Lie groups. In this talk we present a recent gene ralization of this theorem to Lie pseudo-groups and the perspective it pr ovides on the equivariant moving frame for Lie pseudo-groups. From this ne w point of view Cartan's equivalence method emerges naturally.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Eivind Schneider (University of Hradec Králové) DTSTART:20211124T180000Z DTEND:20211124T184500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/17 DESCRIPTION:Title: Differential invariants of Kundt spacetimes\nby Eivind Sc hneider (University of Hradec Králové) as part of BIRS workshop:Moving F rames and their Modern Applications\n\n\nAbstract\nWe compute generators f or the algebra of rational scalar differential invariants of general and d egenerate Kundt spacetimes. Special attention is given to dimensions 3 and 4 since in those dimensions the degenerate Kundt metrics are known to be exactly the Lorentzian metrics that can not be distinguished by polynomial curvature invariants constructed from the Riemann tensor and its covarian t derivatives. The talk is based on joint work with Boris Kruglikov.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Needham (Florida State University) DTSTART:20211124T200000Z DTEND:20211124T204500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/18 DESCRIPTION:Title: The Gromov-Wasserstein distance and distributional invariants of datasets\nby Tom Needham (Florida State University) as part of BIR S workshop:Moving Frames and their Modern Applications\n\n\nAbstract\nhe G romov-Wasserstein (GW) distance is a generalization of the standard Wasser stein distance between two probability measures on a given ambient metric space. The GW distance assumes that these two probability measures might l ive on different ambient metric spaces and therefore implements an actua l comparison of pairs of metric measure spaces. A metric-measure space is a triple (X\,dX\,muX) where (X\,dX) is a metric space and muX is a Borel probability measure over X.\n\nIn practical applications\, this distance i s estimated either directly via gradient based optimization approaches\, o r through the computation of lower bounds which arise from distributional invariants of metric-measure spaces. One particular such invariant is the so-called ‘global distance distribution’ which precisely encodes the d istribution of pairwise distances between points in a given metric measure space. This invariant has been used in many applications yet its classifi catory power is not yet well understood.\n\nThis talk will overview the co nstruction of the GW distance\, the stability of distributional invariants \, and will also discuss some results regarding the injectivity of the glo bal distribution of distances for smooth planar curves\, hypersurfaces\, a nd metric trees. \n\nPart of this work is joint with Facundo Memoli.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Milson (Dalhousie University) DTSTART:20211124T204500Z DTEND:20211124T213000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/19 DESCRIPTION:Title: The Karlhede algorithm and the Cartan equivalence method\ nby Robert Milson (Dalhousie University) as part of BIRS workshop:Moving F rames and their Modern Applications\n\n\nAbstract\nIn general relativity\, the invariant classification of spacetimes is typically formulated in ter ms of a pseudo-algorithm proposed by Anders Karlhede in 1980. At first g lance\, this algorithm and its subsequent refinements do not bear much res emblence to Cartan's method for the equivalence of G-structures. Indeed\, even if one limits the scope of the equivalence method to that of Riemann ian geometries\, it is difficult to perceive the relation between the two approaches. To wit\, Karlhede's algorithm does not make use of the bund le of orthogonal frames and relies instead on iterated normalizations of t he curvature tensor. My aim will be to explain the relativity approach t o an audience familiar with the Cartan formalism and to highlight some com putational advantages of this way of doing equivalence problems.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Boris Kruglikov (UiT the Arctic University of Norway) DTSTART:20211124T220000Z DTEND:20211124T224500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/20 DESCRIPTION:Title: Relative differential invariants\nby Boris Kruglikov (UiT the Arctic University of Norway) as part of BIRS workshop:Moving Frames a nd their Modern Applications\n\n\nAbstract\nI will revisit the old story\, addressing some general results and providing new examples.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin (University of Tromso) DTSTART:20211125T160000Z DTEND:20211125T164500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/21 DESCRIPTION:Title: On metric invariants of spherical harmonics\nby Valentin Lychagin (University of Tromso) as part of BIRS workshop:Moving Frames and their Modern Applications\n\n\nAbstract\nThe field of rational algebraic and differential SO(3)-invariants of spherical harmonics were described a nd were used for the description of regular SO(3)-orbits of spherical har monics in an algebraic and differential setting.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Emilio Musso (Politecnico of Turin) DTSTART:20211125T164500Z DTEND:20211125T173000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/22 DESCRIPTION:Title: Holomorphic conformal geometry of isotropic curves in the com plex quadric\nby Emilio Musso (Politecnico of Turin) as part of BIRS w orkshop:Moving Frames and their Modern Applications\n\n\nAbstract\nLet $\\ Q_3$ be the $3$-dimensional complex quadric equipped with its holomorphic conformal structure. We use the method of moving frame to study conformal geometry of isotropic holomorphic curves in $\\Q_3$ and their interrelatio ns with relevant classes of surfaces in Riemannian and Lorentzian space-fo rms. This is a joint work with Lorenzo Nicolodi.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Ekaterina Shemyakova (University of Toledo) DTSTART:20211125T180000Z DTEND:20211125T183000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/23 DESCRIPTION:Title: On super Plücker embedding and cluster algebras\nby Ekat erina Shemyakova (University of Toledo) as part of BIRS workshop:Moving Fr ames and their Modern Applications\n\n\nAbstract\nThere has been active wo rk towards definition of super cluster algebras (Ovsienko\, Ovsienko-Shapi ro\, and Li-Mixco-Ransingh-Srivastava)\, but the notion is still a mystery . In the talk\, we present our construction of “super Pluecker embedding ” for Grassmannian of $r|s$-planes in $n|m$-space. (Only a very special case was considered before in the literature\, namely\, of $2|0$-planes i n $4|1$-space\, by Cervantes-Fioresi-Lledo.) The straightforward algebraic construction of exterior powers goes through for the Grassmannian $G_{r|0 }(n|m)$\, i.e. completely even planes in the superspace. For the general c ase of $r|s$-planes\, a more complicated construction is needed. Our super Pluecker map takes the Grassmann supermanifold $G_{r|s}(V)$ to a “weigh ted projective space” $P_{1\,-1}(\\Lambda^{r|s}(V)\\oplus \\Lambda^{s|rs }(\\Pi V))$\, with weights $+1\, −1$. Here $\\Lambda^{r|s}(V)$ denotes t he $(r|s)$th exterior power of a superspace $V$ and $\\Pi$ is the parity reversion functor. We identify the super analog of Pluecker coordinates an d show that our map is an embedding. We investigate the super analog of th e Pluecker relations. We obtain them for arbitrary $r|s$ and $n|m$. The ca se $r|0$ is relevant for conjectural super cluster algebras. Also\, we con sider another type of relations suggested by H. Khudaverdian and show that they are equivalent to (super) Pluecker relations for $r|s = 2|0$ (this i s new even in the classical case)\, but in general are only a\nconsequence of the Pluecker relations. \n\n(Based on a joint work with Th. Voronov.)\ n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Werner Seiler (Kassel University) DTSTART:20211126T160000Z DTEND:20211126T164500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/24 DESCRIPTION:Title: Singularities of General systems of differential equations\nby Werner Seiler (Kassel University) as part of BIRS workshop:Moving Fr ames and their Modern Applications\n\n\nAbstract\nThe classical\, differen tial topological theory of singularities of \ndifferential equations is ma inly concerned with scalar ordinary \ndifferential equations of first or s econd order with an emphasis on \nclassifications and normal forms. We pre sent an extension of the basic \ndefinitions to arbitrary systems of ordin ary or partial differential \nequations based on Vessiot theory and some o f the arising open problems. \nWe also relate these results with the notio n of a "regular differential \nequation" - a standard assumption in the ge ometric theory of \ndifferential equations which is rarely made rigorous. If time permits\, \nwe will also discuss the question of how the theory ca n be effective\, \ni.e. translated into algebraic algorithms for detecting singularities \nand for analysing the local solution behaviour.\n\n(Much of the talk is based on the recent article Lange-Hegermann\, \nRobertz\, S eiler\, Seiss: Singularities of Algebraic Differential \nEquations\, Adv. Appl. Math. 131 (2021) 102266.)\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Roman Popovych (University of Vienna) DTSTART:20211126T164500Z DTEND:20211126T173000Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/25 DESCRIPTION:Title: Method of moving frames and computing generalized Casimir ope rators\nby Roman Popovych (University of Vienna) as part of BIRS works hop:Moving Frames and their Modern Applications\n\n\nAbstract\nWe discuss the application of the method of moving frames to computing\ngeneralized C asimir operators of Lie algebras\, i.e.\, invariants of the\ncoadjoint rep resentations of such algebras. We also review results on\nusing the obtain ed purely algebraic algorithm for finding generalized\nCasimir operators o f low-dimensional Lie algebras and series of\nsolvable Lie algebras with s pecific structure of their nilradicals\, in\nparticular\, of the Lie algeb ras of triangular and strictly triangular\nmatrices of an arbitrary fixed dimension.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Illia Hayes (Utah State University) DTSTART:20211126T180000Z DTEND:20211126T184500Z DTSTAMP:20260404T042255Z UID:BIRS-21w5505/26 DESCRIPTION:Title: Joint invariants of primitive actions\nby Illia Hayes (Ut ah State University) as part of BIRS workshop:Moving Frames and their Mode rn Applications\n\n\nAbstract\nWe consider the problem of finding a comple te set of invariants for the product action of a Lie group $G$ on multiple copies of a homogeneous space $G/H$\, where $H$ is a closed Lie subgroup of $G$ and the action is primitive. In the particular the case when $G$ is not simple and the primitive actions have been classified by Golubitsky. We will present a reduction theorem that simplifies the problem of finding invariants and apply it to finding two point invariants in $SU(2)$\, and $SL(2)$.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5505/26/ END:VEVENT END:VCALENDAR