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:20260422T185904Z UID:BIRS-21w5505/1 DESCRIPTION:Title: Moving frames for partial difference equations\nby Peter Hydon (U niversity 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 prolongati on structure generated by the group of translations on $\\mathbb{Z}^N$. Th ey can be modified to cope with finite domains. Difference moving frames p roduce group-invariant reductions of partial difference equations. In part icular\, they yield invariant formulations of Euler-Lagrange difference eq uations and an equivariant version of Noether's Theorem. We discuss these\ , with application to a Toda-type system that stems from the cross-ratio a nd discrete potential KdV equations.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Hans Munthe-Kaas (University of Bergen Norway) DTSTART:20211122T164500Z DTEND:20211122T173000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/2 DESCRIPTION:Title: Connection Algebras\nby Hans Munthe-Kaas (University of Bergen No rway) as part of BIRS workshop:Moving Frames and their Modern Applications \n\n\nAbstract\nAn affine connection defines a product on the vector field s of a manifold\, and more generally on sections of a vector bundle. We s tudy algebras defined by connections. The structure and combinatorics of t he algebra is important for understanding series developments of flows on the manifold. \n\nInvariant connections\, where the geometric picture was developed by Nomizu 1954\, are interesting also on the algebraic side. In particular euclidean geometries yield flat and torsion free connections wh ich give rise to pre-Lie algebras\, which is the foundation of Butcher-ser es\, Branched Rough Path Theory and the Connes-Kreimer Hopf algebra. Lie g roups and Klein geometries have natural flat connections with parallel tor sion which yield post-Lie algebras\, Lie-Butcher series\, the MKW Hopf alg ebra and Planarly Branched Rough Paths. Symmetric spaces have torsion free connections with parallel curvature. We call the algebras Lie-Admissible- Triple-Algebras\, but these are not properly understood yet\, and a rough path theory has not yet been developed in this case. \n\nRecent work in pr ogress show that post-Lie algebras play a crucial role in the understandin g of more general connections\, in particular the Levi—Civita connection on a general Riemannian manifold. \n\nThe talk will give an overview of t he area\, as well as going into the most recent results. I would like to s park discussions on relations between \nConnection Algebras and Moving Fra mes.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Ruddy (University of San Francisco) DTSTART:20211122T180000Z DTEND:20211122T184500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/3 DESCRIPTION:Title: The moving frame method for iterated integrals: orthogonal invariants \nby Michael Ruddy (University of San Francisco) as part of BIRS works hop:Moving Frames and their Modern Applications\n\n\nAbstract\nCurves in E uclidean space enjoy a natural action of the orthogonal group on its ambie nt space. We apply the Fels-Olver moving frame method paired with the log- signature transform to construct a set of integral invariants for curves i n $\\mathbb{R}^d$ under rigid motions and to compare curves up to rigid mo tions (and tree-like extensions). In particular we show that one can const ruct a set of invariants that characterize the equivalence class of the tr uncated iterated-integrals signature under orthogonal transformations.\n LOCATION:https://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:20260422T185904Z 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\nAbstrac t\nIn this talk I will summarize work with Anna Calini and Jing-Ping Wang on the discretization of $W_n$ algebras. I will then introduce the discret e analogue of the algebra of differential and pseudo-differential operator s\, and I will show that two natural Poisson brackets defined on this alge bra coincides with the brackets that were used to integrate discrete syste ms associated to the $W_n$ algebras. This is ongoing work with Anton Isozi mov.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Mireille Boutin (Purdue University) DTSTART:20211122T204500Z DTEND:20211122T213000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/5 DESCRIPTION:Title: How to recognize an unlabeled point configuration from noisy measurem ents\nby Mireille Boutin (Purdue University) as part of BIRS workshop: Moving Frames and their Modern Applications\n\n\nAbstract\nGiven is an (un known) point configuration in ${\\mathbb R}^d$. We obtain noisy measuremen ts of the points\, and would like to characterize the shape of the point c onfiguration. More specifically\, let $\\rho(x)$ be a probability density function from which the noisy point measurements are obtained. We would li ke to characterize the orbit $\\{ \\rho(g\\cdot x) | g\\in E(d) \\} $\, w here $E(d)$ denotes the Euclidean group acting on ${\\mathbb R}^d$. I will consider the case where $\\rho(x)$ is a mixture of Gaussians\, rewrite th e problem as an algebraic question\, and provide a solution.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Linyu Peng (Keio University) DTSTART:20211122T220000Z DTEND:20211122T224500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/6 DESCRIPTION:Title: Symmetries and Noether’s conservation laws of semi-discrete equatio ns\nby Linyu Peng (Keio University) as part of BIRS workshop:Moving Fr ames and their Modern Applications\n\n\nAbstract\nSemi-discrete equations not only can be semi-discretisations of partial differential equa- tions o r semi-continuum limits of partial difference equations\, but also arise a s mechanical and physical systems themselves\, e.g.\, the Toda lattice and interconnected systems in mechanics. Symmetries are fundamentally importa nt properties that help us to under- stand the solvability/integrability o f equations. In this talk\, we will introduce a general treatment for comp uting continuous symmetries of semi-discrete equations through the lineari zed symmetry condition and extend Noether’s two theorems. Worked example s will be provided. This is joint work with Peter Hydon (University of Ken t).\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Debra Lewis (University of California - Santa Cruz) DTSTART:20211122T224500Z DTEND:20211122T230500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/7 DESCRIPTION:Title: Geometry in the service of equity: moving frames in learning analytic s\nby Debra Lewis (University of California - Santa Cruz) as part of B IRS workshop:Moving Frames and their Modern Applications\n\n\nAbstract\nIn novations in pedagogy and placement can increase the equity of STEM instru ction\, but identification of a robust portfolio of outcome measurements t hat are easily interpreted by stakeholders can be challenging. Elementary geometry can facilitate communication between analysts and administrators without suppression of potentially crucial information for the sake of sim plicity. Moving frames provide a versatile\, powerful tool for decomposing multidimensional outcome data into full cohort trends and deviations of o utcomes for sub-cohorts of interest from those trends. If gains in one mea sure are accompanied by losses in other measures (e.g. average course grad es in the first STEM course following a preparatory math course increase b ecause all but the highest scoring students in the prep course immediately leave STEM)\, characterizing those changes using linear transformations o f outcome vectors can potentially reveal patterns that are difficult to re cognize in tables of scalar data.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Oleg Morozov (AGH University of Science and Technology) DTSTART:20211123T160000Z DTEND:20211123T164500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/8 DESCRIPTION:Title: Lax representations via moving frames\nby Oleg Morozov (AGH Unive rsity of Science and Technology) as part of BIRS workshop:Moving Frames an d their Modern Applications\n\n\nAbstract\nLax representations of nonlinea r PDEs are widely recognized as the key feature of integrable systems. Dif ferent phenomena thereof\, such as bi-Hamiltonian structures\, recursion o perators\, nonlocal symmetries\, etc.\, can be derived from the Lax repres entations.  Therefore the problem to determine whether a given PDE admit s a Lax representation is of great importance.  In this talk\, I will di scuss how the structure theory of Lie pseudogroups in combination with the theory of infinite-dimensional Lie algebras can be applied to tackle this problem. Considerations will be based on the moving frame technique.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Artur Sergyeyev (Silesian University in Opava) DTSTART:20211123T164500Z DTEND:20211123T173000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/9 DESCRIPTION:Title: Multidimensional integrability via contact geometry\nby Artur Ser gyeyev (Silesian University in Opava) as part of BIRS workshop:Moving Fram es and their Modern Applications\n\n\nAbstract\nWe give an explicit effect ive construction for a large new\nclass of partial differential systems in four independent variables\nthat are integrable in the sense of soliton t heory\, thus showing inter\nalia that there is significantly more of such systems than it appeared\nbefore. This is achieved by employing contact ve ctor fields in\ndimension three in the construction of associated Lax pair s\; please\nsee A. Sergyeyev\, Lett. Math. Phys. 108 (2018)\, no. 2\, 359- 376\n(arXiv:1401.2122) for further details.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Ivey (College of Charleston) DTSTART:20211123T180000Z DTEND:20211123T184500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/10 DESCRIPTION:Title: Darboux-integrable elliptic systems and their extensions: Problems a nd prospects\nby Thomas Ivey (College of Charleston) as part of BIRS w orkshop:Moving Frames and their Modern Applications\n\n\nAbstract\nIn a 20 09 paper\, Anderson\, Fels and Vassiliou showed that\, for a class of \nDa rboux-integrable (DI) hyperbolic systems\, a canonical integrable extensio n exists which is constructed using the action of the Vessiot group\, and which splits as the product of two simpler differential systems. Moreover \, 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 constructio n of a canonical integrable extension for elliptic DI systems. In general \, the extension does not split\, but in several examples the extension is contact-equivalent to a prolongation of the Cauchy-Riemann equations\, le ading to solution formulas in terms of holomorphic functions. If time per mits\, we will discuss an application of these ideas to the isometric embe dding problem for certain surfaces of revolution.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Fels (Utah State University) DTSTART:20211123T200000Z DTEND:20211123T204500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/11 DESCRIPTION:Title: Equations of Lie type and Darboux integrability\nby Mark Fels (U tah State University) as part of BIRS workshop:Moving Frames and their Mod ern Applications\n\n\nAbstract\nEquations of Lie type are fundamental in t he theory of moving frames and these equations \nhave an interesting and r ich history. Equations of Lie type appear in the equations for the recons truction problem for curves with prescribed differential invariants. By st udying equations of Lie type\, E. Vessiot discovered a generalization of these equations which remarkably turn out to underlie the integration proc ess for partial differential equations that can be integrated by the metho d of Darboux. I will explain this relationship and demonstrate it with e xamples.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Roman Smirnov (Dalhousie University) DTSTART:20211123T204500Z DTEND:20211123T213000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/12 DESCRIPTION:Title: Applications of the method of moving frames to the theory of orthogo nal separation of variables\nby Roman Smirnov (Dalhousie University) a s part of BIRS workshop:Moving Frames and their Modern Applications\n\n\nA bstract\nWe will review the main applications of the method of moving fram es to the theory of orthogonal separation of variables in pseudo-Riemannia n spaces of constant curvature. In this context\, the method of moving fra mes arises as an indispensable tool in the study of algebraic and geometri c properties of Killing tensors (symmetry operators)  that determine the orthogonal separation of variables in problems of classical (quantum) mech anics.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis The (UiT The Arctic University of Norway) DTSTART:20211123T220000Z DTEND:20211123T224500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/13 DESCRIPTION:Title: A Cartan-theoretic classification of multiply-transitive (2\,3\,5)-d istributions\nby Dennis The (UiT The Arctic University of Norway) as p art of BIRS workshop:Moving Frames and their Modern Applications\n\n\nAbst ract\nGeneric rank 2 distributions on 5-manifolds\, i.e. (2\,3\,5)-distrib utions\, are interesting geometric structures arising in the study of non- holonomic kinematical systems (e.g. two 2-spheres rolling on each other wi thout twisting or slipping)\, underdetermined ODE of Monge type\, conforma l 5-manifolds with special holonomy\, etc. The origins of their study date to Élie Cartan's "5-variables" paper of 1910\, where he gave a tour-de-f orce application of his method of equivalence. In particular\, he obtaine d a canonical coframing\, discovered a fundamental (tensorial) curvature q uantity (the Cartan quartic)\, and gave a (almost complete) local classifi cation of structures that are multiply-transitive\, i.e. (locally) homogen eous with isotropy of positive dimension. In my talk\, I'll revisit this homogeneous classification and present it from a modern Cartan-geometric p erspective.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Sehun Chun (Yonsei University) DTSTART:20211123T224500Z DTEND:20211123T233000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/14 DESCRIPTION:Title: Moving frames for the numerical solution of PDEs and beyond in appli cations to Meteorology\, Cardiology\, and Neuroscience\nby Sehun Chun (Yonsei University) as part of BIRS workshop:Moving Frames and their Moder n Applications\n\n\nAbstract\nFirst introduced as orthonormal basis vector s in the numerical solution of PDEs on curved surfaces\, moving frame algo rithms have been proved competitively accurate and stable for various PDEs \, particularly with high-order discretization schemes. The PDEs include c onservational laws\, diffusion equations\, shallow water equations\, and M axwell’s equations. High-order discretization schemes mean continuous/di scontinuous Galerkin method or spectral/hp methods. The most striking feat ure of moving frames is that moving frames simplifies the type of medium i n PDEs. A simple representation of anisotropy by the adjusted length of th e frames in diffusion equations or a general representation of rotation su rfaces by moving frames provides significant advantages in numerical algor ithms. Beyond the spatial representation of complex domain\, moving frames aligned along with wave propagation yields connection and Riemann curvatu re tensor to help to identify and predict the flow pattern. One applicatio n of such an algorithm is to analyze the cardiac electric flow where a lar ge amount of a specific component of the Riemann curvature tensor implies conduction block and consequently the possibility of reentry and fibrillat ion. Another application is to construct a numerical algorithm to simulate neural spike propagation along with a spreading neural fiber bundle in th e brain’s white matter to reveal the geometric structure of the brain co nnectivity. The most recent research also applies moving frames to a field of ‘time’ to achieve the spacetime analysis of time-dependent propaga tion in the heart and brain. All these moving frames applications demonstr ate the beautiful simplicity of moving frames in the complex propagation p henomena in complex domains. However\, a question still hangs in the air a bout its restrictions and real-world interpretation of connection and curv ature.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Evelyne Hubert (INRIA Sophia Antipolis France) DTSTART:20211124T160000Z DTEND:20211124T164500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/15 DESCRIPTION:Title: Algebraic moving frame and beyond\nby Evelyne Hubert (INRIA Soph ia Antipolis France) as part of BIRS workshop:Moving Frames and their Mode rn Applications\n\n\nAbstract\nIn this talk I wish to review variations on the constructions of rational invariants and the key role of sections the rein. \n\nThe moving frame  by Fels & Olver (1999) provided a method to c ompute local invariants. In practice it relies on 1/ making explicit the s olution of the application of the implicit function theorem 2/ fighting th rough symbolic expressions involving radicals. For a fully algorithmic app roach [Hubert Kogan FoCM 2007] recasted the problem in algebraic terms and offered a construction of local invariant as algebraic functions given by the Gröbner basis of their defining ideal. On the way we proved that we could also compute a generating set of rational invariants [Hubert Kogan J SC 2007]\, which are global invariants.\n\nThe general construction gave t he intuition to refined constructions for specific group actions\, relevan t in applications and offering further connections.  Such is the case of scalings\, with a new take on the Buckingham-Pi theorem\,  [Hubert Labahn FoCM 2013] and the action of the orthogonal group on homogeneous polynomi als in in 3D [Görlach Hubert Papadopoulo FoCM 2019] with a computational take on the  slices  of Seshadri (1962).\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Orn Arnaldsson (University of Iceland) DTSTART:20211124T164500Z DTEND:20211124T173000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/16 DESCRIPTION:Title: The equivariant moving frame for Lie pseudo-groups and Cartan's equi valence method\nby Orn Arnaldsson (University of Iceland) as part of B IRS workshop:Moving Frames and their Modern Applications\n\n\nAbstract\nUn derpinning the equivariant moving frame is a basic theorem on congruence o f submanifolds in Lie groups. In this talk we present a recent generalizat ion of this theorem to Lie pseudo-groups and the perspective it provides on the equivariant moving frame for Lie pseudo-groups. From this new point of view Cartan's equivalence method emerges naturally.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Eivind Schneider (University of Hradec Králové) DTSTART:20211124T180000Z DTEND:20211124T184500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/17 DESCRIPTION:Title: Differential invariants of Kundt spacetimes\nby Eivind Schneider (University of Hradec Králové) as part of BIRS workshop:Moving Frames a nd their Modern Applications\n\n\nAbstract\nWe compute generators for the algebra of rational scalar differential invariants of general and degenera te Kundt spacetimes. Special attention is given to dimensions 3 and 4 sinc e in those dimensions the degenerate Kundt metrics are known to be exactly the Lorentzian metrics that can not be distinguished by polynomial curvat ure invariants constructed from the Riemann tensor and its covariant deriv atives. The talk is based on joint work with Boris Kruglikov.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Needham (Florida State University) DTSTART:20211124T200000Z DTEND:20211124T204500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/18 DESCRIPTION:Title: The Gromov-Wasserstein distance and distributional invariants of dat asets\nby Tom Needham (Florida State University) as part of BIRS works hop:Moving Frames and their Modern Applications\n\n\nAbstract\nhe Gromov-W asserstein (GW) distance is a generalization of the standard Wasserstein d istance between two probability measures on a given ambient metric space. The GW distance assumes that these two probability measures might live on  different ambient metric spaces and therefore implements an actual comp arison of pairs of metric measure spaces. A metric-measure space is a tri ple (X\,dX\,muX) where (X\,dX) is a metric space and muX is a Borel probab ility measure over X.\n\nIn practical applications\, this distance is esti mated either directly via gradient based optimization approaches\, or thro ugh the computation of lower bounds which arise from distributional invari ants of metric-measure spaces. One particular such invariant is the so-cal led ‘global distance distribution’ which precisely encodes the distrib ution of pairwise distances between points in a given metric measure space . This invariant has been used in many applications yet its classificatory power is not yet well understood.\n\nThis talk will overview the construc tion of the GW distance\, the stability of distributional invariants\, and will also discuss some results regarding the injectivity of the global di stribution of distances for smooth planar curves\, hypersurfaces\, and met ric trees. \n\nPart of this work is joint with Facundo Memoli.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Milson (Dalhousie University) DTSTART:20211124T204500Z DTEND:20211124T213000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/19 DESCRIPTION:Title: The Karlhede algorithm and the Cartan equivalence method\nby Rob ert Milson (Dalhousie University) as part of BIRS workshop:Moving Frames a nd their Modern Applications\n\n\nAbstract\nIn general relativity\, the in variant classification of spacetimes is typically formulated in terms of a pseudo-algorithm proposed by Anders Karlhede in 1980. At first glance\, this algorithm and its subsequent refinements do not bear much resemblenc e to Cartan's method for the equivalence of G-structures. Indeed\, even i f one limits the scope of the equivalence method to that of Riemannian geo metries\, it is difficult to perceive the relation between the two approac hes. To wit\, Karlhede's algorithm does not make use of the bundle of o rthogonal frames and relies instead on iterated normalizations of the curv ature tensor. My aim will be to explain the relativity approach to an au dience familiar with the Cartan formalism and to highlight some computatio nal advantages of this way of doing equivalence problems.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Boris Kruglikov (UiT the Arctic University of Norway) DTSTART:20211124T220000Z DTEND:20211124T224500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/20 DESCRIPTION:Title: Relative differential invariants\nby Boris Kruglikov (UiT the Ar ctic University of Norway) as part of BIRS workshop:Moving Frames and thei r Modern Applications\n\n\nAbstract\nI will revisit the old story\, addres sing some general results and providing new examples.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin (University of Tromso) DTSTART:20211125T160000Z DTEND:20211125T164500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/21 DESCRIPTION:Title: On metric invariants of spherical harmonics\nby Valentin Lychagi n (University of Tromso) as part of BIRS workshop:Moving Frames and their Modern Applications\n\n\nAbstract\nThe field of rational algebraic and dif ferential SO(3)-invariants of spherical harmonics were described and were used for the description of regular SO(3)-orbits of spherical harmonics in an algebraic and differential setting.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Emilio Musso (Politecnico of Turin) DTSTART:20211125T164500Z DTEND:20211125T173000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/22 DESCRIPTION:Title: Holomorphic conformal geometry of isotropic curves in the complex qu adric\nby Emilio Musso (Politecnico of Turin) as part of BIRS workshop :Moving Frames and their Modern Applications\n\n\nAbstract\nLet $\\Q_3$ be the $3$-dimensional complex quadric equipped with its holomorphic conform al structure. We use the method of moving frame to study conformal geometr y of isotropic holomorphic curves in $\\Q_3$ and their interrelations with relevant classes of surfaces in Riemannian and Lorentzian space-forms. Th is is a joint work with Lorenzo Nicolodi.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Ekaterina Shemyakova (University of Toledo) DTSTART:20211125T180000Z DTEND:20211125T183000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/23 DESCRIPTION:Title: On super Plücker embedding and cluster algebras\nby Ekaterina S hemyakova (University of Toledo) as part of BIRS workshop:Moving Frames an d their Modern Applications\n\n\nAbstract\nThere has been active work towa rds definition of super cluster algebras (Ovsienko\, Ovsienko-Shapiro\, an d Li-Mixco-Ransingh-Srivastava)\, but the notion is still a mystery. In th e talk\, we present our construction of “super Pluecker embedding” for Grassmannian of $r|s$-planes in $n|m$-space. (Only a very special case w as considered before in the literature\, namely\, of $2|0$-planes in $4|1$ -space\, by Cervantes-Fioresi-Lledo.) The straightforward algebraic constr uction of exterior powers goes through for the Grassmannian $G_{r|0}(n|m)$ \, i.e. completely even planes in the superspace. For the general case of $r|s$-planes\, a more complicated construction is needed. Our super Plueck er map takes the Grassmann supermanifold $G_{r|s}(V)$ to a “weighted pro jective space” $P_{1\,-1}(\\Lambda^{r|s}(V)\\oplus \\Lambda^{s|rs}(\\Pi V))$\, with weights $+1\, −1$. Here $\\Lambda^{r|s}(V)$ denotes the $(r| s)$th exterior power of a superspace $V$ and $\\Pi$ is the parity reversi on functor. We identify the super analog of Pluecker coordinates and show that our map is an embedding. We investigate the super analog of the Pluec ker relations. We obtain them for arbitrary $r|s$ and $n|m$. The case $r|0 $ is relevant for conjectural super cluster algebras. Also\, we consider a nother type of relations suggested by H. Khudaverdian and show that they a re equivalent to (super) Pluecker relations for $r|s = 2|0$ (this is new e ven 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://researchseminars.org/talk/BIRS-21w5505/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Werner Seiler (Kassel University) DTSTART:20211126T160000Z DTEND:20211126T164500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/24 DESCRIPTION:Title: Singularities of General systems of differential equations\nby W erner Seiler (Kassel University) as part of BIRS workshop:Moving Frames an d their Modern Applications\n\n\nAbstract\nThe classical\, differential to pological theory of singularities of \ndifferential equations is mainly co ncerned with scalar ordinary \ndifferential equations of first or second o rder with an emphasis on \nclassifications and normal forms. We present an extension of the basic \ndefinitions to arbitrary systems of ordinary or partial differential \nequations based on Vessiot theory and some of the a rising open problems. \nWe also relate these results with the notion of a "regular differential \nequation" - a standard assumption in the geometric theory of \ndifferential equations which is rarely made rigorous. If time permits\, \nwe will also discuss the question of how the theory can be ef fective\, \ni.e. translated into algebraic algorithms for detecting singul arities \nand for analysing the local solution behaviour.\n\n(Much of the talk is based on the recent article Lange-Hegermann\, \nRobertz\, Seiler\, Seiss: Singularities of Algebraic Differential \nEquations\, Adv. Appl. M ath. 131 (2021) 102266.)\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Roman Popovych (University of Vienna) DTSTART:20211126T164500Z DTEND:20211126T173000Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/25 DESCRIPTION:Title: Method of moving frames and computing generalized Casimir operators< /a>\nby Roman Popovych (University of Vienna) as part of BIRS workshop:Mov ing Frames and their Modern Applications\n\n\nAbstract\nWe discuss the app lication of the method of moving frames to computing\ngeneralized Casimir operators of Lie algebras\, i.e.\, invariants of the\ncoadjoint representa tions of such algebras. We also review results on\nusing the obtained pure ly algebraic algorithm for finding generalized\nCasimir operators of low-d imensional Lie algebras and series of\nsolvable Lie algebras with specific structure of their nilradicals\, in\nparticular\, of the Lie algebras of triangular and strictly triangular\nmatrices of an arbitrary fixed dimensi on.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Illia Hayes (Utah State University) DTSTART:20211126T180000Z DTEND:20211126T184500Z DTSTAMP:20260422T185904Z UID:BIRS-21w5505/26 DESCRIPTION:Title: Joint invariants of primitive actions\nby Illia Hayes (Utah Stat e University) as part of BIRS workshop:Moving Frames and their Modern Appl ications\n\n\nAbstract\nWe consider the problem of finding a complete 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 si mple and the primitive actions have been classified by Golubitsky. We will present a reduction theorem that simplifies the problem of finding invari ants and apply it to finding two point invariants in $SU(2)$\, and $SL(2)$ .\n LOCATION:https://researchseminars.org/talk/BIRS-21w5505/26/ END:VEVENT END:VCALENDAR