BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joseph Palmer (University of Illinois\, Urbana-Champaign) DTSTART:20210503T150000Z DTEND:20210503T152500Z DTSTAMP:20260422T212928Z UID:JGPW2021/1 DESCRIPTION:Title: Hamiltonian $S^1$-spaces\, semitoric integrable systems\, and hyperbolic singularities\nby Joseph Palmer (University of Illinois\, Urbana-Champ aign) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nA Hamilt onian action of $S^1$ on a symplectic 4-manifold comes with a real valued Hamiltonian function $J$. When we can we find a smooth map $H$ such that $ (J\,H)$ is an integrable system? Moreover\, what can we say about the prop erties of the resulting system $(J\,H)$ in different situations? We explor e these questions and how their answers relates to toric integrable system s\, semitoric integrable systems\, and a class of integrable systems with hyperbolic singularities which generalize semitoric systems. This is joint work with S. Hohloch.\n LOCATION:https://researchseminars.org/talk/JGPW2021/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Abasheva (Columbia University\; Higher School of Economics) DTSTART:20210503T153000Z DTEND:20210503T155500Z DTSTAMP:20260422T212928Z UID:JGPW2021/2 DESCRIPTION:Title: Non-algebraicity of hypercomplex nilmanifolds\nby Anna Abasheva (Colu mbia University\; Higher School of Economics) as part of Junior Global Poi sson Workshop II\n\n\nAbstract\nThis is a joint work with Misha Verbitsky\ , arXiv:2103.05528\n\nA hypercomplex manifold $X$ is a manifold equipped w ith an action of the quaternion algebra on its tangent bundle satisfying a n integrability condition. Every hypercomplex manifold has a whole 2-spher e of complex structures\; in this way it makes sense to talk about a gener ic complex structure $L$ on a $X$. It turns out that if $X$ is a compact hyperkähler manifold then the complex manifold $X_L$ is non-algebraic for a generic complex structure (Fujiki\, 87). Furthermore\, $X_L$ admits no rational non-trivial morphisms onto an algebraic variety ( = “algebraic dimension of $X_L$ vanishes”). By a later result by Misha Verbitsky (199 5) all the subvarieties of $X_L$ for a generic $L$ are trianalytic\, namel y\, they are complex analytic with respect to every complex structure. Con sequently\, $X_L$ doesn’t contain even-dimensional subvarieties (f.e. cu rves and divisors).\n\nIt might be tempting to conjecture that similar ass ertions hold for hypercomplex manifolds\; this is\, however\, false in gen eral. Nevertheless\, the first assertion turns out to hold for so called h ypercomplex nilmanifolds. A nilmanifold is a quotient of a nilpotent Lie g roup by a lattice. A left-invariant (hyper)complex structure on a Lie grou p is inherited by the quotient\; in this way it makes sense to talk about (hyper)complex nilmanifolds. Complex nilmanifolds are non-Kähler\, except for complex tori. Under an additional assumption on a hypercomplex nilman ifold (the existence of an HKT-structure) we are able to prove the asserti on about subvarieties. Moreover\, we provide a classification of trianalyt ic subvarieties in this case. My talk will be dedicated to the explanation of these results.\n LOCATION:https://researchseminars.org/talk/JGPW2021/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Kryczka (LAREMA\, University of Angers) DTSTART:20210503T160000Z DTEND:20210503T162500Z DTSTAMP:20260422T212928Z UID:JGPW2021/3 DESCRIPTION:Title: Local gauge field theory from the perspective of non-linear PDE geometry< /a>\nby Jacob Kryczka (LAREMA\, University of Angers) as part of Junior Gl obal Poisson Workshop II\n\n\nAbstract\nHigher structures and derived geom etry have become ubiquitous tools when studying the mathematics of quantum field theory. Specifically\, shifted Poisson structures and their quantiz ation have found application in quantum field and string theory with deriv ed symplectic geometry providing a powerful reinterpretation of the AKSZ f ormalism.\n\nIn the most `basic' setting\, these notions appear when descr ibing the homotopical space of critical points of an action functional.\nR ather than start with the critical locus\, we would like to study the corr esponding space of solutions of the equation of motion and the natural geo metric structures it possesses. The upshot of this type of an approach is that we can study non-linear PDEs which are not necessarily of Euler-Lagra nge form.\n\nIn my talk I will describe a functorial approach to non-linea r PDEs in the presence of symmetries. We will pay special attention to des cribing gauge field theories and the derived covariant phase space\, equip ped with its canonical shifted symplectic form.\n LOCATION:https://researchseminars.org/talk/JGPW2021/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Alejandro Barbosa Torres (University of Sao Paulo-IME) DTSTART:20210503T163000Z DTEND:20210503T165500Z DTSTAMP:20260422T212928Z UID:JGPW2021/4 DESCRIPTION:Title: Equivariant Cohomology Models for Differentiable Stacks\nby Luis Alej andro Barbosa Torres (University of Sao Paulo-IME) as part of Junior Globa l Poisson Workshop II\n\n\nAbstract\nWe introduce the concept of equivaria nt cohomology in the smooth manifold case and the notion of differentiable stacks. Then we consider an action of a Lie group on a differentiable sta ck in the sense of Romagny and consider the stacky quotient associated to this action. Consequently\, we construct an atlas that makes these stacky quotient a differentiable stack. Using that the nerve of the associated Li e groupoid of that stack gives its the homotopy type\, we provide a Borel model for equivariant cohomology in this context. In order to follow the c lassical approach for equivariant cohomology\, we build a Cartan model for differentiable stacks and we prove that both models compute the same coho mology as the proposed by the Borel model.\n LOCATION:https://researchseminars.org/talk/JGPW2021/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Geoffrey Scott DTSTART:20210503T181500Z DTEND:20210503T190000Z DTSTAMP:20260422T212928Z UID:JGPW2021/5 DESCRIPTION:Title: Professional Development Session\nby Geoffrey Scott as part of Junior Global Poisson Workshop II\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/JGPW2021/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephane Geudens (KU Leuven) DTSTART:20210504T080000Z DTEND:20210504T082500Z DTSTAMP:20260422T212928Z UID:JGPW2021/6 DESCRIPTION:Title: The Poisson saturation of regular submanifolds\nby Stephane Geudens ( KU Leuven) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nI w ill talk about a class of submanifolds in Poisson geometry\, which are def ined in terms of a constant rank condition. Their main feature is the fact that their local Poisson saturation is smooth. I will give a normal form for the Poisson structure on the local saturation\, and discuss some conse quences.\n LOCATION:https://researchseminars.org/talk/JGPW2021/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Karoline van Gemst (University of Sheffield) DTSTART:20210504T083000Z DTEND:20210504T085500Z DTSTAMP:20260422T212928Z UID:JGPW2021/7 DESCRIPTION:Title: Frobenius manifolds\, mirror symmetry and integrable systems\nby Karo line van Gemst (University of Sheffield) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nFrobenius manifolds were introduced by Boris Du brovin in the early 90’s as a means to describe 2-dimensional topologica l field theories in a coordinate-free way. Now\, however\, they arise in s eemingly very distant mathematical areas and provide a bridge between them . Examples of such topics are enumerative geometry\, singularity theory an d integrable systems. In fact\, mirror symmetry can be phrased as an isomo rphism of Frobenius manifolds. \n\nIn this talk I will give a brief overvi ew of what a Frobenius manifold is and how they are useful in the context of mirror symmetry. I will then present recent results obtained together w ith Andrea Brini. Lastly\, I will highlight the connection between Frobeni us manifolds and integrable systems\, and an application of our mirror the orem in this context.\n\nhttps://arxiv.org/abs/2103.12673\n LOCATION:https://researchseminars.org/talk/JGPW2021/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Sechin (Skoltech) DTSTART:20210504T090000Z DTEND:20210504T092500Z DTSTAMP:20260422T212928Z UID:JGPW2021/8 DESCRIPTION:Title: Quantum R-matrix identities and Interacting Integrable Tops\nby Ivan Sechin (Skoltech) as part of Junior Global Poisson Workshop II\n\n\nAbstra ct\nIntegrability of classical integrable systems\, for example\, multi-pa rticle Calogero–Moser system\, is based on some functional identities on rational\, trigonometric\, or elliptic functions\, which ensure the exist ence of Lax pair and the Poisson commutativity of integrals of motion. It appears that some quantum R-matrices satisfy the matrix analogues of the r elations\, known as associative Yang–Baxter equation and its degeneratio ns. This fact allows us to use such quantum R-matrices in Lax pairs instea d of scalar functions and construct new classical integrable systems.\n\nI will describe the example of the application of quantum R-matrices relati ons in classical integrability\, introducing the system of interacting int egrable tops\, generalizing both Calogero–Moser systems of particles and Euler tops. I will also show how the resulting integrable structures simu ltaneously contain the properties of particle and top systems. If time per mits\, I briefly discuss the quantization of these structures\, in the ell iptic case it leads to quadratic quantum algebras which generalize both Sk lyanin algebra and Felder elliptic quantum group.\n LOCATION:https://researchseminars.org/talk/JGPW2021/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Irina Bobrova (HSE University) DTSTART:20210504T093000Z DTEND:20210504T095500Z DTSTAMP:20260422T212928Z UID:JGPW2021/9 DESCRIPTION:Title: On some structures of the second Painlevé equation and related hierarchi es\nby Irina Bobrova (HSE University) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nThis talk is divided into two parts. The first part is general: we will discuss what the Painlevé equations are and wha t structures they have\, namely integrability\, confluences\, Hamiltonian structures\, sigma-coordinates and symmetries. In the second part\, we wil l consider some integrable hierarchies associated with the second Painlev é equation\, their sigma-coordinates\, symmetries\, and further generaliz ations to non-commutative cases.\n\nhttps://arxiv.org/abs/2010.10617\, htt ps://arxiv.org/abs/2012.11010\n LOCATION:https://researchseminars.org/talk/JGPW2021/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Mazzocco (University of Birmingham) DTSTART:20210505T133000Z DTEND:20210505T144500Z DTSTAMP:20260422T212928Z UID:JGPW2021/10 DESCRIPTION:Title: A lecture on quantisation\nby Marta Mazzocco (University of Birmingh am) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nIn this le cture I will discuss some elementary ideas related to quantisation leading to finding the famous KZ equation by quantising co-adjoint orbits in a ve ry simple and explicit example.\n LOCATION:https://researchseminars.org/talk/JGPW2021/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Augusto Bassani Varea (USP) DTSTART:20210505T150000Z DTEND:20210505T152500Z DTSTAMP:20260422T212928Z UID:JGPW2021/11 DESCRIPTION:Title: Invariant generalized complex structures on flag manifolds\nby Carlo s Augusto Bassani Varea (USP) as part of Junior Global Poisson Workshop II \n\n\nAbstract\nThe aim of this talk is to describe the invariant generali zed complex structures look on a maximal flag manifold in terms of a fixed root system associated to the complex semisimple Lie algebra determining the flag manifold. This is a joint work with Luiz A. B. San Martin.\n LOCATION:https://researchseminars.org/talk/JGPW2021/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Fridrich Valach (Imperial College London) DTSTART:20210505T153000Z DTEND:20210505T155500Z DTSTAMP:20260422T212928Z UID:JGPW2021/12 DESCRIPTION:Title: On a generalisation of Lie and Courant algebroids\, and its application to exceptional generalised geometry\nby Fridrich Valach (Imperial Coll ege London) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nI will introduce and discuss the notion of G-algebroids. These objects provi de a common generalisation for Lie\, Courant\, and a special class of Leib niz algebroids used in exceptional generalised geometry (the 3 classes cor respond to taking G to be the A\, D\, E simple groups\, respectively). I w ill present a classification result in the exact case and provide an algeb roid formulation for the recently introduced Poisson–Lie U-duality. This is a joint work arXiv:2103.01139 with M. Bugden\, O. Hulik\, and D. Waldr am.\n LOCATION:https://researchseminars.org/talk/JGPW2021/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiudi Tang (University of Toronto) DTSTART:20210505T160000Z DTEND:20210505T162500Z DTSTAMP:20260422T212928Z UID:JGPW2021/13 DESCRIPTION:Title: Symplectic excision\nby Xiudi Tang (University of Toronto) as part o f Junior Global Poisson Workshop II\n\n\nAbstract\nWe consider closed subs ets of a noncompact symplectic manifold and determine when they can be rem oved by a symplectomorphism\, in which case we say the subsets are symplec tically excisable. We prove that\, in the case of a ray and more generally \, the embedding of the epigraph of a lower semi-continuous function\, the re is a time-independent Hamiltonian flow that excises it from a noncompac t symplectic manifold.\n\nhttps://arxiv.org/abs/2101.03534\n LOCATION:https://researchseminars.org/talk/JGPW2021/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Zapata-Carratala (University of Edinburgh) DTSTART:20210505T163000Z DTEND:20210505T165500Z DTSTAMP:20260422T212928Z UID:JGPW2021/14 DESCRIPTION:Title: Poly-Jacobi Geometry: a Serendipitous Discovery\nby Carlos Zapata-Ca rratala (University of Edinburgh) as part of Junior Global Poisson Worksho p II\n\n\nAbstract\nWith motivations in the implementation of physical dim ension into geometric mechanics\, I will introduce the formalism of dimens ioned algebra and the unit-free approach to Jacobi geometry. These will be shown to lead to a natural generalization of Jacobi/Poisson geometry wher e many constructions\, such as products and quotients\, become much more n atural. Finally\, I will present a breadth of structures\, tentatively cal led Poly-Jacobi\, which are natural to define within this formalism but do n't seem to have been identified in the Poisson literature.\n LOCATION:https://researchseminars.org/talk/JGPW2021/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Alekseev (University of Geneva) DTSTART:20210506T140000Z DTEND:20210506T150000Z DTSTAMP:20260422T212928Z UID:JGPW2021/15 DESCRIPTION:Title: Poisson and Quasi-Poisson Structureson Moduli Spaces of Connections\ nby Anton Alekseev (University of Geneva) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nThe purpose of a topic-based discussion sessio n is to discuss some open problems\, questions\, and vision in a subtopic of Poisson geometry with junior researchers being the target audience. The main goal is to make the discussion informal and friendly\, and to formul ate some open problems in a simple way that young researchers can understa nd and get excited about.\n LOCATION:https://researchseminars.org/talk/JGPW2021/15/ END:VEVENT END:VCALENDAR