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:20260404T094310Z UID:JGPW2021/1 DESCRIPTION:Title: Hamiltonian $S^1$-spaces\, semitoric integrable systems\, and hype rbolic singularities\nby Joseph Palmer (University of Illinois\, Urban a-Champaign) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nA Hamiltonian 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 t he properties of the resulting system $(J\,H)$ in different situations? We explore these questions and how their answers relates to toric integrable systems\, semitoric integrable systems\, and a class of integrable system s with hyperbolic singularities which generalize semitoric systems. This i s joint work with S. Hohloch.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Abasheva (Columbia University\; Higher School of Economics) DTSTART:20210503T153000Z DTEND:20210503T155500Z DTSTAMP:20260404T094310Z UID:JGPW2021/2 DESCRIPTION:Title: Non-algebraicity of hypercomplex nilmanifolds\nby Anna Abashev a (Columbia University\; Higher School of Economics) as part of Junior Glo bal Poisson Workshop II\n\n\nAbstract\nThis is a joint work with Misha Ver bitsky\, arXiv:2103.05528\n\nA hypercomplex manifold $X$ is a manifold equ ipped with an action of the quaternion algebra on its tangent bundle satis fying an integrability condition. Every hypercomplex manifold has a whole 2-sphere of complex structures\; in this way it makes sense to talk about a generic complex structure $L$ on a $X$. It turns out that if $X$ is a c ompact hyperkähler manifold then the complex manifold $X_L$ is non-algebr aic for a generic complex structure (Fujiki\, 87). Furthermore\, $X_L$ adm its no rational non-trivial morphisms onto an algebraic variety ( = “alg ebraic dimension of $X_L$ vanishes”). By a later result by Misha Verbits ky (1995) all the subvarieties of $X_L$ for a generic $L$ are trianalytic\ , namely\, they are complex analytic with respect to every complex structu re. Consequently\, $X_L$ doesn’t contain even-dimensional subvarieties ( f.e. curves and divisors).\n\nIt might be tempting to conjecture that simi lar assertions hold for hypercomplex manifolds\; this is\, however\, false in general. Nevertheless\, the first assertion turns out to hold for so c alled hypercomplex nilmanifolds. A nilmanifold is a quotient of a nilpoten t Lie group by a lattice. A left-invariant (hyper)complex structure on a L ie group 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 nilmanifold (the existence of an HKT-structure) we are able to prove the assertion about subvarieties. Moreover\, we provide a classification of tr ianalytic subvarieties in this case. My talk will be dedicated to the expl anation of these results.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Kryczka (LAREMA\, University of Angers) DTSTART:20210503T160000Z DTEND:20210503T162500Z DTSTAMP:20260404T094310Z UID:JGPW2021/3 DESCRIPTION:Title: Local gauge field theory from the perspective of non-linear PDE ge ometry\nby Jacob Kryczka (LAREMA\, University of Angers) as part of Ju nior Global Poisson Workshop II\n\n\nAbstract\nHigher structures and deriv ed geometry have become ubiquitous tools when studying the mathematics of quantum field theory. Specifically\, shifted Poisson structures and their quantization have found application in quantum field and string theory wit h derived symplectic geometry providing a powerful reinterpretation of the AKSZ formalism.\n\nIn the most `basic' setting\, these notions appear whe n describing the homotopical space of critical points of an action functio nal.\nRather than start with the critical locus\, we would like to study t he corresponding space of solutions of the equation of motion and the natu ral geometric structures it possesses. The upshot of this type of an appro ach is that we can study non-linear PDEs which are not necessarily of Eule r-Lagrange form.\n\nIn my talk I will describe a functorial approach to no n-linear PDEs in the presence of symmetries. We will pay special attention to describing gauge field theories and the derived covariant phase space\ , equipped with its canonical shifted symplectic form.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Alejandro Barbosa Torres (University of Sao Paulo-IME) DTSTART:20210503T163000Z DTEND:20210503T165500Z DTSTAMP:20260404T094310Z UID:JGPW2021/4 DESCRIPTION:Title: Equivariant Cohomology Models for Differentiable Stacks\nby Lu is Alejandro Barbosa Torres (University of Sao Paulo-IME) as part of Junio r Global Poisson Workshop II\n\n\nAbstract\nWe introduce the concept of eq uivariant cohomology in the smooth manifold case and the notion of differe ntiable stacks. Then we consider an action of a Lie group on a differentia ble stack in the sense of Romagny and consider the stacky quotient associa ted to this action. Consequently\, we construct an atlas that makes these stacky quotient a differentiable stack. Using that the nerve of the associ ated Lie groupoid of that stack gives its the homotopy type\, we provide a Borel model for equivariant cohomology in this context. In order to follo w the classical approach for equivariant cohomology\, we build a Cartan mo del for differentiable stacks and we prove that both models compute the sa me cohomology as the proposed by the Borel model.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Geoffrey Scott DTSTART:20210503T181500Z DTEND:20210503T190000Z DTSTAMP:20260404T094310Z 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://stable.researchseminars.org/talk/JGPW2021/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephane Geudens (KU Leuven) DTSTART:20210504T080000Z DTEND:20210504T082500Z DTSTAMP:20260404T094310Z UID:JGPW2021/6 DESCRIPTION:Title: The Poisson saturation of regular submanifolds\nby Stephane Ge udens (KU Leuven) as part of Junior Global Poisson Workshop II\n\n\nAbstra ct\nI will talk about a class of submanifolds in Poisson geometry\, which are defined in terms of a constant rank condition. Their main feature is t he fact that their local Poisson saturation is smooth. I will give a norma l form for the Poisson structure on the local saturation\, and discuss som e consequences.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Karoline van Gemst (University of Sheffield) DTSTART:20210504T083000Z DTEND:20210504T085500Z DTSTAMP:20260404T094310Z UID:JGPW2021/7 DESCRIPTION:Title: Frobenius manifolds\, mirror symmetry and integrable systems\n by Karoline van Gemst (University of Sheffield) as part of Junior Global P oisson Workshop II\n\n\nAbstract\nFrobenius manifolds were introduced by B oris Dubrovin in the early 90’s as a means to describe 2-dimensional top ological field theories in a coordinate-free way. Now\, however\, they ari se in seemingly very distant mathematical areas and provide a bridge betwe en them. Examples of such topics are enumerative geometry\, singularity th eory and integrable systems. In fact\, mirror symmetry can be phrased as a n isomorphism of Frobenius manifolds. \n\nIn this talk I will give a brief overview of what a Frobenius manifold is and how they are useful in the c ontext of mirror symmetry. I will then present recent results obtained tog ether with Andrea Brini. Lastly\, I will highlight the connection between Frobenius manifolds and integrable systems\, and an application of our mir ror theorem in this context.\n\nhttps://arxiv.org/abs/2103.12673\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Sechin (Skoltech) DTSTART:20210504T090000Z DTEND:20210504T092500Z DTSTAMP:20260404T094310Z UID:JGPW2021/8 DESCRIPTION:Title: Quantum R-matrix identities and Interacting Integrable Tops\nb y Ivan Sechin (Skoltech) as part of Junior Global Poisson Workshop II\n\n\ nAbstract\nIntegrability of classical integrable systems\, for example\, m ulti-particle Calogero–Moser system\, is based on some functional identi ties on rational\, trigonometric\, or elliptic functions\, which ensure th e existence of Lax pair and the Poisson commutativity of integrals of moti on. It appears that some quantum R-matrices satisfy the matrix analogues o f the relations\, known as associative Yang–Baxter equation and its dege nerations. This fact allows us to use such quantum R-matrices in Lax pairs instead of scalar functions and construct new classical integrable system s.\n\nI will describe the example of the application of quantum R-matrices relations in classical integrability\, introducing the system of interact ing integrable tops\, generalizing both Calogero–Moser systems of partic les and Euler tops. I will also show how the resulting integrable structur es simultaneously contain the properties of particle and top systems. If t ime permits\, I briefly discuss the quantization of these structures\, in the elliptic case it leads to quadratic quantum algebras which generalize both Sklyanin algebra and Felder elliptic quantum group.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Irina Bobrova (HSE University) DTSTART:20210504T093000Z DTEND:20210504T095500Z DTSTAMP:20260404T094310Z UID:JGPW2021/9 DESCRIPTION:Title: On some structures of the second Painlevé equation and related hi erarchies\nby Irina Bobrova (HSE University) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nThis talk is divided into two parts. Th e first part is general: we will discuss what the Painlevé equations are and what structures they have\, namely integrability\, confluences\, Hamil tonian structures\, sigma-coordinates and symmetries. In the second part\, we will consider some integrable hierarchies associated with the second P ainlevé equation\, their sigma-coordinates\, symmetries\, and further gen eralizations to non-commutative cases.\n\nhttps://arxiv.org/abs/2010.10617 \, https://arxiv.org/abs/2012.11010\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Mazzocco (University of Birmingham) DTSTART:20210505T133000Z DTEND:20210505T144500Z DTSTAMP:20260404T094310Z UID:JGPW2021/10 DESCRIPTION:Title: A lecture on quantisation\nby Marta Mazzocco (University of B irmingham) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nIn this lecture I will discuss some elementary ideas related to quantisation leading to finding the famous KZ equation by quantising co-adjoint orbits in a very simple and explicit example.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Augusto Bassani Varea (USP) DTSTART:20210505T150000Z DTEND:20210505T152500Z DTSTAMP:20260404T094310Z UID:JGPW2021/11 DESCRIPTION:Title: Invariant generalized complex structures on flag manifolds\nb y Carlos Augusto Bassani Varea (USP) as part of Junior Global Poisson Work shop II\n\n\nAbstract\nThe aim of this talk is to describe the invariant g eneralized complex structures look on a maximal flag manifold in terms of a fixed root system associated to the complex semisimple Lie algebra dete rmining the flag manifold. This is a joint work with Luiz A. B. San Martin .\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Fridrich Valach (Imperial College London) DTSTART:20210505T153000Z DTEND:20210505T155500Z DTSTAMP:20260404T094310Z UID:JGPW2021/12 DESCRIPTION:Title: On a generalisation of Lie and Courant algebroids\, and its appli cation to exceptional generalised geometry\nby Fridrich Valach (Imperi al College London) as part of Junior Global Poisson Workshop II\n\n\nAbstr act\nI will introduce and discuss the notion of G-algebroids. These object s provide a common generalisation for Lie\, Courant\, and a special class of Leibniz algebroids used in exceptional generalised geometry (the 3 clas ses correspond to taking G to be the A\, D\, E simple groups\, respectivel y). I will present a classification result in the exact case and provide a n algebroid formulation for the recently introduced Poisson–Lie U-dualit y. This is a joint work arXiv:2103.01139 with M. Bugden\, O. Hulik\, and D . Waldram.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiudi Tang (University of Toronto) DTSTART:20210505T160000Z DTEND:20210505T162500Z DTSTAMP:20260404T094310Z UID:JGPW2021/13 DESCRIPTION:Title: Symplectic excision\nby Xiudi Tang (University of Toronto) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nWe consider clos ed subsets of a noncompact symplectic manifold and determine when they can be removed by a symplectomorphism\, in which case we say the subsets are symplectically excisable. We prove that\, in the case of a ray and more ge nerally\, the embedding of the epigraph of a lower semi-continuous functio n\, there is a time-independent Hamiltonian flow that excises it from a no ncompact symplectic manifold.\n\nhttps://arxiv.org/abs/2101.03534\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Zapata-Carratala (University of Edinburgh) DTSTART:20210505T163000Z DTEND:20210505T165500Z DTSTAMP:20260404T094310Z UID:JGPW2021/14 DESCRIPTION:Title: Poly-Jacobi Geometry: a Serendipitous Discovery\nby Carlos Za pata-Carratala (University of Edinburgh) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nWith motivations in the implementation of physi cal dimension into geometric mechanics\, I will introduce the formalism of dimensioned algebra and the unit-free approach to Jacobi geometry. These will be shown to lead to a natural generalization of Jacobi/Poisson geomet ry where many constructions\, such as products and quotients\, become much more natural. Finally\, I will present a breadth of structures\, tentativ ely called Poly-Jacobi\, which are natural to define within this formalism but don't seem to have been identified in the Poisson literature.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Alekseev (University of Geneva) DTSTART:20210506T140000Z DTEND:20210506T150000Z DTSTAMP:20260404T094310Z UID:JGPW2021/15 DESCRIPTION:Title: Poisson and Quasi-Poisson Structureson Moduli Spaces of Connectio ns\nby Anton Alekseev (University of Geneva) as part of Junior Global Poisson Workshop II\n\n\nAbstract\nThe purpose of a topic-based discussion session is to discuss some open problems\, questions\, and vision in a su btopic of Poisson geometry with junior researchers being the target audien ce. The main goal is to make the discussion informal and friendly\, and to formulate some open problems in a simple way that young researchers can u nderstand and get excited about.\n LOCATION:https://stable.researchseminars.org/talk/JGPW2021/15/ END:VEVENT END:VCALENDAR