\nIn the variational calculus\, the action functio nal is the integral of a local expression in the fields and their derivati ves. The symmetries of the action may be expressed by the classical Batali n-Vilkovisky master equation\, which is a Maurer-Cartan equation for funct ionals of the classical fields\, ghost fields expressing the symmetries of the theory\, and certain auxilliary fields known as antifields.\n

\nThe Batalin-Vilkovisky formalism has a natural extension in functionals are lifted to densities. In the first part of today's talk\, I explain thi s extension. which relies on the Soloviev bracket in the variational calcu lus\, originally introduced in the study of general relativity.\n

\ nSymmetries of a field theory involving diffeomorphisms of the world sheet do not really fit into the formalism of the variational calculus. In my a rticle ""Covariance in the Batalin-Vilkovisky formalism""\, I explain ho w to take into account such symmetries of the world sheet by incorporating a curvature term into the Batalin-Vilkovisky master equation\, associated to a differential graded Lie algebra with curvature. This construction is the subject of the second part of the talk.\n

\nI will finish with a few words on the work of Bonechi\, Cattaneo\, Qiu and Zabzine\, who stu died the extension of our formalism to quantum field theory."\n LOCATION:https://researchseminars.org/talk/globalpoisson/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Lisa Jeffrey (University of Toronto) DTSTART;VALUE=DATE-TIME:20201210T161500Z DTEND;VALUE=DATE-TIME:20201210T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/24 DESCRIPTION:Title: Flat connections and the $SU(2)$ commutator map\nby Lisa Jeffr ey (University of Toronto) as part of Global Poisson webinar\n\n\nAbstract \nThis talk is joint work with Nan-Kuo Ho\, Paul Selick and Eugene Xia. We describe the space of conjugacy classes of representations of the fundame ntal group of a genus 2 oriented 2-manifold into $G:=SU(2)$. \n\n1. We ide ntify the cohomology ring and a cell decomposition of a space homotopy equ ivalent to the space of commuting pairs in $SU(2)$. \n2. We compute the co homology of the space $M:=\\mu^{-1}(-I)$ where $\\mu: G^4 \\to G$ is the p roduct of commutators. \n3. We give a new proof of the cohomology of $A:=M /G$\, both as a group and as a ring. The group structure is due to Atiyah and Bott in their landmark 1983 paper. The ring structure is due to Michae l Thaddeus 1992. \n4. We compute the cohomology of the total space of the prequantum line bundle over $A$. \n5. We identify the transition functions of the induced SO(3) bundle $M\\to A$. \n\nTo appear in QJM (Atiyah memor ial special issue). arXiv:2005.07390\n LOCATION:https://researchseminars.org/talk/globalpoisson/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonid Polterovich (Tel Aviv University) DTSTART;VALUE=DATE-TIME:20201105T161500Z DTEND;VALUE=DATE-TIME:20201105T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/25 DESCRIPTION:Title: Approximate representations and quantization\nby Leonid Polter ovich (Tel Aviv University) as part of Global Poisson webinar\n\n\nAbstrac t\nWe discuss some links between Ulam-type stability for algebras and gr oups ("approximate representations are close to genuine representations") and quantization\, with applications to classification of quantizations and Hamiltonian actions of finitely presented groups. (with L.Charles\, L .Ioos\, D.Kazhdan).\n LOCATION:https://researchseminars.org/talk/globalpoisson/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Vitagliano (University of Salerno) DTSTART;VALUE=DATE-TIME:20201112T161500Z DTEND;VALUE=DATE-TIME:20201112T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/26 DESCRIPTION:Title: Calculus up to Homotopy on the Space of Solutions of a PDE\nby Luca Vitagliano (University of Salerno) as part of Global Poisson webinar\ n\n\nAbstract\nEvery partial differential equation (PDE) can be encoded in a geometric object\, what is sometimes called a diffiety\, which is a sub manifold of an appropriate type in an infinite jet space. There is a Lie a lgebroid naturally attached to a diffiety\, and the associated Lie algebro id cohomology contains important coordinate independent information on the PDE: variational principles\, symmetries\, conservation laws\, recursion operators\, etc. To some extent these cohomologies can also be interpreted as vector fields\, differential forms\, tensors\, etc. on the space of so lutions. This interpretation is supported by the fact that we find the app ropriate algebraic structures in cohomology. I will review this theory and show that those algebraic structures do actually come from homotopy algeb ras at the level of cochains\, confirming an old conjecture of A. M. Vinog radov that “the calculus on the space of solutions of a PDE is a calculu s up to homotopy”.\n LOCATION:https://researchseminars.org/talk/globalpoisson/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Megumi Harada (McMaster University) DTSTART;VALUE=DATE-TIME:20201126T161500Z DTEND;VALUE=DATE-TIME:20201126T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/27 DESCRIPTION:Title: Newton-Okounkov bodies\, integrable systems\, and convergence of po larizations\nby Megumi Harada (McMaster University) as part of Global Poisson webinar\n\n\nAbstract\nLet $X$ be a smooth irreducible complex alg ebraic variety of dimension $n$ and $L$ a very ample Hermitian line bundle . In this talk I will recount\, in very broad strokes\, two interconnected stories related to the symplectic geometry of $X$. The first story is tha t the theory of Newton-Okounkov bodies\, and the toric degenerations to w hich they give rise\, can provide -- in rather general situations -- const ructions of integrable systems on $X$. The main tool in the first story is the gradient-Hamiltonian vector field. The second story concerns the ``in dependence of polarization'' issue which arises in the theory of geometric quantization. Specifically\, given a toric degeneration of $(X\,L)$ satis fying some technical hypotheses\, we construct a deformation $\\{J_s\\}$ o f the complex structure on $X$ and bases $B_s$ of $H^0(X\, L\, J_s)$ so t hat $J_0$ is the standard complex structure and\, in the limit as $s \\to \\infty$\, the basis elements approach dirac-delta distributions centered at Bohr-Sommerfeld fibers of the moment map associated to the integrable s ystem on $X$ (constructed using the first story). This significantly gene ralizes previous results in geometric quantization proving independence of polarization between Kahler quantizations and real polarizations.\n LOCATION:https://researchseminars.org/talk/globalpoisson/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Ioan Marcut (Radboud Universiteit Nijmegen) DTSTART;VALUE=DATE-TIME:20201203T161500Z DTEND;VALUE=DATE-TIME:20201203T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/28 DESCRIPTION:Title: Poisson non-degeneracy of the Lie algebra $\\mathfrak{sl}(2\,\\math bb{C})=\\mathfrak{so}(3\,1)$\nby Ioan Marcut (Radboud Universiteit Nij megen) as part of Global Poisson webinar\n\n\nAbstract\n"In this talk\, I will revisit the classical problem of linearizing Poisson structures aroun d fixed points\, introduced by Alan Weinstein. If\nthe isotropy Lie algebr a at the fixed point is semi-simple\, the problem has been settled in most cases\, through the works of Conn\, Weinstein\, Monnier and Zung. The low est dimensional semi-simple Lie algebra for which the problem was still op en is $\\mathfrak{sl}(2\,\\mathbb{C})=\\mathfrak{so}(3\,1)$. Together with my PhD student Florian Zeiser we have shown that $\\mathfrak{sl}(2\,\\mat hbb{C})$ is the first non-compact semi-simple Lie algebra that is Poisson non-degenerate""\, in the sense that a version of Conn's theorem holds for this Lie algebra. I will explain the main ingredients of the proof."""\n LOCATION:https://researchseminars.org/talk/globalpoisson/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Marius Crainic (Utrecht University) DTSTART;VALUE=DATE-TIME:20201217T161500Z DTEND;VALUE=DATE-TIME:20201217T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/29 DESCRIPTION:Title: From Poisson Geometry to (almost) geometric structures\nby Mari us Crainic (Utrecht University) as part of Global Poisson webinar\n\n\nAbs tract\nI will report on an approach to general geometric structures (with an eye on integrability) based on groupoids endowed with multiplicative st ructures\; Poisson geometry (with its symplectic groupoids\, Hamiltonian t heories and Morita equivalences) will provide us with some guiding princip les. This allows one to discuss general "almost structures" and an integra bility theorem based on Nash-Moser techniques (and this also opens up the way for a general "smooth Cartan-Kahler theorem"). This report is based on collaborations/discussions with Francesco Cataffi (almost structures)\, I oan Marcut (Nash-Moser techniques)\, Maria Amelia Salzar (Pfaffian groupoi ds).\n LOCATION:https://researchseminars.org/talk/globalpoisson/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Melrose (MIT) DTSTART;VALUE=DATE-TIME:20210114T161500Z DTEND;VALUE=DATE-TIME:20210114T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/30 DESCRIPTION:Title: Resolution of Lie algebroids and quantization\nby Richard Melro se (MIT) as part of Global Poisson webinar\n\n\nAbstract\nI will give an o verview of what is known about the resolution of Lie algebroids -- limited for the most part to the `geometric case' of a subalgebra of the Lie alge bra of vector fields on a manifold. This gives a direct quantization with corresponding algebras (and modules) of pseudodifferential operators. In p articular I will make the case that the notion of a groupoid is inadequate here even though there is as yet no precise replacement for it.\n LOCATION:https://researchseminars.org/talk/globalpoisson/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergei Tabachnikov (Penn State) DTSTART;VALUE=DATE-TIME:20210121T161500Z DTEND;VALUE=DATE-TIME:20210121T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/31 DESCRIPTION:Title: Cross-ratio dynamics on ideal polygons\nby Sergei Tabachnikov ( Penn State) as part of Global Poisson webinar\n\n\nAbstract\nDefine a rela tion between labeled ideal polygons in the hyperbolic space by requiring t hat the complex distances (a combination of the distance and the angle) be tween their respective sides equal c\; the complex number c is a parameter of the relation. This defines a 1-parameter family of maps on the moduli space of ideal polygons in the hyperbolic space (or\, in its real version\ , in the hyperbolic plane). I shall discuss complete integrability of this family of maps and related topics\, including its connection with the Kor teweg-de Vries equation.\n LOCATION:https://researchseminars.org/talk/globalpoisson/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiaomeng Xu (Peking University) DTSTART;VALUE=DATE-TIME:20210128T130000Z DTEND;VALUE=DATE-TIME:20210128T140000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/33 DESCRIPTION:Title: Stokes phenomenon and quantum Ginzburg-Weinstein isomorphisms\n by Xiaomeng Xu (Peking University) as part of Global Poisson webinar\n\n\ nAbstract\nThis talk first gives an introduction to the Stokes matrices of meromorphic linear systems of ordinary differential equations. It then us es the quantum Stokes matrices to construct the quantization of a family o f Ginzburg-Weinstein isomorphisms from ${\\frak g \\frak l}_n^*$ to the du al Poisson Lie group ${\\rm GL}_n^*$ found by Boalch. In the end\, it give s explicit formula for the quantization\, as special Drinfeld isomorphisms from the quantum group $U_\\hbar({\\frak g \\frak l}_n)$ to the classical $U({\\frak g \\frak l}_n)$\, and briefly discusses the relation with repr esentation theory of quantum groups.\n LOCATION:https://researchseminars.org/talk/globalpoisson/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Edward Witten (Institute for Advanced Study) DTSTART;VALUE=DATE-TIME:20210211T161500Z DTEND;VALUE=DATE-TIME:20210211T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/34 DESCRIPTION:Title: Quantization by Branes and Geometric Langlands\nby Edward Witte n (Institute for Advanced Study) as part of Global Poisson webinar\n\n\nAb stract\nIn this talk\, which is based on work with D. Gaiotto\, I will exp lain a quantum field theory perspective on recent developments in the geom etric Langlands program by P. Etinghof\, E. Frenkel\, and D. Kazhdan (see their paper https://arxiv.org/abs/1908.09677).\n LOCATION:https://researchseminars.org/talk/globalpoisson/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Chenchang Zhu (Göttingen) DTSTART;VALUE=DATE-TIME:20210218T161500Z DTEND;VALUE=DATE-TIME:20210218T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/35 DESCRIPTION:Title: Classifying space $BG$ as a symplectic stack\nby Chenchang Zhu (Göttingen) as part of Global Poisson webinar\n\n\nAbstract\nIt is proba bly well known to people who know it well that $BG$ carries a sort of sym plectic structure\, if the Lie algebra of $G$ is quadratic Lie algebra. In this talk\, we explore various differential-geometric (1-group\, 2-grou p\, double-group) models to realise this (2-shift) symplectic structure in concrete formulas and show the equivalences between them.\n\nIn the infin ite dimensional models (2-group\, double-group)\, Segal's symplectic form on based loop groups turns out to be additionally multiplicative or almost so. These models are equivalent to a finite dimensional model with Carta n 3-form and Karshon-Weinstein 2-form via Morita Equivalence. All these fo rms give rise to the first Pontryagin class on $BG$. Moreover\, they are r elated to the original invariant pairing on the Lie algebra through an exp licit integration and Van Est procedure. Finally\, as you might have guess ed\, the associated String group $BString(G)$ may be seen as a prequantiza tion of this symplectic structure. From the math-physics point of view\, w hat is behind is the Chern-Simons sigma model.\n LOCATION:https://researchseminars.org/talk/globalpoisson/35/ END:VEVENT BEGIN:VEVENT SUMMARY:David Martínez Torres (PUC-Rio) DTSTART;VALUE=DATE-TIME:20210225T161500Z DTEND;VALUE=DATE-TIME:20210225T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/36 DESCRIPTION:Title: Coregular submanifolds and Poisson submersions\nby David Martí nez Torres (PUC-Rio) as part of Global Poisson webinar\n\n\nAbstract\nThis talk discusses aspects of the theory of submanifolds and submersions in P oisson geometry. In the first part we present the general picture concerni ng manifolds which inherit a Poisson structure from an ambient Poisson man ifold\, and among those\, we select a class (coregular submanifolds) which have particularly nice functorial properties. The second part is devoted to Poisson submersions with coregular fibers. Coregular submersions restri ct nicely over symplectic leaves in the base (coupling property)\, and we determine when they split into commuting vertical and horizontal Poisson s tructures. In the last part we present instances in which such coregular P oisson submersions appear. Our illustrations all revolve around Poisson ac tions of Poisson-Lie groups. This is joint work with L. Brambila and P. Fr ejlich.\n LOCATION:https://researchseminars.org/talk/globalpoisson/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Francis Bischoff (University of Oxford) DTSTART;VALUE=DATE-TIME:20210304T161500Z DTEND;VALUE=DATE-TIME:20210304T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/37 DESCRIPTION:Title: Lie Groupoids and differential equations\nby Francis Bischoff (University of Oxford) as part of Global Poisson webinar\n\n\nAbstract\nTh is talk will discuss applications of Lie groupoids to the study of differe ntial equations with singularities. Several classes of singular differenti al equations\, or flat connections\, can be recast as representations of L ie algebroids\, and by integration\, correspond to Lie groupoid representa tions. This perspective allows us to introduce new tools to the study of t hese equations. In this talk\, I will give an overview of this approach\, with a focus on the case of differential equations with logarithmic singul arities along certain (possibly singular) submanifolds that are associated to reductive groups. Whereas the traditional approach to classification r elies heavily on the use of power series\, I will explain how the use of L ie groupoids gives rise to a more geometric approach.\n LOCATION:https://researchseminars.org/talk/globalpoisson/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Zheng Hua (University of Hong Kong) DTSTART;VALUE=DATE-TIME:20210311T131500Z DTEND;VALUE=DATE-TIME:20210311T141500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/38 DESCRIPTION:Title: Semiclassical limits of Feigin-Odesskii elliptic algebras via deriv ed geometry\nby Zheng Hua (University of Hong Kong) as part of Global Poisson webinar\n\n\nAbstract\nIn 1980s\, Feigin and Odesskii constructed the elliptic algebras $Q_{n\,k}(C\,\\eta)$ generalizing the construction o f Sklyanin and Cherednik. Here n\,k are coprime positive integers\, $C$ is a complex elliptic curve and $\\eta$ is a point on $C$. Elliptic algebras are quantization of polynomial algebras. They are conjectured to be regu lar in the sense of Artin and Schelter for all parameters. Homological a nd representation theoretical properties of elliptic algebras are studied via Poisson geometry of their semiclassical limits. We will discuss variou s results about these Poisson structures\, e.g. classification of symplect ic leaves\, bihamiltonian structures and so on. The main technical tool is derived geometry\, in particular the work of Calaque-Pantev-Toen-Vaquie-V ezzosi. This is based on the joint work with Alexander Polishchuk.\n LOCATION:https://researchseminars.org/talk/globalpoisson/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Yunhe Sheng (Jilin University) DTSTART;VALUE=DATE-TIME:20210408T121500Z DTEND;VALUE=DATE-TIME:20210408T131500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/39 DESCRIPTION:Title: Deformations\, cohomology and homotopy of relative Rota-Baxter Lie algebras\nby Yunhe Sheng (Jilin University) as part of Global Poisson webinar\n\n\nAbstract\nRota-Baxter operators were originally defined on a commutative associative algebra by Rota. Then it was defined on Lie algebr as as the operator form of the classical Yang-Baxter equation. Kupershmidt introduced a more general notion called O-operator (later called relative Rota-Baxter operator) for arbitrary representation. Rota-Baxter operators have fruitful applications in mathematical physics. We determine the L- infty-algebra that characterizes relative Rota-Baxter Lie algebras as Maur er-Cartan elements. As applications\, first we determine the L-infty-algeb ra that controls deformations of a relative Rota-Baxter Lie algebra and sh ow that it is an extension of the dg Lie algebra controlling deformations of the underlying Lie algebra and representation by the dg Lie algebra con trolling deformations of the relative Rota-Baxter operator. Then we define the cohomology of relative Rota-Baxter Lie algebras and relate it to their infinitesimal deformations. In particular the cohomolgoy of Rota-B axter Lie algebras and triangular Lie bialgebras are given. Finally we int roduce the notion of homotopy relative Rota-Baxter operators and show that the underlying structure is pre-Lie-infinity algebras. This talk is based on joint works with Chenming Bai\, Li Guo\, Andrey Lazarev and Rong Tang. \n LOCATION:https://researchseminars.org/talk/globalpoisson/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Nigel Higson (Penn State) DTSTART;VALUE=DATE-TIME:20210506T151500Z DTEND;VALUE=DATE-TIME:20210506T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/40 DESCRIPTION:Title: An introduction to the hypoelliptic Laplacian\nby Nigel Higson (Penn State) as part of Global Poisson webinar\n\n\nAbstract\nJean-Michel Bismut's hypoelliptic Laplacian is a one-parameter family of linear differ ential operators that interpolates between the Laplacian and the geodesic flow. It may be constructed in a variety of contexts\, but in this lectu re I shall concentrate on symmetric spaces. Here a special mechanism comes into play\, as a result of which the heat traces associated to all the op erators in the family remain constant throughout the interpolation. By s tudying the limits at both ends of the family\, remarkable formulas are ob tained\, including for example the Selberg trace formula. All this requi res a heavy dose of analysis in the spirit of\, but more complicated than\ , the local index theory of Dirac operators. But in this talk I shall most ly ignore the analysis and concentrate on a few basic ideas\, in the hope that they may eventually lead to a more geometric understanding of the hyp oelliptic Laplacian.\n LOCATION:https://researchseminars.org/talk/globalpoisson/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiao-Jun Chen (Sichuan University) DTSTART;VALUE=DATE-TIME:20210610T121500Z DTEND;VALUE=DATE-TIME:20210610T131500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/41 DESCRIPTION:Title: Batalin-Vilkovisky and gravity algebras on Poisson manifolds with semisimple modular symmetry\nby Xiao-Jun Chen (Sichuan University) as part of Global Poisson webinar\n\n\nAbstract\nIn this talk\, we study the "twisted" Poincare duality of smooth Poisson manifolds\, and show that\, if the modular symmetry is semisimple\, that is\, the modular vector is d iagonalizable\, there is a mixed complex associated to the Poisson comple x which\, combining with the twisted Poincare duality\, gives a Batalin-V ilkovisky algebra structure on the Poisson cohomology\, and a gravity alg ebra structure on the negative cyclic Poisson homology. This generalizes the previous results obtained by Xu et al for unimodular Poisson algebras . We also show that these two algebraic structures are preserved under K ontsevich's deformation quantization\, and in the case of polynomial algeb ras they are also preserved by Koszul duality. This talk is based on a jo int work with Liu\, Yu and Zeng.\n LOCATION:https://researchseminars.org/talk/globalpoisson/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Tobias Diez (TU Delft) DTSTART;VALUE=DATE-TIME:20210318T161500Z DTEND;VALUE=DATE-TIME:20210318T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/42 DESCRIPTION:Title: Group-valued momentum maps for diffeomorphism groups\nby Tobias Diez (TU Delft) as part of Global Poisson webinar\n\n\nAbstract\nIn math ematical physics\, some conserved quantities have a discrete nature\, for example because they have a topological origin. These conservation laws ca nnot be captured by the usual momentum map. I will present a generalized n otion of a momentum map taking values in a Lie group\, which is able to in clude discrete conversed quantities. It is inspired by the Lu-Weinstein mo mentum map for Poisson Lie group actions\, but the groups involved do not necessarily have to be Poisson Lie groups. The most interesting applicatio ns include momentum maps for diffeomorphism groups which take values in gr oups of Cheeger-Simons differential characters. As an important example\, I will show that the Teichmüller space with the Weil-Petersson symplectic form can be realized as symplectic orbit reduced space.\n LOCATION:https://researchseminars.org/talk/globalpoisson/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Scheimbauer (TU München) DTSTART;VALUE=DATE-TIME:20210325T161500Z DTEND;VALUE=DATE-TIME:20210325T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/43 DESCRIPTION:Title: Derived symplectic geometry and AKSZ topological field theories \nby Claudia Scheimbauer (TU München) as part of Global Poisson webinar\ n\n\nAbstract\nDerived algebraic geometry and derived symplectic geometry in the sense of Pantev-Toen-Vaquié-Vezzosi allows for a reinterpretation/ analog of the classical AKSZ construction for certain $\\sigma$-models. Af ter recalling this procedure I will explain how it can be extended to give a fully extended oriented TFT in the sense of Lurie with values in a high er category whose objects are $n$-shifted symplectic derived stacks and (h igher) morphisms are (higher) Lagrangian correspondences. It is given by t aking mapping stacks with a fixed target building and describes ``semi-cla ssical TFTs". This is joint work in progress with Damien Calaque and Rune Haugseng.\n LOCATION:https://researchseminars.org/talk/globalpoisson/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Fock (IRMA\, Strasbourg) DTSTART;VALUE=DATE-TIME:20210401T151500Z DTEND;VALUE=DATE-TIME:20210401T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/44 DESCRIPTION:Title: Momentum map of general relativity\nby Vladimir Fock (IRMA\, St rasbourg) as part of Global Poisson webinar\n\n\nAbstract\nWe study an app roach to general relativity using vielbein with values in a Clifford algeb ra. This approach allows to simplify computations and in particular define a hidden $\\mathfrak{sl}(2) \\times \\mathfrak{sl}(2)$ symmetry (and even affine $\\mathfrak{sl}(4)$ one in the Kaehler case). This formalism all ows to compute in simple terms the phase space of the theory and the actio n of the diffeomorphisms on it. The main feature of this situation is that diffeomorphisms do not form a group\, but a groupoid. We will discuss the reason for this situation and suggest an analogue of the momentum map. Jo int work with P. Goussard.\n LOCATION:https://researchseminars.org/talk/globalpoisson/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Zambon (KU Leuven) DTSTART;VALUE=DATE-TIME:20210415T151500Z DTEND;VALUE=DATE-TIME:20210415T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/45 DESCRIPTION:Title: Deformations of Lagrangian submanifolds in log-symplectic geometry< /a>\nby Marco Zambon (KU Leuven) as part of Global Poisson webinar\n\n\nA bstract\nLog-symplectic manifolds constitute a class of Poisson manifolds that in many respects behave like symplectic ones. We address the question of whether Lagrangian submanifolds and their deformations are as well-beh aved as in symplectic geometry. Since the case of Lagrangians transversal to the singular locus is well understood\, we focus on Lagrangian submanif olds contained in the singular locus. We establish a normal form theorem a round such submanifolds\, and show that their deformations are governed by a DGLA. The latter allows to draw geometric consequences: we discuss when a Lagrangian admits deformations not contained in the singular locus\, an d we give precise criteria for unobstructedness of first order deformation s.\n\nThis talk is based on joint work with Stephane Geudens.\n LOCATION:https://researchseminars.org/talk/globalpoisson/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Rubtsov (University of Angers) DTSTART;VALUE=DATE-TIME:20210422T151500Z DTEND;VALUE=DATE-TIME:20210422T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/46 DESCRIPTION:Title: Associative Yang-Baxter equation: from double Poisson structures to modular forms\nby Vladimir Rubtsov (University of Angers) as part of Global Poisson webinar\n\n\nAbstract\nI shall give a survey of various ava tars of Associative Yang-Baxter Equations from (double) Poisson structur e existence conditions to a form of the trisecant Fay identity and as some equations on generating functions for period polynomials of (quasi-)modul ar forms.\n LOCATION:https://researchseminars.org/talk/globalpoisson/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Yakov Eliashberg (Stanford) DTSTART;VALUE=DATE-TIME:20210429T151500Z DTEND;VALUE=DATE-TIME:20210429T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/47 DESCRIPTION:Title: Topology of the space of tight contact structures on $\\mathbb{R}^3 $\nby Yakov Eliashberg (Stanford) as part of Global Poisson webinar\n\ n\nAbstract\n30 years ago I proved that any tight contact structure on $\\ mathbb{R}^3$ is equivalent to the standard one. In the same paper I sugges ted that one can establish along the same lines the contractibility of the space of fixed at infinity tight contact structure on $\\mathbb{R}^3$. Recently we proved this claim in our joint work with N. Mishachev. The pro of is based on the study of topology of 1-dimensional foliations and fun ctions on the 2-sphere.\n LOCATION:https://researchseminars.org/talk/globalpoisson/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Linhui Shen (Michigan State University) DTSTART;VALUE=DATE-TIME:20210513T121500Z DTEND;VALUE=DATE-TIME:20210513T131500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/48 DESCRIPTION:Title: Moduli spaces of $G$-local systems and Poisson geometry\nby Lin hui Shen (Michigan State University) as part of Global Poisson webinar\n\n \nAbstract\nLet $G$ be a split semi-simple algebraic group over $\\mathbb{ Q}$. We introduce a natural cluster structure on moduli spaces of framed $ G$-local systems over surfaces with marked points. As a consequence\, the moduli spaces of $G$-local systems admit natural Poisson structures\, and can be further quantized. We will study the principal series representatio ns of such quantum spaces. If time permits\, I will discuss its applicatio ns in the study of quantum groups. This talk will mainly be based on joint work with A.B. Goncharov (arXiv:1904.10491).\n LOCATION:https://researchseminars.org/talk/globalpoisson/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Adriano Tomassini (Parma) DTSTART;VALUE=DATE-TIME:20210520T151500Z DTEND;VALUE=DATE-TIME:20210520T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/49 DESCRIPTION:Title: $\\overline{\\partial}$ Harmonic forms on compact almost Hermitian manifolds\nby Adriano Tomassini (Parma) as part of Global Poisson webi nar\n\n\nAbstract\n"Let $M$ be a smooth manifold of dimension $2n$ and let $J$ be an almost-complex structure on $M$. Then\, $J$ induces on the spac e of forms $A^\\bullet(M)$ a natural bigrading\, namely\n$$\nA^\\bullet(M) =\\bigoplus_{p+q=\\bullet}A^{p\,q}(M).\n$$\nAccordingly\, the exterior der ivative $d$ splits into four operators\n$$\nd:A^{p\,q}(M)\\to A^{p+2\,q-1} (M)\\oplus A^{p+1\,q}(M)\\oplus A^{p\,q+1}(X)\\oplus A^{p-1\,q+2}(M)\n$$\n $$\nd=\\mu+\\partial+\\overline{\\partial}+\\bar\\mu\,\n$$\nwhere $\\mu$ a nd $\\bar\\mu$ are differential operators that are linear over functions.\ n\nLet $g$ be a Hermitian metric on $(M\,J)$. Denote by $$\\Delta_{\\overl ine{\\partial}}:=\\overline{\\partial}\\\,\\overline{\\partial}^*+\\overli ne{\\partial}^*\\overline{\\partial}$$ the $\\overline{\\partial}$-Laplaci an. Then $\\Delta_{\\overline{\\partial}}$ is an elliptic differential ope rator. We study the space of $\\overline{\\partial}$-harmonic forms on $(M \,J\,g)$. Some explicit examples will be discussed. Special results are ob tained for $\\dim_\\mathbb{R} M=4$. This a joint work with Nicoletta Tardi ni."\n LOCATION:https://researchseminars.org/talk/globalpoisson/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Bonechi (INFN\, Florence) DTSTART;VALUE=DATE-TIME:20210527T151500Z DTEND;VALUE=DATE-TIME:20210527T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/50 DESCRIPTION:Title: Bihamiltonian systems and invariant polynomials\nby Francesco B onechi (INFN\, Florence) as part of Global Poisson webinar\n\n\nAbstract\n Motivated by the problem of quantization of the symplectic groupoid we stu dy a class of bihamiltonian systems defined on compact hermitian symmetric spaces. Indeed\, a Poisson Nijenhuis (PN) structure defines a (singular) real polarization of the symplectic groupoid integrating any of the Poisso n structures appearing in the bihamiltonian hierarchy. Despite its singula rity\, this polarization leads to the quantization of complex projective s paces. We will discuss in some detail a way to discuss this polarization i n terms of invariant polynomials of a certain Thimm chain of subalgebras. This approach works for the classical cases\; time permitting\, I will dis cuss some partial results about the exceptional cases.\n LOCATION:https://researchseminars.org/talk/globalpoisson/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Balibanu (Harvard) DTSTART;VALUE=DATE-TIME:20210603T151500Z DTEND;VALUE=DATE-TIME:20210603T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/51 DESCRIPTION:Title: Steinberg slices and group-valued moment maps\nby Ana Balibanu (Harvard) as part of Global Poisson webinar\n\n\nAbstract\nWe define a cla ss of transversal slices in spaces which are quasi-Poisson for the action of a complex semisimple group $G$. This is a multiplicative analogue of Wh ittaker reduction. One example is the multiplicative universal centralizer of $G$\, which is equipped with the usual symplectic structure in this wa y. We construct a smooth partial compactification of $Z$ by taking the clo sure of each centralizer fiber in the wonderful compactification of $G$. B y realizing this partial compactification as a transversal in a larger qua si-Poisson variety\, we show that it is smooth and log-symplectic.\n LOCATION:https://researchseminars.org/talk/globalpoisson/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Charlotte Kirchhoff-Lukat (KU Leuven) DTSTART;VALUE=DATE-TIME:20210617T151500Z DTEND;VALUE=DATE-TIME:20210617T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/52 DESCRIPTION:Title: Exploring the modular class of Dirac structures\nby Charlotte K irchhoff-Lukat (KU Leuven) as part of Global Poisson webinar\n\n\nAbstract \nThe concept of modular class is best known for Poisson structures\, but is naturally defined for any Lie algebroid: It is a class in the first Lie algebroid cohomology. Poisson structures as Lie algebroids have the speci al feature that their dual is isomorphic to the tangent bundle and thus re presentatives are vector fields\, which allows for the definition of the s o-called modular foliation\, locally spanned by Hamiltonian vector fields and the modular vector field. This modular foliation can in turn be viewed as the foliation of a Poisson structure on the total space of the real li ne bundle $\\det (T^\\ast M)$ (Gualtieri-Pym). In this talk\, I will show how to extend these concepts to general real or complex Dirac structures i n exact Courant algebroids and discuss the information contained in the mo dular class of a Dirac structure in some non-Poisson examples. (This is jo int work in progress with Ralph Klaasse.)\n LOCATION:https://researchseminars.org/talk/globalpoisson/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Frejlich (UFRGS) DTSTART;VALUE=DATE-TIME:20210624T151500Z DTEND;VALUE=DATE-TIME:20210624T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/53 DESCRIPTION:Title: The bundle picture of Poisson transversals\nby Pedro Frejlich ( UFRGS) as part of Global Poisson webinar\n\n\nAbstract\nIn this talk\, we describe the nonlinear Grassmannian $PT(M\,\\pi)$ of all closed Poisson tr ansversals of a given Poisson manifold $(M\,\\pi)$\, and show that the tau tological bundle over it carries a canonical coupling Dirac structure. Our main result is that a choice of invariant volume form on the ambient mani fold induces a weak symplectic structure on the nonlinear Grassmannian\, w hich is a coadjoint orbit for the (infinitesimal) action of a certain cent ral extension of the Hamiltonian group -- generalizing the result of Halle r-Vizman in the symplectic case. This is joint work with I. Marcut.\n LOCATION:https://researchseminars.org/talk/globalpoisson/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Waldmann (Würzburg) DTSTART;VALUE=DATE-TIME:20210916T151500Z DTEND;VALUE=DATE-TIME:20210916T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/54 DESCRIPTION:Title: KMS Functionals in Poisson Geometry\nby Stefan Waldmann (Würzb urg) as part of Global Poisson webinar\n\n\nAbstract\nIn this talk I will report on some old results about KMS states in symplectic geometry and pre sent new results in the general Poisson case. The classical KMS condition captures thermodynamical states in classical mechanical systems as a semi- classical limit of the (original) quantum KMS condition used in algebraic quantum field theory. In the symplectic case the classification of KMS fun ctionals is rather simple. In the general Poisson case\, the investigation of the KMS condition for volume forms can be seen as one of the main moti vations for the definition of the modular class by Alan Weinstein. Conside ring more general functionals gives new and interesting structures where i n some simple cases a full classification is available. While the classica l situation is already very rich\, the quantization of classical KMS state s is yet to be explored. The results are a joint work with Nicolò Drago.\ n LOCATION:https://researchseminars.org/talk/globalpoisson/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Theodore Voronov (Manchester) DTSTART;VALUE=DATE-TIME:20210923T151500Z DTEND;VALUE=DATE-TIME:20210923T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/55 DESCRIPTION:Title: Thick morphisms of supermanifolds and bracket structures\nby Th eodore Voronov (Manchester) as part of Global Poisson webinar\n\n\nAbstrac t\nA “thick morphism” of supermanifolds is a generalization of a smoot h map that I introduced in 2014. It is NOT a map\, but it induces a pull-b ack of smooth functions. A peculiar feature of such pull-back is that it i s NONLINEAR --- actually\, it is a formal mapping of the algebras of smoot h functions regarded as infinite-dimensional (super)manifolds. Compare wit h ordinary pull-backs\, which are algebra homomorphisms\, in particular li near. In the talk\, I will give the definition of thick morphisms and expl ain the construction of nonlinear pull-backs. Actually\, because of the no n-linearity\, there are two parallel versions of thick morphisms and the corresponding pull-backs: “bosonic” (acting on even functions) and “ fermionic” (acting on odd functions). Each of them gives rise to a forma l category containing the category of ordinary maps.\n\nMy original motiva tion was constructing L-infinity morphisms for homotopy Poisson or homotop y Schouten brackets. Thick morphisms also make it possible to give adjoint s for nonlinear vector bundle maps (useful for L-infinity algebroids). The re is a nonlinear analog of “functional-algebraic duality” with certai n “nonlinear algebra homomorphisms” taking place of ordinary homomorph isms. In the bosonic case\, thick morphisms also have a quantum version gi ven by particular Fourier integral operators\, which provide L-infinity mo rphisms for “quantum brackets” generated by BV- type operators.\n LOCATION:https://researchseminars.org/talk/globalpoisson/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Yong-Geun Oh (IBS Center for Geometry and Physics & POSTECH) DTSTART;VALUE=DATE-TIME:20210930T131500Z DTEND;VALUE=DATE-TIME:20210930T141500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/56 DESCRIPTION:Title: Non-archimedian deformation of Landau-Ginzburg potentials and Gelfa nd-Cetlin systems\nby Yong-Geun Oh (IBS Center for Geometry and Physic s & POSTECH) as part of Global Poisson webinar\n\n\nAbstract\nUsing the bu lk-deformation of Floer cohomology by Schubert classes and non-Archimedean analysis of Fukaya--Oh--Ohta--Ono's bulk-deformed potential function\, we prove that every complete flag manifold with a monotone Kirillov--Kostant --Souriau symplectic form carries a continuum of non-displaceable Lagrangi an tori which degenerates to a non-torus fiber in the Hausdorff limit. Thi s talk is based on a joint work with Yunhyung Cho and Yoosik Kim.\n LOCATION:https://researchseminars.org/talk/globalpoisson/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiro Tanaka (Texas State University) DTSTART;VALUE=DATE-TIME:20211007T151500Z DTEND;VALUE=DATE-TIME:20211007T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/57 DESCRIPTION:Title: Stable Weinstein geometry through localizations\nby Hiro Tanaka (Texas State University) as part of Global Poisson webinar\n\n\nAbstract\ nMuch of computational math is formula-driven\, while much of categorical math is formalism-driven. Mirror symmetry is rich in part because many of its results are driven by both. With the advent of stable-homotopy-theoret ic invariants in symplectic geometry--such as Nadler-Shende's microlocal c ategories and (on the horizon) spectrally enriched wrapped Fukaya categori es--there has been a real need for better-behaved formalisms in symplectic geometry. (This is because\, now-a-days\, much of stable homotopy theory is possible only thanks to extremely well-constructed formalisms.) In this talk\, we will talk about recent success in constructing the formalism\, especially in the setting of certain non-compact symplectic manifolds call ed Weinstein sectors. The results have concrete geometric consequences\, l ike showing that spaces of embeddings of these manifolds map continuously to spaces of maps between certain invariants. (And in particular\, leads t o higher-homotopy-group generalizations\, in the Weinstein setting\, of th e Seidel homomorphism\, similar to works of Savelyev and Oh-Tanaka.) The m ain result we'll discuss is that the infinity-category of stabilized secto rs can be constructed using the categorically formal process of localizati on. Most of what we discuss is joint with Oleg Lazarev and Zachary Sylvan. \n LOCATION:https://researchseminars.org/talk/globalpoisson/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Dusa McDuff (Barnard College) DTSTART;VALUE=DATE-TIME:20211014T151500Z DTEND;VALUE=DATE-TIME:20211014T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/58 DESCRIPTION:Title: Embedding ellipsoids into Hirzebruch surfaces\nby Dusa McDuff ( Barnard College) as part of Global Poisson webinar\n\n\nAbstract\n"This ta lk will report on joint work with Magill and Weiler concerning the questio n of when an ellipsoid symplectically embeds into the \none-point blowup of CP^2. The precise size of the blowup has a great effect on the correspo nding embedding capacity function. Indeed\, as discovered in earlier work with collaborators\nBertozzi\, Holm\, Maw\, Mwakyoma\, Pires\, and Weiler \, for certain blowup parameters there are infinitely many significant ob structive classes\, which implies that the capacity function has a stairca se. We have now found that the set of these parameters\, though still not fully understood\, displays some very interesting symmetries and recursive patterns."\n LOCATION:https://researchseminars.org/talk/globalpoisson/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Kiumars Kaveh (Pittsburgh) DTSTART;VALUE=DATE-TIME:20211021T151500Z DTEND;VALUE=DATE-TIME:20211021T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/59 DESCRIPTION:Title: On almost toric degenerations of projective varieties and applicati ons to Hamiltonian torus actions\nby Kiumars Kaveh (Pittsburgh) as par t of Global Poisson webinar\n\n\nAbstract\nRoughly speaking\, a toric dege neration of a variety X is a (flat) one-parameter family of irreducible va rieties X_t such that for nonzero t\, X_t is isomorphic to X and X_0 is a (not necessarily normal) toric variety. I will present the recent result t hat any projective variety has an "almost" toric degeneration and will dis cuss applications in constructing Hamiltonian torus actions as well as est imating Gromov widths. I will try to cover needed definitions\, motivation s and background in the talk. This is a joint work with Chris Manon and Ta kuya Murata.\n LOCATION:https://researchseminars.org/talk/globalpoisson/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Si Li (Tsinghua) DTSTART;VALUE=DATE-TIME:20211028T131500Z DTEND;VALUE=DATE-TIME:20211028T141500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/60 DESCRIPTION:Title: Elliptic chiral homology and quantum master equation\nby Si Li (Tsinghua) as part of Global Poisson webinar\n\n\nAbstract\nWe present an effective BV quantization theory for chiral deformation of two dimensional conformal field theories. We explain a connection between the quantum mas ter equation and the chiral homology for vertex operator algebras. As an a pplication\, we construct correlation functions of the curved beta-gamma/b -c system and establish a coupled equation relating to chiral homology gro ups of chiral differential operators. This can be viewed as the vertex alg ebra analogue of the trace map in algebraic index theory.\n LOCATION:https://researchseminars.org/talk/globalpoisson/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Mykola Matviichuk (McGill) DTSTART;VALUE=DATE-TIME:20211104T151500Z DTEND;VALUE=DATE-TIME:20211104T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/61 DESCRIPTION:by Mykola Matviichuk (McGill) as part of Global Poisson webina r\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Yael Karshon (Toronto) DTSTART;VALUE=DATE-TIME:20211111T151500Z DTEND;VALUE=DATE-TIME:20211111T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/62 DESCRIPTION:Title: Complexity one Hamiltonian torus actions\nby Yael Karshon (Toro nto) as part of Global Poisson webinar\n\n\nAbstract\nI will report on my classification\, joint with Sue Tolman\, of Hamiltonian torus actions with two dimensional quotients.\n LOCATION:https://researchseminars.org/talk/globalpoisson/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Izosimov (University of Arizona) DTSTART;VALUE=DATE-TIME:20211118T161500Z DTEND;VALUE=DATE-TIME:20211118T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/63 DESCRIPTION:Title: Lie groupoids in fluid dynamics\nby Anton Izosimov (University of Arizona) as part of Global Poisson webinar\n\n\nAbstract\nIn 1966\, V. Arnold showed that the Euler equation describing the motion of an ideal f luid on a Riemannian manifold can be regarded as the geodesic flow of a ri ght-invariant metric on the Lie group of volume-preserving diffeomorphisms . This insight turned out to be indispensable for the study of Hamiltonian properties and conservation laws in hydrodynamics\, fluid instabilities\, topological properties of flows\, as well as a powerful tool for obtainin g sharper existence and uniqueness results for Euler-type equations. Howev er\, the scope of application of Arnold’s approach is limited to problem s whose symmetries form a group. At the same time\, there are many problem s in fluid dynamics\, such as free boundary problems\, fluid-structure int eractions\, as well as discontinuous fluid flows\, whose symmetries should instead be regarded as a groupoid. In the talk\, I will discuss an extens ion of Arnold's theory from Lie groups to Lie groupoids. The example of vo rtex sheet motion (i.e. fluids with discontinuities) will be addressed in detail. The talk is based on ongoing work with B. Khesin.\n LOCATION:https://researchseminars.org/talk/globalpoisson/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Yanpeng Li (Sichuan University) DTSTART;VALUE=DATE-TIME:20211125T131500Z DTEND;VALUE=DATE-TIME:20211125T141500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/64 DESCRIPTION:Title: On tropical Poisson-Lie theory\nby Yanpeng Li (Sichuan Univers ity) as part of Global Poisson webinar\n\n\nAbstract\nFor a compact Lie gr oup $K$ with the standard Poisson structure\, we first construct a tropica l version for the dual Poisson-Lie group $K^\\ast$. This construction will then help us 1) to establish a relation between $K^\\ast$ and the Langlan ds dual group $G^\\vee$ of the complexification $G:=K^\\mathbb{C}$\; 2) to construct an exhaustion by symplectic embeddings of toric domains for eac h regular coadjoint orbit of $K$. We combine ideas from Poisson-Lie groups \, cluster algebras and the geometric crystals of Berenstein-Kazhdan.\n\nT he talk is based on joint works with A. Alekseev\, A. Berenstein\, B. Hoff man\, and J. Lane.\n LOCATION:https://researchseminars.org/talk/globalpoisson/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Frances Kirwan (Oxford) DTSTART;VALUE=DATE-TIME:20211209T161500Z DTEND;VALUE=DATE-TIME:20211209T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/66 DESCRIPTION:by Frances Kirwan (Oxford) as part of Global Poisson webinar\n \nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Stasheff (University of Pennsylvania) DTSTART;VALUE=DATE-TIME:20211216T161500Z DTEND;VALUE=DATE-TIME:20211216T171500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/67 DESCRIPTION:by Jim Stasheff (University of Pennsylvania) as part of Global Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiang Tang (Washington) DTSTART;VALUE=DATE-TIME:20200618T151500Z DTEND;VALUE=DATE-TIME:20200618T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/68 DESCRIPTION:Title: An index theorem on the tempered dual of a real reductive Lie group \nby Xiang Tang (Washington) as part of Global Poisson webinar\n\n\nAb stract\nLet $G$ be a (real reductive) Lie group. The tempered dual of $G$ is the space of isomorphism classes of irreducible unitary $G$-representat ions that are contained in the (left) regular representation of $G$ on $L^ 2(G)$. In this talk\, we will report our study on the geometry of the te mpered dual. As an application\, we will present an index theorem for prop er cocompact $G$-actions. This talk is based on the joint works with Peter Hochs\, Markus Pflaum\, Hessel Posthuma\, and Yanli Song.\n LOCATION:https://researchseminars.org/talk/globalpoisson/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Gekhtman (Notre Dame) DTSTART;VALUE=DATE-TIME:20200625T151500Z DTEND;VALUE=DATE-TIME:20200625T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/69 DESCRIPTION:Title: Generalized cluster structures related to the Drinfeld double of $\ \mathrm{GL}(n)$\nby Michael Gekhtman (Notre Dame) as part of Global Po isson webinar\n\n\nAbstract\nAs is well-known\, cluster transformations in cluster algebras of geometric type are often modeled on determinant ident ities\, such short Plucker relations\, Desnanot-Jacobi identities and their generalizations. I will present a construction that plays a similar role in a description of generalized cluster transformations and discuss i ts applications to generalized cluster structures in $\\mathrm{GL}(n)$ com patible with a certain subclass of Belavin-Drinfeld Poisson-Lie backers\, in the Drinfeld double of $\\mathrm{GL}(n)$ and in spaces of periodic diff erence operators. Based on a joint work with M. Shapiro and A. Vainshtein. \n LOCATION:https://researchseminars.org/talk/globalpoisson/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Camille Laurent-Gengoux (Lorraine) DTSTART;VALUE=DATE-TIME:20200702T151500Z DTEND;VALUE=DATE-TIME:20200702T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/70 DESCRIPTION:Title: About singular leaves of singular foliations\nby Camille Lauren t-Gengoux (Lorraine) as part of Global Poisson webinar\n\n\nAbstract\nJoin t work with Leonid Ryvkin. For singular foliations\, e.g. symplectic leav es of a Poisson structure or Lie group orbits\, the dimension of the leave s may vary: When it does\, the leaf is said to be singular. We will expla in why (formal) neighborhoods of simply connected leaves have surprisingly simple local models. This is in sharp contrast with Poisson structures or Lie algebroids. We will derive some consequences (sometimes conjectural) of these facts in terms of first return map\, Androulidakis-Skandalis hol onomy groupoid\, and the universal Q-manifold that Lavau\, Strobl and mys elf have previously associated to a singular foliation.\n LOCATION:https://researchseminars.org/talk/globalpoisson/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Susan Tolman (Urbana-Champaign) DTSTART;VALUE=DATE-TIME:20200709T151500Z DTEND;VALUE=DATE-TIME:20200709T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/71 DESCRIPTION:Title: Beyond semitoric\nby Susan Tolman (Urbana-Champaign) as part o f Global Poisson webinar\n\n\nAbstract\nA compact four dimensional complet ely integrable system $f \\colon M \\to \\mathbb R^2$ is {\\bf semitoric}\ nif it has only non-degenerate singularities\, without hyperbolic blocks\, and one of the components of $f$\ngenerates a circle action. Semitoric s ystems have been extensively studied and have many nice properties: for ex ample\, the preimages $f^{-1}(x)$ are all connected. Unfortunately\, al though there are many interesting examples of semitoric systems\, the clas s has some limitation. For example\, there are blowups of $S^2 \\times S^ 2$ with Hamiltonian circle actions which cannot be extended to semitoric s ystems. We expand the class of semitoric systems by allowing certain dege nerate singularities\, which we call {\\bf ephemeral} singularities. We p rove that the preimage $f^{-1}(x)$ is still connected for this larger clas s. We hope that this class will be large enough to include not only all c ompact four manifolds with Hamiltonian circle actions\, but more generally all complexity one spaces.\nBased on joint work with D. Sepe.\n LOCATION:https://researchseminars.org/talk/globalpoisson/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Jiang-Hua Lu (Hong Kong) DTSTART;VALUE=DATE-TIME:20200924T151500Z DTEND;VALUE=DATE-TIME:20200924T161500Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/72 DESCRIPTION:Title: Some examples of algebraic symplectic groupoids\nby Jiang-Hua Lu (Hong Kong) as part of Global Poisson webinar\n\n\nAbstract\nWe constru ct Poisson and symplectic groupoids over a class of polynomial Poisson str uctures on $\\mathbb{C}^n$ whose total spaces are certain configuration sp aces of flags. This is joint work with Victor Mouquin and ShiZhuo Yu.\n LOCATION:https://researchseminars.org/talk/globalpoisson/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexey Bolsinov (Loughborough University) DTSTART;VALUE=DATE-TIME:20220120T160000Z DTEND;VALUE=DATE-TIME:20220120T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/73 DESCRIPTION:by Alexey Bolsinov (Loughborough University) as part of Global Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Aissa Wade (Penn State University) DTSTART;VALUE=DATE-TIME:20220127T130000Z DTEND;VALUE=DATE-TIME:20220127T140000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/74 DESCRIPTION:by Aissa Wade (Penn State University) as part of Global Poisso n webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Mnev (University of Notre Dame) DTSTART;VALUE=DATE-TIME:20220203T160000Z DTEND;VALUE=DATE-TIME:20220203T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/75 DESCRIPTION:by Pavel Mnev (University of Notre Dame) as part of Global Poi sson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Evens (University of Notre Dame) DTSTART;VALUE=DATE-TIME:20220217T160000Z DTEND;VALUE=DATE-TIME:20220217T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/76 DESCRIPTION:by Samuel Evens (University of Notre Dame) as part of Global P oisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Hsuan-Yi Liao (Tsing-Hua University) DTSTART;VALUE=DATE-TIME:20220224T130000Z DTEND;VALUE=DATE-TIME:20220224T140000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/77 DESCRIPTION:by Hsuan-Yi Liao (Tsing-Hua University) as part of Global Pois son webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne Moreau (Orsay) DTSTART;VALUE=DATE-TIME:20220303T160000Z DTEND;VALUE=DATE-TIME:20220303T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/78 DESCRIPTION:by Anne Moreau (Orsay) as part of Global Poisson webinar\n\nAb stract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Gutt (Université libre de Bruxelles) DTSTART;VALUE=DATE-TIME:20220310T160000Z DTEND;VALUE=DATE-TIME:20220310T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/79 DESCRIPTION:by Simone Gutt (Université libre de Bruxelles) as part of Glo bal Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergei Gukov (Caltech) DTSTART;VALUE=DATE-TIME:20220317T160000Z DTEND;VALUE=DATE-TIME:20220317T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/80 DESCRIPTION:by Sergei Gukov (Caltech) as part of Global Poisson webinar\n\ nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu Li (MPI) DTSTART;VALUE=DATE-TIME:20220331T120000Z DTEND;VALUE=DATE-TIME:20220331T130000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/81 DESCRIPTION:by Yu Li (MPI) as part of Global Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Milen Yakimov (Northeastern) DTSTART;VALUE=DATE-TIME:20220407T160000Z DTEND;VALUE=DATE-TIME:20220407T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/82 DESCRIPTION:by Milen Yakimov (Northeastern) as part of Global Poisson webi nar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Strobl (Lyon 1) DTSTART;VALUE=DATE-TIME:20220421T160000Z DTEND;VALUE=DATE-TIME:20220421T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/83 DESCRIPTION:by Thomas Strobl (Lyon 1) as part of Global Poisson webinar\n\ nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikita Nikolaev (Sheffield) DTSTART;VALUE=DATE-TIME:20220505T160000Z DTEND;VALUE=DATE-TIME:20220505T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/84 DESCRIPTION:by Nikita Nikolaev (Sheffield) as part of Global Poisson webin ar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Crooks (Northeastern University) DTSTART;VALUE=DATE-TIME:20211202T160000Z DTEND;VALUE=DATE-TIME:20211202T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/85 DESCRIPTION:Title: Symplectic reduction along a submanifold\nby Peter Crooks (Nort heastern University) as part of Global Poisson webinar\n\n\nAbstract\nNoet her's perspective on conserved quantities gives rise to quotient construct ions in symplectic geometry. The most classical such construction is Marsd en-Weinstein-Meyer reduction\, while more modern variants include Ginzburg -Kazhdan reduction\, Kostant-Whittaker reduction\, Mikami-Weinstein reduct ion\, symplectic cutting\, and symplectic implosion.\n\nI will outline a g eneralization of the quotient constructions mentioned above. This generali zation will be shown to have versions in the smooth\, holomorphic\, comple x algebraic\, and derived symplectic contexts. As a corollary\, I will der ive a concrete and Lie-theoretic construction of "universal" symplectic qu otients.\n\nThis represents joint work with Maxence Mayrand.\n LOCATION:https://researchseminars.org/talk/globalpoisson/85/ END:VEVENT BEGIN:VEVENT SUMMARY:TBA DTSTART;VALUE=DATE-TIME:20220324T160000Z DTEND;VALUE=DATE-TIME:20220324T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/86 DESCRIPTION:by TBA as part of Global Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/86/ END:VEVENT BEGIN:VEVENT SUMMARY:TBA DTSTART;VALUE=DATE-TIME:20220414T160000Z DTEND;VALUE=DATE-TIME:20220414T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/87 DESCRIPTION:by TBA as part of Global Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/87/ END:VEVENT BEGIN:VEVENT SUMMARY:TBA DTSTART;VALUE=DATE-TIME:20220428T120000Z DTEND;VALUE=DATE-TIME:20220428T130000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/88 DESCRIPTION:by TBA as part of Global Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/88/ END:VEVENT BEGIN:VEVENT SUMMARY:TBA DTSTART;VALUE=DATE-TIME:20220512T160000Z DTEND;VALUE=DATE-TIME:20220512T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/89 DESCRIPTION:by TBA as part of Global Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/89/ END:VEVENT BEGIN:VEVENT SUMMARY:TBA DTSTART;VALUE=DATE-TIME:20220519T160000Z DTEND;VALUE=DATE-TIME:20220519T170000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/90 DESCRIPTION:by TBA as part of Global Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/90/ END:VEVENT BEGIN:VEVENT SUMMARY:TBA DTSTART;VALUE=DATE-TIME:20220526T120000Z DTEND;VALUE=DATE-TIME:20220526T130000Z DTSTAMP;VALUE=DATE-TIME:20211128T080606Z UID:globalpoisson/91 DESCRIPTION:by TBA as part of Global Poisson webinar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/globalpoisson/91/ END:VEVENT END:VCALENDAR