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BEGIN:VEVENT
SUMMARY:Eckhard Meinrenken (Toronto)
DTSTART:20200416T151500Z
DTEND:20200416T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/1
DESCRIPTION:Title: Van Est differentiation and Van Est integration\nby Eckhard Mein
renken (Toronto) as part of Global Poisson webinar\n\nLecture held in Zoom
.\n\nAbstract\nThe classical Van Est theory relates the smooth cohomology
of Lie groups with the cohomology of the associated Lie algebra. Some aspe
cts of this theory generalize to Lie groupoids and their Lie algebroids. I
n this talk\, we revisit the van Est theory using the Perturbation Lemma f
rom homological algebra. This leads to precise descriptions of the van Est
differentiation and integration at the level of cochains. The talk is bas
ed on recent work with Maria Amelia Salazar.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rui Loja Fernandes (Urbana-Champaign)
DTSTART:20200409T151500Z
DTEND:20200409T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/2
DESCRIPTION:Title: Local models around Poisson submanifolds\nby Rui Loja Fernandes
(Urbana-Champaign) as part of Global Poisson webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/globalpoisson/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20200423T151500Z
DTEND:20200423T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/3
DESCRIPTION:Title: Short star-products for filtered quantizations\nby Pavel Etingof
(MIT) as part of Global Poisson webinar\n\nLecture held in Zoom.\n\nAbstr
act\nLet $A$ be a filtered Poisson algebra with Poisson bracket $\\lbrace{
\,\\rbrace}$ of degree $-2$. A {\\it star product} on $A$ is an associativ
e product $*: A\\otimes A\\to A$ given by $$a*b=ab+\\sum_{i\\ge 1}C_i(a\,b
)\,$$ where $C_i$ has degree $-2i$ and $C_1(a\,b)-C_1(b\,a)=\\lbrace{a\,b\
\rbrace}$. We call the product * {\\it even} if $C_i(a\,b)=(-1)^iC_i(b\,
a)$ for all $i$\, and call it {\\it short} if $C_i(a\,b)=0$ whenever $i>{\
\rm min}({\\rm deg}(a)\, {\\rm deg}(b))$.\n\nMotivated by three-dimensiona
l $N=4$ superconformal field theory\, In 2016 Beem\, Peelaers and Rastelli
considered short even star-products for homogeneous symplectic singularit
ies (more precisely\, hyperK\\"ahler cones) and conjectured that that they
exist and depend on finitely many parameters. We prove the dependence on
finitely many parameters in general and existence for a large class of exa
mples\, using the connection of this problem with zeroth Hochschild homolo
gy of quantizations suggested by Kontsevich.\n\nBeem\, Peelaers and Rastel
li also computed the first few terms of short quantizations for Kleinian s
ingularities of type A\, which were later computed to all orders by Dedush
enko\, Pufu and Yacoby. We will discuss some generalizations of these resu
lts.\n\nThis is joint work with Douglas Stryker.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Weinstein (UC Berkeley and Stanford)
DTSTART:20200430T151500Z
DTEND:20200430T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/4
DESCRIPTION:Title: Failure of Twisted Poisson Property for Monopole Plasma\nby Alan
Weinstein (UC Berkeley and Stanford) as part of Global Poisson webinar\n\
nLecture held in Zoom.\n\nAbstract\nAlthough the dynamical system for a ch
arged particle in a continuous background distribution of magnetic monopo
les is given by a twisted Poisson structure\, that for a plasma of such
particles is not. (Joint work with Manuel Lainz and Cristina Sardón)\n
LOCATION:https://researchseminars.org/talk/globalpoisson/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brent Pym (McGill)
DTSTART:20200507T151500Z
DTEND:20200507T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/5
DESCRIPTION:Title: Holonomic Poisson manifolds\nby Brent Pym (McGill) as part of Gl
obal Poisson webinar\n\nLecture held in Zoom.\n\nAbstract\nHolonomicity is
a new sort of nondegeneracy condition for\nholomorphic Poisson structures
\, closely related to the notion of a log\nsymplectic form\, and intimatel
y connected with the geometry of\nWeinstein's modular vector field. It e
ncompasses many natural Poisson\nstructures arising in gauge theory\, repr
esentation theory\, and algebraic\ngeometry. The motivation for the defi
nition comes from deformation\ntheory: a Poisson manifold is holonomic whe
n its space of deformations\nis "as finite-dimensional as possible"\, in a
sense I will make precise\nduring the talk (via D-modules). I will desc
ribe the basic theory and\nexamples of holonomic Poisson manifolds\, along
with some concrete\nclassification results\, including the discovery of m
any new irreducible\ncomponents of the moduli space of Poisson fourfolds.
This talk is based\non joint works with Schedler\, and Matviichuk--Sche
dler.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda (UPC)
DTSTART:20200514T151500Z
DTEND:20200514T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/6
DESCRIPTION:Title: From b-Poisson manifolds to singular contact structures\nby Eva
Miranda (UPC) as part of Global Poisson webinar\n\nLecture held in Zoom.\n
\nAbstract\nTaking as starting point motivating examples from celestial me
chanics and fluid dynamics\, we introduce the odd-dimensional counterpart
of b-Poisson/log-symplectic structures as Jacobi structures with transvers
ality conditions.\nWe discuss the basic theory and some constructions. In
particular\, we prove that a connected component of a convex hypersurf
ace of a contact manifold can be realized as a connected component of the
critical set of a $b^m$-contact structure. In dimension 3\, this construct
ion yields the existence of a generic set of surfaces $Z$ such that the pa
ir $(M\,Z)$ is a $b^{2k}$-contact manifold and $Z$ is its critical hypersu
rface.\n\n We also consider classical problems in Hamiltonian/Reeb dynam
ics and address the Weinstein conjecture on the existence of periodic orbi
ts of the Reeb vector field in this singular set-up. We end up this talk w
ith some applications of this singular Weinstein conjecture to the motivat
ing examples discussed at the beginning.\n\nThis is joint work with Cédri
c Oms.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Reshetikhin (UC Berkeley)
DTSTART:20200521T151500Z
DTEND:20200521T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/7
DESCRIPTION:Title: Integrable systems of Calogero-Moser type and moduli spaces of flat
connections\nby Nicolai Reshetikhin (UC Berkeley) as part of Global Po
isson webinar\n\nLecture held in Zoom.\n\nAbstract\nThe talk will be focus
ed on spin Calogero-Moser systems related to symmetric spaces. They have n
atural generalizations related to moduli spaces of flat connections.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Ratiu (EPFL and Shanghai)
DTSTART:20200528T151500Z
DTEND:20200528T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/8
DESCRIPTION:Title: Differential character valued momentum maps and the Teichmüller spa
ce\nby Tudor Ratiu (EPFL and Shanghai) as part of Global Poisson webin
ar\n\n\nAbstract\nIt is well-known that the actions of several diffeomorph
ism groups of geometric interest do not admit momentum maps. The definitio
n of the Teichmüller space via Riemannian geometry strongly suggest that
it is a symplectic reduced space. I will present an extension of the class
ical momentum map which always exists for actions of diffeomorphism groups
possessing the crucial Noether property. This extended momentum map has n
o longer values in (pre)duals of Lie algebras\; its values are in differen
tial character groups. This extended momentum map encodes discrete topolog
ical information\, something the classical momentum map cannot do. In orde
r to focus the presentation\, the Teichmüller space will serve as the exa
mple of this theory. The talk is based on joint work with Tobias Diez from
TU Delft.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHÉS)
DTSTART:20200604T151500Z
DTEND:20200604T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/9
DESCRIPTION:Title: Quantum minimal surface and noncommutative Kaehler geometry\nby
Maxim Kontsevich (IHÉS) as part of Global Poisson webinar\n\n\nAbstract\n
I will talk about several interrelated topics\, based on works 1903.10792
and 2003.03171. Minimal surfaces in Euclidean space can be approximated (i
n sense of Berezin-Toeplitz quantization) by representations of Yang-Mills
algebra given by relations $\\forall i\\\,\\sum_j[X_j\,[X_j\,X_i]]=0$ whe
re $X_i$ are self-adjoint operators. Similarly\, complex affine curves are
approximated by representations of hermitian Yang-Mills algebra $\\sum_k
[Z_k^\\dagger\,Z_k]=\\hbar\\cdot id$ where $Z_i$ are commuting operators (
but not self-adjoint in general). I will explain how the latter equation a
ppears in the context of a version of Kaehler geometry for noncommutative
algebras.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Khesin (Toronto)
DTSTART:20200611T151500Z
DTEND:20200611T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/10
DESCRIPTION:Title: Hamiltonian geometry of compressible fluids\nby Boris Khesin (T
oronto) as part of Global Poisson webinar\n\n\nAbstract\nWe describe a geo
metric framework to study Newton's equations on infinite-dimensional confi
guration spaces of diffeomorphisms and smooth probability densities. It tu
rns out that several important PDEs of hydrodynamical origin can be descri
bed in this framework in a natural way. In particular\, the so-called Made
lung transform between the Schrödinger-type equations on wave functions a
nd Newton's equations on densities turns out to be a Kähler map between t
he corresponding phase spaces\, equipped with the Fubini-Study and Fisher-
Rao information metrics. This is a joint work with G.Misiolek and K.Modin.
\n
LOCATION:https://researchseminars.org/talk/globalpoisson/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Sklyanin (York)
DTSTART:20200528T080000Z
DTEND:20200528T100000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/12
DESCRIPTION:Title: Groupes de Lie et espaces des modules\nby Evgeny Sklyanin (York
) as part of Global Poisson webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/globalpoisson/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Mazzocco (University of Birmingham)
DTSTART:20200716T151500Z
DTEND:20200716T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/13
DESCRIPTION:Title: Quantum uniformisation and CY algebras\nby Marta Mazzocco (Univ
ersity of Birmingham) as part of Global Poisson webinar\n\n\nAbstract\nIn
this talk\, I will discuss a special class of quantum del Pezzo surfaces.
In particular I will introduce the generalised Sklyanin-Painlevé algebra
and characterise its PBW/PHS/Koszul properties. This algebra contains as l
imiting cases the generalised Sklyanin algebra\, Etingof-Ginzburg and Etin
gof-Oblomkov-Rains quantum del Pezzo and the quantum monodromy manifolds o
f the Painlevé equations.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reyer Sjamaar (Cornell University)
DTSTART:20200723T151500Z
DTEND:20200723T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/14
DESCRIPTION:Title: Reduction and quantization for log symplectic manifolds\nby Rey
er Sjamaar (Cornell University) as part of Global Poisson webinar\n\n\nAbs
tract\nKirillov's orbit method suggests that the classical analogue of a r
epresentation of a Lie group G is a Hamiltonian G-action on a symplectic m
anifold M. The classical analogue of isotypical subspaces should then be t
he symplectic quotients of M. This "quantization commutes with reduction"
problem was articulated in the 80's by Guillemin and Sternberg and solved
by them in the context of Kaehler quantization and homogeneous quantizatio
n. In the 90's Meinrenken solved an index-theoretic version of the problem
. Yi Lin\, Yiannis Loizides\, Yanli Song\, and I have been trying to exten
d Meinrenken’s theorem to log symplectic manifolds\, and this talk will
be a progress report on our work.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Gualtieri (University of Toronto)
DTSTART:20200730T151500Z
DTEND:20200730T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/15
DESCRIPTION:Title: Branes in symplectic groupoids\nby Marco Gualtieri (University
of Toronto) as part of Global Poisson webinar\n\n\nAbstract\nAfter an intr
oduction to coisotropic A-branes in symplectic manifolds and their role in
mirror symmetry\, I will explain how the problem of holomorphic quantizat
ion of Poisson brackets may be recast\, and in some cases solved\, as a pr
oblem of computing morphisms between coisotropic branes in symplectic grou
poids. This is joint work with Francis Bischoff and Joshua Lackman\n\n
Please register to obtain the password. Use your full name and institution
al email address.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrique Bursztyn (IMPA)
DTSTART:20200806T151500Z
DTEND:20200806T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/16
DESCRIPTION:Title: Morita equivalence of formal Poisson structures and links with defo
rmation quantization\nby Henrique Bursztyn (IMPA) as part of Global Po
isson webinar\n\n\nAbstract\nThe classical notion of Morita equivalence of
algebras has a geometric version for Poisson manifolds (due to Xu)\, def
ined in terms of Weinstein's dual pairs. A natural question is whether the
se two parallel Morita theories could be related by quantization. Motivate
d by this question\, this talk will discuss an extension of Morita equival
ence of Poisson manifolds to the setting of {\\em formal} Poisson structur
es\, and present a result characterizing Morita equivalent formal Poisson
structures vanishing in zeroth order in terms of ``B-field transformations
'' (joint work with I. Ortiz and S. Waldmann). Using the correspondence be
tween formal Poisson structures and star products (due to Kontsevich)\, th
is result leads to a concrete link between Morita equivalence in Poisson g
eometry and noncommutative algebra via deformation quantization.\n\nPlease
register to obtain the password. Use your full name and institutional ema
il address.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (Universität Zürich)
DTSTART:20200813T151500Z
DTEND:20200813T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/17
DESCRIPTION:Title: Complexified Floer homology and skein modules\nby Pavel Safrono
v (Universität Zürich) as part of Global Poisson webinar\n\nAbstract: TB
A\n\nPlease register to obtain the password. Use your full name and instit
utional email address.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Sabatini (Universität zu Köln)
DTSTART:20200917T151500Z
DTEND:20200917T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/18
DESCRIPTION:Title: Some topological properties of monotone complexity one spaces
\nby Silvia Sabatini (Universität zu Köln) as part of Global Poisson web
inar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/globalpoisson/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nigel Hitchin (University of Oxford)
DTSTART:20201008T151500Z
DTEND:20201008T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/19
DESCRIPTION:Title: Teichmueller spaces and the geometry of geodesics\nby Nigel Hit
chin (University of Oxford) as part of Global Poisson webinar\n\n\nAbstrac
t\nThe talk concerns a moduli space of representations of the fundamental
group of a compact surface into the group of Hamiltonian diffeomorphisms o
f $\\mathbb{S}^1 \\times \\mathbb{R}$. The motivation comes from applying
the ideas of Higgs bundles for $\\mathrm{SL}(N\,\\mathbb{R})$ with $N$ equ
al to infinity.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alajandro Cabrera (UFRJ)
DTSTART:20201015T151500Z
DTEND:20201015T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/20
DESCRIPTION:Title: Semiclassical aspects of quantization: Local symplectic groupoids\,
generating functions and the Poisson sigma model\nby Alajandro Cabrer
a (UFRJ) as part of Global Poisson webinar\n\n\nAbstract\nThe aim of this
talk is to present three results related to local symplectic groupoids i
n connection to quantization of the underlying Poisson manifold. We first
review the notion of a generating function $S$ for such local symplectic g
roupoids and outline the first result stating that such $S$ always exist a
nd how to construct them. When the Poisson manifold is a coordinate space\
, we provide an explicit (integral) formula for $S$. The second result mak
es reference to quantization: we show that the formal Taylor expansion $S_
K$ of the coordinate $S$ yields the tree-level part of Kontsevich's quanti
zation formula\, as first studied by Cattaneo-Dherin-Felder. We also sketc
h how the (non-formal) analytic formula for $S$ actually "explains" the gr
aph structure of $S_K$\, using Butcher series techniques. Finally\, the t
hird result relates $S$ to the functional perspective underlying the Poiss
on Sigma Model: we can recover $S$ by evaluating a functional on a set of
solutions ("semiclassical fields") for a system of PDEs on a disk\, which
we also show how to solve (non-perturbatively). We comment on conclusions
and further directions at the end.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavol Ševera (University of Geneva)
DTSTART:20201022T151500Z
DTEND:20201022T161500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/21
DESCRIPTION:Title: Quantization of Poisson Hopf algebras and moduli of flat connection
s\nby Pavol Ševera (University of Geneva) as part of Global Poisson w
ebinar\n\n\nAbstract\nI will describe a universal quantization of Poisson
Hopf algebras using simplicial methods\, i.e. nerves of Hopf algebras (a j
oint work with Jan Pulmann). The motivation for this method comes from mod
uli spaces of flat connections on surfaces with decorated boundaries (an o
lder joint work with David Li-Bland).\n
LOCATION:https://researchseminars.org/talk/globalpoisson/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Cattaneo (Universität Zürich)
DTSTART:20201029T161500Z
DTEND:20201029T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/22
DESCRIPTION:Title: Hamilton-Jacobi and Quantum Chern-Simons on Cylinders\nby Alber
to Cattaneo (Universität Zürich) as part of Global Poisson webinar\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/globalpoisson/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezra Getzler (University of Northwestern)
DTSTART:20201119T161500Z
DTEND:20201119T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/23
DESCRIPTION:Title: Classical field theory\, variational calculus\, and the Batalin-Vil
kovisky formalism\nby Ezra Getzler (University of Northwestern) as pa
rt of Global Poisson webinar\n\n\nAbstract\n"The Batalin-Vilkovisky formal
ism extends Noether's approach to classical field theories\, which is rest
ricted to the Euler-Lagrange locus (or ""on-shell""\, as physicists say)\,
off-shell. This is of course important in the study of quantization of fi
eld theories\, since the quantized theory is not restricted to the Euler-L
agrange locus.\n
\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:20201210T161500Z
DTEND:20201210T171500Z
DTSTAMP:20260422T212829Z
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:20201105T161500Z
DTEND:20201105T171500Z
DTSTAMP:20260422T212829Z
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:20201112T161500Z
DTEND:20201112T171500Z
DTSTAMP:20260422T212829Z
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:20201126T161500Z
DTEND:20201126T171500Z
DTSTAMP:20260422T212829Z
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:20201203T161500Z
DTEND:20201203T171500Z
DTSTAMP:20260422T212829Z
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:20201217T161500Z
DTEND:20201217T171500Z
DTSTAMP:20260422T212829Z
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:20210114T161500Z
DTEND:20210114T171500Z
DTSTAMP:20260422T212829Z
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:20210121T161500Z
DTEND:20210121T171500Z
DTSTAMP:20260422T212829Z
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:20210128T130000Z
DTEND:20210128T140000Z
DTSTAMP:20260422T212829Z
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:20210211T161500Z
DTEND:20210211T171500Z
DTSTAMP:20260422T212829Z
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:20210218T161500Z
DTEND:20210218T171500Z
DTSTAMP:20260422T212829Z
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:20210225T161500Z
DTEND:20210225T171500Z
DTSTAMP:20260422T212829Z
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:20210304T161500Z
DTEND:20210304T171500Z
DTSTAMP:20260422T212829Z
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:20210311T131500Z
DTEND:20210311T141500Z
DTSTAMP:20260422T212829Z
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:20210408T121500Z
DTEND:20210408T131500Z
DTSTAMP:20260422T212829Z
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:20210506T151500Z
DTEND:20210506T161500Z
DTSTAMP:20260422T212829Z
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:20210610T121500Z
DTEND:20210610T131500Z
DTSTAMP:20260422T212829Z
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:20210318T161500Z
DTEND:20210318T171500Z
DTSTAMP:20260422T212829Z
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:20210325T161500Z
DTEND:20210325T171500Z
DTSTAMP:20260422T212829Z
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:20210401T151500Z
DTEND:20210401T161500Z
DTSTAMP:20260422T212829Z
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:20210415T151500Z
DTEND:20210415T161500Z
DTSTAMP:20260422T212829Z
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:20210422T151500Z
DTEND:20210422T161500Z
DTSTAMP:20260422T212829Z
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:20210429T151500Z
DTEND:20210429T161500Z
DTSTAMP:20260422T212829Z
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:20210513T121500Z
DTEND:20210513T131500Z
DTSTAMP:20260422T212829Z
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:20210520T151500Z
DTEND:20210520T161500Z
DTSTAMP:20260422T212829Z
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:20210527T151500Z
DTEND:20210527T161500Z
DTSTAMP:20260422T212829Z
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:20210603T151500Z
DTEND:20210603T161500Z
DTSTAMP:20260422T212829Z
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:20210617T151500Z
DTEND:20210617T161500Z
DTSTAMP:20260422T212829Z
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:20210624T151500Z
DTEND:20210624T161500Z
DTSTAMP:20260422T212829Z
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:20210916T151500Z
DTEND:20210916T161500Z
DTSTAMP:20260422T212829Z
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:20210923T151500Z
DTEND:20210923T161500Z
DTSTAMP:20260422T212829Z
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:20210930T131500Z
DTEND:20210930T141500Z
DTSTAMP:20260422T212829Z
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:20211007T151500Z
DTEND:20211007T161500Z
DTSTAMP:20260422T212829Z
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:20211014T151500Z
DTEND:20211014T161500Z
DTSTAMP:20260422T212829Z
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:20211021T151500Z
DTEND:20211021T161500Z
DTSTAMP:20260422T212829Z
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:20211028T131500Z
DTEND:20211028T141500Z
DTSTAMP:20260422T212829Z
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:20211104T151500Z
DTEND:20211104T161500Z
DTSTAMP:20260422T212829Z
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:20211111T151500Z
DTEND:20211111T161500Z
DTSTAMP:20260422T212829Z
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:20211118T161500Z
DTEND:20211118T171500Z
DTSTAMP:20260422T212829Z
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:20211125T131500Z
DTEND:20211125T141500Z
DTSTAMP:20260422T212829Z
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:20211209T161500Z
DTEND:20211209T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/66
DESCRIPTION:Title: Moment maps for non-reductive group actions in Kähler geometry
\nby Frances Kirwan (Oxford) as part of Global Poisson webinar\n\n\nAbstra
ct\nWhen a complex reductive group $G$ acts linearly on a projective varie
ty $X$\, the GIT quotient $X//G$ can be identified with a symplectic quoti
ent of $X$ by a Hamiltonian action of a maximal compact subgroup $K$ of $G
$. Here the moment map takes values in the (real) dual of the Lie algebra
of $K$\, which embeds naturally in the complex dual of the Lie algebra of
$G$ (as those complex linear maps taking real values on $\\mathfrak{k}$).
The aim of this talk is to discuss an analogue of this description for GIT
quotients by suitable non-reductive actions\, where the analogue of the m
oment map takes values in the complex dual of the Lie algebra of the non-r
eductive group. This is joint work with Gergely Berczi.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Stasheff (University of Pennsylvania)
DTSTART:20211216T161500Z
DTEND:20211216T171500Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/67
DESCRIPTION:Title: Higher holonomy and representations up to homotopy\nby Jim Stas
heff (University of Pennsylvania) as part of Global Poisson webinar\n\n\nA
bstract\n"Given a connection for a smooth vector bundle $p:E\\to M$\, pa
rallel transport with respect to smooth paths in the base space $M$ provid
es a correspondence between smooth vector bundles with flat connection
on $M$ and representations of $\\pi_1(M)$ . Based in part on earlier grou
ndbreaking work of K.T. Chen\, recently this correspondence has been enhan
ced to the level of smooth paths (not homotopy classes) in the base space
$M$ and differential graded vector bundles with generalized flat connect
ions.\n\nClassical parallel transport with respect to smooth paths in the
base space $M$ and the correspondence with representations of $\\pi_1(M)$
will be recalled briefly\, but no familiarity with differential graded vec
tor bundles with generalized flat connections will be assumed."\n
LOCATION:https://researchseminars.org/talk/globalpoisson/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiang Tang (Washington)
DTSTART:20200618T151500Z
DTEND:20200618T161500Z
DTSTAMP:20260422T212829Z
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:20200625T151500Z
DTEND:20200625T161500Z
DTSTAMP:20260422T212829Z
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:20200702T151500Z
DTEND:20200702T161500Z
DTSTAMP:20260422T212829Z
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:20200709T151500Z
DTEND:20200709T161500Z
DTSTAMP:20260422T212829Z
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:20200924T151500Z
DTEND:20200924T161500Z
DTSTAMP:20260422T212829Z
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:20220120T160000Z
DTEND:20220120T170000Z
DTSTAMP:20260422T212829Z
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:Matias del Hoyo (Universidade Federal Fluminense)
DTSTART:20220127T160000Z
DTEND:20220127T170000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/74
DESCRIPTION:Title: Vector bundles over Lie groupoids and related structures\nby Ma
tias del Hoyo (Universidade Federal Fluminense) as part of Global Poisso
n webinar\n\n\nAbstract\nThe differentiation of a Lie groupoid yields a Li
e algebroid and the transverse geometry of a Lie groupoid is encoded in a
differentiable stack. These two constructions admit partial inverses\, thu
s setting a bridge between the theories of algebroids and stacks\, which h
as shown to be useful when dealing for instance with representations and c
ohomology. In this talk\, I will overview vector bundles over Lie groupoid
s\, Lie algebroids\, and differentiable stacks\, explain their key role in
Poisson and Dirac geometries\, discuss their behavior when crossing throu
gh that bridge\, and mention some of my contributions to the subject.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Mnev (University of Notre Dame)
DTSTART:20220203T160000Z
DTEND:20220203T170000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/75
DESCRIPTION:Title: Two field-theoretic viewpoints on the Fukaya-Morse $A_\\infty$-cate
gory\nby Pavel Mnev (University of Notre Dame) as part of Global Poiss
on webinar\n\n\nAbstract\nWe study an enhanced version of the Morse degene
ration of the Fukaya $A_\\infty$-category with higher compositions given b
y counts of gradient flow trees. The enhancement consists in allowing morp
hisms from an object to itself to be chains on the manifold. Higher compos
itions correspond to counting Morse trees passing through a given set of c
hains. We provide two viewpoints on the construction and on the proof of t
he $A_\\infty$-relations for the composition maps. One viewpoint is via an
effective action for the BF theory computed in a special gauge. The other
is via higher topological quantum mechanics. This is a report on a joint
work with O. Chekeres\, A. Losev and D. Youmans\, preprint available at ar
Xiv:2112.12756.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Evens (University of Notre Dame)
DTSTART:20220217T160000Z
DTEND:20220217T170000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/76
DESCRIPTION:Title: On the variety of coisotropic subalgebras\nby Samuel Evens (Uni
versity of Notre Dame) as part of Global Poisson webinar\n\n\nAbstract\nI
will discuss some results due mostly to my students Nicole Kroeger and Doa
n Le on classifying coisotropic subalgebras in a complex semisimple Lie al
gebra with standard Lie bialgebra structure. This work builds on previous
results of Zambon\, and uses my previous work with Jiang-Hua Lu on the va
riety of Lagrangian subalgebras\, along with additional results of Lu on s
pherical conjugacy classes.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hsuan-Yi Liao (National Tsing Hua University)
DTSTART:20220224T130000Z
DTEND:20220224T140000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/77
DESCRIPTION:Title: Homotopy fiber product of manifolds\nby Hsuan-Yi Liao (National
Tsing Hua University) as part of Global Poisson webinar\n\n\nAbstract\nA
main motivation of developing derived differential geometry is to deal wit
h singularities arising from zero loci or intersections of submanifolds. B
oth zero loci and intersections can be considered as fiber products of man
ifolds which may not be manifolds. Thus\, we extend the category of differ
entiable manifolds to a larger category in which one has "homotopy fiber p
roducts". In this talk\, I would like to show a construction\, using vecto
r bundles\, sections and connections\, of homotopy fiber products of manif
olds and explain structures behind the construction. The talk is mainly b
ased on a joint work with Kai Behrend and Ping Xu.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Moreau (Orsay)
DTSTART:20220303T160000Z
DTEND:20220303T170000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/78
DESCRIPTION:Title: Chiral symplectic leaves and arc spaces of Slodowy slices\nby A
nne Moreau (Orsay) as part of Global Poisson webinar\n\n\nAbstract\nIn thi
s talk\, I will present various applications of the notion of chiral sympl
ectic leaves: to quasi-lisse vertex algebras\, to the arc spaces of Slodow
y slices\, to the affine W-algebra at the critical level and the Feigin-Fr
enkel center\, etc. This is based on several joint works with Tomoyuki Ara
kawa.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Gutt (Université libre de Bruxelles)
DTSTART:20220310T160000Z
DTEND:20220310T170000Z
DTSTAMP:20260422T212829Z
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:20220317T160000Z
DTEND:20220317T170000Z
DTSTAMP:20260422T212829Z
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:20220331T120000Z
DTEND:20220331T130000Z
DTSTAMP:20260422T212829Z
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:20220407T150000Z
DTEND:20220407T160000Z
DTSTAMP:20260422T212829Z
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:20220421T150000Z
DTEND:20220421T160000Z
DTSTAMP:20260422T212829Z
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:20220505T160000Z
DTEND:20220505T170000Z
DTSTAMP:20260422T212829Z
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:20211202T160000Z
DTEND:20211202T170000Z
DTSTAMP:20260422T212829Z
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:Allen Knutson (Cornell University)
DTSTART:20220324T160000Z
DTEND:20220324T170000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/86
DESCRIPTION:by Allen Knutson (Cornell University) as part of Global Poisso
n webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/globalpoisson/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aissa Wade (Penn State University)
DTSTART:20220414T150000Z
DTEND:20220414T160000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/87
DESCRIPTION:by Aissa Wade (Penn State University) as part of Global Poisso
n webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/globalpoisson/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhangju Liu (Peking University)
DTSTART:20220428T120000Z
DTEND:20220428T130000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/88
DESCRIPTION:by Zhangju Liu (Peking University) as part of Global Poisson w
ebinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/globalpoisson/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Oms (École normale supérieure de Lyon)
DTSTART:20220512T160000Z
DTEND:20220512T170000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/89
DESCRIPTION:by Cédric Oms (École normale supérieure de Lyon) as part of
Global Poisson webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/globalpoisson/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Roytenberg (Utrecht University)
DTSTART:20220519T160000Z
DTEND:20220519T170000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/90
DESCRIPTION:by Dmitry Roytenberg (Utrecht University) as part of Global Po
isson webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/globalpoisson/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20220526T120000Z
DTEND:20220526T130000Z
DTSTAMP:20260422T212829Z
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
BEGIN:VEVENT
SUMMARY:Kai Behrend (Univercity of British Columbia)
DTSTART:20220210T160000Z
DTEND:20220210T170000Z
DTSTAMP:20260422T212829Z
UID:globalpoisson/92
DESCRIPTION:Title: Some remarks on Lagrangian intersections in the algebraic case\
nby Kai Behrend (Univercity of British Columbia) as part of Global Poisson
webinar\n\n\nAbstract\nSome years ago\, in joint work with B. Fantechi\,
we constructed brackets on the higher structure sheaves of Lagrangian inte
rsections\, and compatible Batalin-Vilkovisky operators\, when certain ori
entations are chosen (see our contribution to Manin’s 70th birthday fest
schrift). This lead to a de-Rham type cohomology theory for Lagrangian int
ersections. In the interim\, much progress has been made on a better under
standing of the origin of these structures\, and some related conjectures
have been proved. We will explain some of these results.\n
LOCATION:https://researchseminars.org/talk/globalpoisson/92/
END:VEVENT
END:VCALENDAR