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SUMMARY:Infinite staircases in the symplectic ball packing problem
DTSTART;VALUE=DATE-TIME:20230919T110000Z
DTEND;VALUE=DATE-TIME:20230919T115000Z
DTSTAMP;VALUE=DATE-TIME:20240424T141012Z
UID:indico-contribution-272-2836@indico.ph.ed.ac.uk
DESCRIPTION:Speakers: Ana Rita Pires (University of Edinburgh)\nThe symple
ctic version of the problem of packing K balls into a ball in the densest
way possible (in 4 dimensions) can be extended to that of symplectically e
mbedding an ellipsoid into a ball as small as possible. A classic result d
ue to McDuff and Schlenk asserts that the function that encodes this probl
em has a remarkable structure: its graph has infinitely many corners\, det
ermined by Fibonacci numbers\, that fit together to form an infinite stair
case.\n\nThis ellipsoid embedding function can be equally defined for othe
r targets\, and in this talk I discuss for which other targets the functio
n also has an infinite staircase. In the case when these targets can be re
presented by lattice (moment) polygons\, the targets seem to be exactly th
ose whose polygon is reflexive (i.e.\, has one interior lattice point). In
a specific family of irrational polygons\, the answer involves self-simil
ar behavior akin to the Cantor set.\n\nThis talk is based on various proje
cts\, joint with Dan Cristofaro-Gardiner\, Tara Holm\, Alessia Mandini\, M
aria Bertozzi\, Tara Holm\, Emily Maw\, Dusa McDuff\, Grace Mwakyoma\, Mor
gan Weiler\, and Nicki Magill.\n\nhttps://indico.ph.ed.ac.uk/event/272/con
tributions/2836/
LOCATION:JCMB 5323
URL:https://indico.ph.ed.ac.uk/event/272/contributions/2836/
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BEGIN:VEVENT
SUMMARY:Symplectic geometry of Coulomb branches
DTSTART;VALUE=DATE-TIME:20230919T130000Z
DTEND;VALUE=DATE-TIME:20230919T135000Z
DTSTAMP;VALUE=DATE-TIME:20240424T141012Z
UID:indico-contribution-272-2835@indico.ph.ed.ac.uk
DESCRIPTION:Speakers: Gwyn Bellamy (University of Glasgow)\nIn their landm
ark paper in 2016\, Braverman-Finkelberg-Nakajima gave a mathematically ri
gour definition of the Coulomb branch of 3d N=4 supersymmetric gauge theor
ies (of cotangent type). This broad class of spaces have many remarkable p
roperties and are expected to play a key role in developing a geometric re
presentation theory around "double affine Grassmannians". In particular\,
they conjectured that these spaces should be examples of symplectic singu
larities. In this talk I'll describe some of the basic properties of these
spaces and outline a simple proof of the fact that they have do indeed ha
ve symplectic singularities.\n\nhttps://indico.ph.ed.ac.uk/event/272/contr
ibutions/2835/
LOCATION:JCMB 5323
URL:https://indico.ph.ed.ac.uk/event/272/contributions/2835/
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BEGIN:VEVENT
SUMMARY:From symplectic to Poisson manifolds and back
DTSTART;VALUE=DATE-TIME:20230919T160000Z
DTEND;VALUE=DATE-TIME:20230919T170000Z
DTSTAMP;VALUE=DATE-TIME:20240424T141012Z
UID:indico-contribution-272-2837@indico.ph.ed.ac.uk
DESCRIPTION:Speakers: Eva Miranda (Universitat Politècnica de Catalunya +
CRM-Barcelona)\nb-Structures and other generalizations (such as E-symplec
tic structures) are ubiquitous and sometimes hidden\, unexpectedly\, in a
number of problems including the space of pseudo-Riemannian geodesics and
regularization transformations of the three-body problem. E-symplectic ma
nifolds include symplectic manifolds with boundary\, manifolds with corne
rs\, compactified cotangent bundles and regular symplectic foliations. Th
eir deformation quantization was studied à la Fedosov by Nest and Tsygan.
How general can such structures be? In this talk\, I first explain how to
associate an E-symplectic structure\nto a Poisson structure with transver
se structure of semisimple type (joint work with Ryszard Nest) and I will
connect this to a result by Cahen\, Gutt and Rawnsley on tangential star p
roducts. This result illustrates how E-symplectic manifolds serve as a tr
ampoline to the investigation of the geometry of Poisson manifolds and the
different facets of their quantization. This should let us address a numb
er of open questions in Poisson Geometry and the study of its quantization
from a brand-new perspective.\n\nhttps://indico.ph.ed.ac.uk/event/272/con
tributions/2837/
LOCATION:Nucleus Yew Lecture Theatre
URL:https://indico.ph.ed.ac.uk/event/272/contributions/2837/
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SUMMARY:Quantum cohomology as a deformation of symplectic cohomology
DTSTART;VALUE=DATE-TIME:20230919T140000Z
DTEND;VALUE=DATE-TIME:20230919T145000Z
DTSTAMP;VALUE=DATE-TIME:20240424T141012Z
UID:indico-contribution-272-2834@indico.ph.ed.ac.uk
DESCRIPTION:Speakers: Nick Sheridan (University of Edinburgh)\nLet M be a
compact symplectic manifold\, and D a normal-crossings symplectic divisor
in M. We give a criterion (which can be naturally expressed in terms of th
e Kodaira dimension of M and log Kodaira dimension of M \\ D\, in the cont
ext where M and D come from the realm of algebraic geometry) under which t
he quantum cohomology of M is a deformation of the symplectic cohomology o
f M \\ D. We will give an idea of what quantum cohomology and symplectic c
ohomology are. We will also show that the `skeleton' of M \\ D has strong
symplectic rigidity properties in this context\, and explain some conjectu
res about what happens when our criterion is not satisfied. If time permit
s we will explain the relationship with mirror symmetry. This is joint wor
k with Strom Borman and Umut Varolgunes.\n\nhttps://indico.ph.ed.ac.uk/eve
nt/272/contributions/2834/
LOCATION:JCMB 5323
URL:https://indico.ph.ed.ac.uk/event/272/contributions/2834/
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SUMMARY:Morse homology of the complex Chern—Simons functional from deriv
ed symplectic geometry
DTSTART;VALUE=DATE-TIME:20230919T100000Z
DTEND;VALUE=DATE-TIME:20230919T105000Z
DTSTAMP;VALUE=DATE-TIME:20240424T141012Z
UID:indico-contribution-272-2833@indico.ph.ed.ac.uk
DESCRIPTION:Speakers: Pavel Safronov (University of Edinburgh)\nThe Chern
—Simons functional is defined on the non-compact infinite-dimensional sp
ace of connections and so its Morse homology is not well-defined. However\
, its critical locus\, the moduli space of flat connections\, is finite-di
mensional. I will explain how one can use shifted symplectic geometry of t
he moduli space of flat connections to define the relevant Morse homology
groups and outline connections to other objects\, such as skein modules of
3-manifolds and Donaldson-Thomas invariants. This talk is based on work i
n progress joint with Sam Gunningham.\n\nhttps://indico.ph.ed.ac.uk/event/
272/contributions/2833/
LOCATION:JCMB 5323
URL:https://indico.ph.ed.ac.uk/event/272/contributions/2833/
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