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SUMMARY:Józef H. Przytycki (George Washington University)
DTSTART;VALUE=DATE-TIME:20220527T130000Z
DTEND;VALUE=DATE-TIME:20220527T140000Z
DTSTAMP;VALUE=DATE-TIME:20220816T040430Z
UID:RVAGeometryFestival2022/1
DESCRIPTION:Title: Extreme Khovanov homology of 4-braids in polynomial time\nby Józef H. Przytycki (George Washington University) as part of Richm
ond Geometry Festival 2022\n\n\nAbstract\nWe start from a gentle introduct
ion to Khovanov homology\, and the sphere conjecture for circle graphs.\n
We have following problem/motivation in mind:\nComputing Khovanov h
omology of links is NP-hard. Thus finding the homotopy type of its geometr
ic realization is also NP-hard.\nWe conjecture that for braid diagrams of
fixed number of strings finding homotopy type of geometric\nrealization (a
nd its homology) has polynomial time complexity with respect to the number
of crossings.\nThe conjecture is wild open but its solution would have a
big impact on understanding of Khovanov homology.\nAs a step toward a solu
tion of the conjecture we prove the following results (they have topologic
al and computational flavor).\n\nFirst we show that the Independence Simpl
icial Complex (ISC)\, $I(w)$ associated to 4-braid diagram $w$ (that is ge
ometric realization\nof extreme Khovanov homology) is either contractible
or\nhomotopy equivalent to a sphere\, wedge of 2 spheres (possibly of diff
erent dimensions)\, a wedge of 3-spheres\n at least two of them of the sam
e dimension\, or a wedge of four spheres at least three of them\n of the s
ame dimension. On the algorithmic side we prove that finding the homotopy
type\n of $I(w)$ can be done in polynomial time with respect to the number
of crossings in $w$.\n This is a joint work with Marithania Silvero.\n
LOCATION:https://researchseminars.org/talk/RVAGeometryFestival2022/1/
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SUMMARY:Ana Peón-Nieto (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20220527T150000Z
DTEND;VALUE=DATE-TIME:20220527T160000Z
DTSTAMP;VALUE=DATE-TIME:20220816T040430Z
UID:RVAGeometryFestival2022/2
DESCRIPTION:Title: The global nilpotent cone in rank 3\nby Ana Peón-Niet
o (University of Birmingham) as part of Richmond Geometry Festival 2022\n\
n\nAbstract\nI will discuss joint ongoing work with Christian Pauly (Nice)
about the zero fiber of the Hitchin map\, emerging from our aim to unders
tand Drinfeld's conjecture in arbitrary rank. The study of the latter\, an
d more generally\, of wobbly bundles\, has led to a deeper understanding o
f this crucial subscheme. After introducing the basics\, I will explain so
me interesting phenomena\, such as the existence of fully wobbly fixed poi
nt components\, or the configuration of C* flows.\n
LOCATION:https://researchseminars.org/talk/RVAGeometryFestival2022/2/
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BEGIN:VEVENT
SUMMARY:Marcos Mariño (University of Geneva)
DTSTART;VALUE=DATE-TIME:20220527T173000Z
DTEND;VALUE=DATE-TIME:20220527T183000Z
DTSTAMP;VALUE=DATE-TIME:20220816T040430Z
UID:RVAGeometryFestival2022/3
DESCRIPTION:Title: Resurgence and quantum topology\nby Marcos Mariño (Un
iversity of Geneva) as part of Richmond Geometry Festival 2022\n\n\nAbstra
ct\nQuantum theories often lead to perturbative series which encode geomet
ric information. In this talk I will argue that\, in the case of complex C
hern-Simons theory\, perturbative series secretly encode integer invariant
s related to enumerative problems (counting of BPS states). The framework
which makes this relation possible is the theory of resurgence\, where per
turbative series are related by Stokes transitions\, and the integer invar
iants arise as Stokes constants. I will illustrate these claims with expli
cit examples related to quantum invariants of hyperbolic knots.\n
LOCATION:https://researchseminars.org/talk/RVAGeometryFestival2022/3/
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SUMMARY:Sergei Gukov (California Institute of Technology)
DTSTART;VALUE=DATE-TIME:20220527T190000Z
DTEND;VALUE=DATE-TIME:20220527T200000Z
DTSTAMP;VALUE=DATE-TIME:20220816T040430Z
UID:RVAGeometryFestival2022/4
DESCRIPTION:Title: Complex Chern-Simons theory: Spin^c structures and quantum
groups at generic q\nby Sergei Gukov (California Institute of Technol
ogy) as part of Richmond Geometry Festival 2022\n\n\nAbstract\nAbout 20 ye
ars ago\, when it was realized that the A-polynomial defines a "spectral c
urve" for complex Chern-Simons theory\, it opened many new doors for exact
perturbative calculations. It also gave clear indications that a non-pert
urbative definition of the theory is intimately related to quantum groups
at generic q. However\, at that time\, the theory was expected to be "boso
nic"\, i.e. did not require a choice of Spin or Spin^c structures. A caref
ul study of non-perturbative complex Chern-Simons theory during the past 5
years led to a somewhat unexpected conclusion that\, as a TQFT\, i.e. as
a theory that enjoys a complete set of cutting-and-gluing (surgery) operat
ions\, it does depend on Spin^c structures. In retrospect\, there are many
good conceptual reasons for this somewhat surprising conclusion\, which w
e review in this talk\, also connecting non-perturbative complex Chern-Sim
ons theory to other 3-manifold invariants (and TQFTs) decorated by Spin an
d Spn^c structure\, including Rokhlin invariants\, Seiberg-Witten invarian
ts\, Turaev torsion\, Heegaard Floer homology\, "correction terms" (a.k.a.
d-invariants)\, etc.\n
LOCATION:https://researchseminars.org/talk/RVAGeometryFestival2022/4/
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SUMMARY:Rahul Pandharipande (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20220528T130000Z
DTEND;VALUE=DATE-TIME:20220528T140000Z
DTSTAMP;VALUE=DATE-TIME:20220816T040430Z
UID:RVAGeometryFestival2022/5
DESCRIPTION:Title: The GW/DT correspondence in families\nby Rahul Pandhar
ipande (ETH Zurich) as part of Richmond Geometry Festival 2022\n\n\nAbstra
ct\nLet X be a nonsingular projective complex 3-fold. The GW/DT correspond
ence relates the Gromov-Witten theory of stable maps to X to the Donaldson
-Thomas theory of sheaves on X. If\, instead\, we have a family of 3-folds
over a base B\, there is a GW/DT correspondence over the base. The equiva
riant theory is an example. The correspondence for families has been studi
ed in very few other cases. After a precise formulation of the general cor
respondence\, I will discuss a non-trivial example related to the Hilbert
scheme of points of the plane.\n
LOCATION:https://researchseminars.org/talk/RVAGeometryFestival2022/5/
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SUMMARY:Angela Ortega (Humboldt University in Berlin)
DTSTART;VALUE=DATE-TIME:20220528T150000Z
DTEND;VALUE=DATE-TIME:20220528T160000Z
DTSTAMP;VALUE=DATE-TIME:20220816T040430Z
UID:RVAGeometryFestival2022/6
DESCRIPTION:Title: Generically finite Prym maps\nby Angela Ortega (Humbol
dt University in Berlin) as part of Richmond Geometry Festival 2022\n\n\nA
bstract\nGiven a finite morphism between smooth projective curves one can
canonically\nassociate it a polarised abelian variety\, the Prym variety.\
nThis induces a map from the moduli space of coverings to the moduli space
\nof polarized abelian varieties\, known as the Prym map.\nIt is a classic
al result that the Prym map is generically injective\nfor étale double co
verings over curves of genus at least 7.\n\nIn this talk I will show the g
lobal injectivity of the Prym map for\nramified double coverings over curv
es of genus $g \\geq 1$ and ramified in\nat least 6 points. This is a join
t work with J.C. Naranjo.\n\nI will finish with an overview on what is kno
wn for the degree of the Prym\nmap for ramified cyclic coverings of degree
$d \\geq 2$.\n
LOCATION:https://researchseminars.org/talk/RVAGeometryFestival2022/6/
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BEGIN:VEVENT
SUMMARY:Maciej Borodzik (University of Warsaw)
DTSTART;VALUE=DATE-TIME:20220528T173000Z
DTEND;VALUE=DATE-TIME:20220528T183000Z
DTSTAMP;VALUE=DATE-TIME:20220816T040430Z
UID:RVAGeometryFestival2022/7
DESCRIPTION:Title: Link lattice homology\nby Maciej Borodzik (University
of Warsaw) as part of Richmond Geometry Festival 2022\n\n\nAbstract\nWe de
fine link lattice homology for plumbed links in 3-manifolds generalizing t
he constructions of Ozsvath\, Stipsicz and Szabo\, and Gorsky and Nemethi.
Building on recent work of Zemke\, we\nshow that for links in plumbed ra
tional homology spheres\, link lattice homology is equal to link Floer hom
ology. As a result\, we prove that for plumbed L-space links in integer ho
mology spheres\, the\nmultivariable Alexander polynomial determines their
link Floer chain complex. This is a joint work with Beibei Liu and Ian Zem
ke.\n
LOCATION:https://researchseminars.org/talk/RVAGeometryFestival2022/7/
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SUMMARY:Patricia Cahn (Smith College)
DTSTART;VALUE=DATE-TIME:20220528T190000Z
DTEND;VALUE=DATE-TIME:20220528T200000Z
DTSTAMP;VALUE=DATE-TIME:20220816T040430Z
UID:RVAGeometryFestival2022/8
DESCRIPTION:Title: Trisected 4-Manifolds as Branched Covers of the 4-Sphere\nby Patricia Cahn (Smith College) as part of Richmond Geometry Festival
2022\n\n\nAbstract\nTrisections of 4-manifolds\, introduced by Gay and Ki
rby as a 4-dimensional analog of Heegaard splittings in dimension 3\, are
a powerful mechanism for importing techniques from 3-dimensional topology
into dimension 4. A branched cover of the 4-sphere\, equipped with its st
andard trisection\, along a (possibly singular) surface in bridge position
\, gives rise to a trisected 4-manifold. A natural question is which tris
ected 4-manifolds arise this way\, and for those that do\, what can be sai
d about the degree of the cover or complexity of the branching set. We di
scuss this problem for the case of geometrically simply-connected 4-manifo
lds\, joint with Blair\, Kjuchukova and Meier\, and give applications to k
not theory and the generalized Slice-Ribbon problem\, joint with Kjuchukov
a.\n
LOCATION:https://researchseminars.org/talk/RVAGeometryFestival2022/8/
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