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BEGIN:VEVENT
SUMMARY:Józef H. Przytycki (George Washington University)
DTSTART:20220527T130000Z
DTEND:20220527T140000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/1
DESCRIPTION:Title: Extreme Khovanov homology of 4-braids in polynomial
time\nby Józef H. Przytycki (George Washington University) as part o
f Richmond Geometry Festival 2022\n\n\nAbstract\nWe start from a gentle in
troduction to Khovanov homology\, and the sphere conjecture for circle gra
phs.\n We have following problem/motivation in mind:\nComputing Kho
vanov homology of links is NP-hard. Thus finding the homotopy type of its
geometric realization is also NP-hard.\nWe conjecture that for braid diagr
ams of fixed number of strings finding homotopy type of geometric\nrealiza
tion (and 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 solution of the conjecture we prove the following results (they have to
pological and computational flavor).\n\nFirst we show that the Independenc
e Simplicial Complex (ISC)\, $I(w)$ associated to 4-braid diagram $w$ (tha
t is geometric realization\nof extreme Khovanov homology) is either contra
ctible or\nhomotopy equivalent to a sphere\, wedge of 2 spheres (possibly
of different dimensions)\, a wedge of 3-spheres\n at least two of them of
the same dimension\, or a wedge of four spheres at least three of them\n o
f the same dimension. On the algorithmic side we prove that finding the ho
motopy 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 Silver
o.\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Peón-Nieto (University of Birmingham)
DTSTART:20220527T150000Z
DTEND:20220527T160000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/2
DESCRIPTION:Title: The global nilpotent cone in rank 3\nby Ana Pe
ón-Nieto (University of Birmingham) as part of Richmond Geometry Festival
2022\n\n\nAbstract\nI will discuss joint ongoing work with Christian Paul
y (Nice) about the zero fiber of the Hitchin map\, emerging from our aim t
o understand Drinfeld's conjecture in arbitrary rank. The study of the lat
ter\, and more generally\, of wobbly bundles\, has led to a deeper underst
anding of this crucial subscheme. After introducing the basics\, I will ex
plain some interesting phenomena\, such as the existence of fully wobbly f
ixed point components\, or the configuration of C* flows.\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Mariño (University of Geneva)
DTSTART:20220527T173000Z
DTEND:20220527T183000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/3
DESCRIPTION:Title: Resurgence and quantum topology\nby Marcos Mari
ño (University of Geneva) as part of Richmond Geometry Festival 2022\n\n\
nAbstract\nQuantum theories often lead to perturbative series which encode
geometric information. In this talk I will argue that\, in the case of co
mplex Chern-Simons theory\, perturbative series secretly encode integer in
variants related to enumerative problems (counting of BPS states). The fra
mework which makes this relation possible is the theory of resurgence\, wh
ere perturbative series are related by Stokes transitions\, and the intege
r invariants arise as Stokes constants. I will illustrate these claims wit
h explicit examples related to quantum invariants of hyperbolic knots.\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (California Institute of Technology)
DTSTART:20220527T190000Z
DTEND:20220527T200000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/4
DESCRIPTION:Title: Complex Chern-Simons theory: Spin^c structures and
quantum groups at generic q\nby Sergei Gukov (California Institute of
Technology) as part of Richmond Geometry Festival 2022\n\n\nAbstract\nAbou
t 20 years ago\, when it was realized that the A-polynomial defines a "spe
ctral curve" for complex Chern-Simons theory\, it opened many new doors fo
r exact perturbative calculations. It also gave clear indications that a n
on-perturbative definition of the theory is intimately related to quantum
groups at generic q. However\, at that time\, the theory was expected to b
e "bosonic"\, i.e. did not require a choice of Spin or Spin^c structures.
A careful 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)
operations\, it does depend on Spin^c structures. In retrospect\, there a
re many good conceptual reasons for this somewhat surprising conclusion\,
which we review in this talk\, also connecting non-perturbative complex Ch
ern-Simons theory to other 3-manifold invariants (and TQFTs) decorated by
Spin and Spn^c structure\, including Rokhlin invariants\, Seiberg-Witten i
nvariants\, Turaev torsion\, Heegaard Floer homology\, "correction terms"
(a.k.a. d-invariants)\, etc.\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Pandharipande (ETH Zurich)
DTSTART:20220528T130000Z
DTEND:20220528T140000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/5
DESCRIPTION:Title: The GW/DT correspondence in families\nby Rahul
Pandharipande (ETH Zurich) as part of Richmond Geometry Festival 2022\n\n\
nAbstract\nLet X be a nonsingular projective complex 3-fold. The GW/DT cor
respondence relates the Gromov-Witten theory of stable maps to X to the Do
naldson-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
equivariant theory is an example. The correspondence for families has bee
n studied in very few other cases. After a precise formulation of the gene
ral correspondence\, I will discuss a non-trivial example related to the H
ilbert scheme of points of the plane.\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Ortega (Humboldt University in Berlin)
DTSTART:20220528T150000Z
DTEND:20220528T160000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/6
DESCRIPTION:Title: Generically finite Prym maps\nby Angela Ortega
(Humboldt University in Berlin) as part of Richmond Geometry Festival 2022
\n\n\nAbstract\nGiven a finite morphism between smooth projective curves o
ne can canonically\nassociate it a polarised abelian variety\, the Prym va
riety.\nThis induces a map from the moduli space of coverings to the modul
i space\nof polarized abelian varieties\, known as the Prym map.\nIt is a
classical result that the Prym map is generically injective\nfor étale do
uble coverings over curves of genus at least 7.\n\nIn this talk I will sho
w the global injectivity of the Prym map for\nramified double coverings ov
er curves of genus $g \\geq 1$ and ramified in\nat least 6 points. This is
a joint work with J.C. Naranjo.\n\nI will finish with an overview on what
is known for the degree of the Prym\nmap for ramified cyclic coverings of
degree $d \\geq 2$.\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Borodzik (University of Warsaw)
DTSTART:20220528T173000Z
DTEND:20220528T183000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/7
DESCRIPTION:Title: Link lattice homology\nby Maciej Borodzik (Univ
ersity of Warsaw) as part of Richmond Geometry Festival 2022\n\n\nAbstract
\nWe define link lattice homology for plumbed links in 3-manifolds general
izing the constructions of Ozsvath\, Stipsicz and Szabo\, and Gorsky and N
emethi. Building on recent work of Zemke\, we\nshow that for links in plu
mbed rational homology spheres\, link lattice homology is equal to link Fl
oer homology. As a result\, we prove that for plumbed L-space links in int
eger homology spheres\, the\nmultivariable Alexander polynomial determines
their link Floer chain complex. This is a joint work with Beibei Liu and
Ian Zemke.\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patricia Cahn (Smith College)
DTSTART:20220528T190000Z
DTEND:20220528T200000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/8
DESCRIPTION:Title: Trisected 4-Manifolds as Branched Covers of the 4-S
phere\nby Patricia Cahn (Smith College) as part of Richmond Geometry F
estival 2022\n\n\nAbstract\nTrisections of 4-manifolds\, introduced by Gay
and Kirby as a 4-dimensional analog of Heegaard splittings in dimension 3
\, are a powerful mechanism for importing techniques from 3-dimensional to
pology into dimension 4. A branched cover of the 4-sphere\, equipped with
its standard trisection\, along a (possibly singular) surface in bridge p
osition\, gives rise to a trisected 4-manifold. A natural question is whi
ch trisected 4-manifolds arise this way\, and for those that do\, what can
be said about the degree of the cover or complexity of the branching set.
We discuss this problem for the case of geometrically simply-connected 4
-manifolds\, joint with Blair\, Kjuchukova and Meier\, and give applicatio
ns to knot theory and the generalized Slice-Ribbon problem\, joint with Kj
uchukova.\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Welcome message
DTSTART:20220527T124500Z
DTEND:20220527T130000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/9
DESCRIPTION:Title: Welcome message\nby Welcome message as part of
Richmond Geometry Festival 2022\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Informal discussion
DTSTART:20220527T141500Z
DTEND:20220527T150000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/10
DESCRIPTION:Title: Informal discussion on gather.town\nby Informa
l discussion as part of Richmond Geometry Festival 2022\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Poster session
DTSTART:20220527T161500Z
DTEND:20220527T173000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/11
DESCRIPTION:Title: Poster session\nby Poster session as part of R
ichmond Geometry Festival 2022\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Informal discussion
DTSTART:20220527T184500Z
DTEND:20220527T190000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/12
DESCRIPTION:Title: Informal discussion on gather.town\nby Informa
l discussion as part of Richmond Geometry Festival 2022\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swatee Naik (NSF)
DTSTART:20220527T203000Z
DTEND:20220527T213000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/13
DESCRIPTION:Title: Applying for grants: panel discussion\nby Swat
ee Naik (NSF) as part of Richmond Geometry Festival 2022\n\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Informal discussion
DTSTART:20220528T141500Z
DTEND:20220528T150000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/14
DESCRIPTION:Title: Informal discussion on gather.town\nby Informa
l discussion as part of Richmond Geometry Festival 2022\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Informal discussion
DTSTART:20220528T161500Z
DTEND:20220528T173000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/15
DESCRIPTION:Title: Informal discussion on gather.town\nby Informa
l discussion as part of Richmond Geometry Festival 2022\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Informal discussion
DTSTART:20220528T184500Z
DTEND:20220528T190000Z
DTSTAMP:20260404T095040Z
UID:RVAGeometryFestival2022/16
DESCRIPTION:Title: Informal discussion on gather.town\nby Informa
l discussion as part of Richmond Geometry Festival 2022\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RVAGeometryFestival2022/
16/
END:VEVENT
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