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SUMMARY:Okke van Garderen (Max-Planck Institute)
DTSTART;VALUE=DATE-TIME:20220317T090000Z
DTEND;VALUE=DATE-TIME:20220317T100000Z
DTSTAMP;VALUE=DATE-TIME:20240329T150058Z
UID:HubEG/1
DESCRIPTION:Title: Sy
mmetry & vanishing in the DT theory of cDV singularities\nby Okke van
Garderen (Max-Planck Institute) as part of Events Hub: Enumerative geometr
y\n\n\nAbstract\nDonaldson–Thomas theory was conceived as a method of co
unting certain sheaves in Calabi-Yau threefolds\, which are supposed to en
code ‘BPS numbers’ in string theory. More recent developments have led
to broader\, refined versions of this theory\, which produce motivic or c
ohomological invariants from moduli spaces of semistable objects in the de
rived category. In this talk I will focus on DT theory for crepant resolut
ions of compound Du-Val singularities\, which include threefold flops\, as
well as some divisor-to-curve contractions and quotient singularities. I
will explain how one can determine the moduli of semistable objects in thi
s setting via a tilting method that is governed by Dynkin diagram combinat
orics. Using this\, I will show that the motivic incarnations of the BPS n
umbers vanish for K-theory classes outside an associated root lattice\, an
d exhibit additional symmetries among these invariants. To make this expli
cit\, I will use the example of a dihedral quotient singularity\, for whic
h the invariants can be fully calculated.\n\nZoom: 941 5513 6832 Code: YMS
C\n
LOCATION:https://researchseminars.org/talk/HubEG/1/
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BEGIN:VEVENT
SUMMARY:Henry Liu (Oxford)
DTSTART;VALUE=DATE-TIME:20220331T090000Z
DTEND;VALUE=DATE-TIME:20220331T100000Z
DTSTAMP;VALUE=DATE-TIME:20240329T150058Z
UID:HubEG/2
DESCRIPTION:Title: Qu
asimaps and stable pairs\nby Henry Liu (Oxford) as part of Events Hub:
Enumerative geometry\n\n\nAbstract\nQuasimaps to Hilbert schemes of surfa
ces S resemble the Donaldson-Thomas theory of S times a curve. This corres
pondence can be made precise for the appropriate DT stability chamber\, na
mely the so-called Bryan-Steinberg stable pairs. I will explain why BS pai
rs and quasimaps are equivalent whenever they are comparable. Quasimaps ha
ve been used recently to study 3d mirror symmetry\, which when pushed thro
ugh this equivalence has implications for some aspects of sheaf-counting t
heories\, including the (DT) crepant resolution conjecture.\n\nZoom: 849 9
63 1368 Code: YMSC\n
LOCATION:https://researchseminars.org/talk/HubEG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Lian
DTSTART;VALUE=DATE-TIME:20220407T090000Z
DTEND;VALUE=DATE-TIME:20220407T100000Z
DTSTAMP;VALUE=DATE-TIME:20240329T150058Z
UID:HubEG/3
DESCRIPTION:Title: Cu
rve-counting with fixed domain (“Tevelev degrees”)\nby Carl Lian a
s part of Events Hub: Enumerative geometry\n\n\nAbstract\nWe will consider
the following problem: if (C\,x_1\,...\,x_n) is a fixed general pointed c
urve\, and X is a fixed target variety with general points y_1\,...\,y_n\,
then how many maps f:C -> X in a given homology class are there\, such th
at f(x_i)=y_i? When considered virtually in Gromov-Witten theory\, the ans
wer may be expressed in terms of the quantum cohomology of X\, leading to
explicit formulas in some cases (Buch-Pandharipande). The geometric questi
on is more subtle\, though in the presence of sufficient positivity\, it i
s expected that the virtual answers are enumerative. I will give an overvi
ew of recent progress on various aspects of this problem\, including joint
work with Farkas\, Pandharipande\, and Cela\, as well as work of other au
thors.\n\nZoom: 849 963 1368 Code: YMSC\n
LOCATION:https://researchseminars.org/talk/HubEG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yalong Cao
DTSTART;VALUE=DATE-TIME:20220519T080000Z
DTEND;VALUE=DATE-TIME:20220519T090000Z
DTSTAMP;VALUE=DATE-TIME:20240329T150058Z
UID:HubEG/4
DESCRIPTION:Title: Go
pakumar-Vafa type invariants of holomorphic symplectic 4-folds\nby Yal
ong Cao as part of Events Hub: Enumerative geometry\n\n\nAbstract\nAbstrac
t: Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and o
ne can consider the corresponding reduced theory. In this talk\, we will e
xplain a definition of Gopakumar-Vafa type invariants for such a reduced t
heory. These invariants are conjectured to be integers and have alternativ
e interpretations using sheaf theoretic moduli spaces. Our conjecture is p
roved for the product of two K3 surfaces\, which naturally leads to a clos
ed formula of Fujiki constants of Chern classes of tangent bundles of Hilb
ert schemes of points on K3 surfaces. On a very general holomorphic symple
ctic 4-folds of K3^[2] type\, our conjecture provides a Yau-Zaslow type fo
rmula for the number of isolated genus 2 curves of minimal degree. Based o
n joint works with Georg Oberdieck and Yukinobu Toda.\n\nZoom Meeting ID:
271 534 5558\nPasscode: YMSC\n
LOCATION:https://researchseminars.org/talk/HubEG/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Moreira (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20220526T080000Z
DTEND;VALUE=DATE-TIME:20220526T090000Z
DTSTAMP;VALUE=DATE-TIME:20240329T150058Z
UID:HubEG/5
DESCRIPTION:Title: We
yl symmetry for curve counting invariants via spherical twists\nby Mig
uel Moreira (ETH Zürich) as part of Events Hub: Enumerative geometry\n\n\
nAbstract\nAbstract: Let X be a Calabi-Yau 3-fold containing a ruled surfa
ce W and let B be the homology class of the lines in the ruling. Physics s
uggests that curve counting on X should satisfy some symmetry relating cur
ves in classes β and β’=β+(W.β)B. In this talk I’ll explain how to
make such a symmetry precise with a new rationality result for the Pandha
ripande-Thomas invariants of X. Mathematically\, the symmetry is explained
by a certain involution of the derived category of X constructed using a
particular spherical functor\; our proof is an instance of the general pr
inciple that automorphisms of the derived category should constrain enumer
ative invariants. This is joint work with Tim Buelles and it is highly ins
pired in the proof of rationality for the PT generating series of an orbif
old by Beentjes-Calabrese-Rennemo.\n\nZoom Meeting ID: 271 534 5558 Passco
de: YMSC\n
LOCATION:https://researchseminars.org/talk/HubEG/5/
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