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SUMMARY:Margarida Melo (Roma Tre)
DTSTART:20210629T090000Z
DTEND:20210629T094500Z
DTSTAMP:20260404T094120Z
UID:SMSMS-2021/1
DESCRIPTION:Title: On the top weight cohomology of the moduli space of abelian vari
eties\nby Margarida Melo (Roma Tre) as part of SMSMS 2021 (School on M
irror Symmetry and Moduli Spaces)\n\n\nAbstract\nIn the last few years\, t
ropical methods have been applied quite successfully in understanding seve
ral aspects of the geometry of classical algebro-geometric moduli spaces.
In particular\, in several situations the combinatorics behind compactific
ations of moduli spaces have been given a tropical modular interpretation.
Consequently\, one can study different properties of these (compactified)
spaces by studying their tropical counterparts.\n\nIn this talk\, which i
s based in joint work with Madeleine Brandt\, Juliette Bruce\, Melody Chan
\, Gwyneth Moreland and Corey Wolfe\, I will illustrate this phenomena for
the moduli space Ag of abelian varities of dimension g. In particular\, I
will show how to apply the tropical understanding of the classical toroid
al compactifications of Ag to compute\, for small values of g\, the top we
ight cohomology of Ag.\n\nThe techniques we use follow the breakthrough re
sults and techniques recently developed by Chan-Galatius-Payne in understa
nding the topology of the moduli space of curves via tropical geometry.\n
LOCATION:https://stable.researchseminars.org/talk/SMSMS-2021/1/
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SUMMARY:Nick Sheridan (Edimburgh)
DTSTART:20210629T100000Z
DTEND:20210629T104500Z
DTSTAMP:20260404T094120Z
UID:SMSMS-2021/2
DESCRIPTION:Title: The Gamma and SYZ conjectures\nby Nick Sheridan (Edimburgh)
as part of SMSMS 2021 (School on Mirror Symmetry and Moduli Spaces)\n\n\nA
bstract\nI will give some background on the Gamma Conjecture\, which says
that mirror symmetry does *not* respect integral cycles: rather\, the inte
gral cycles on a complex manifold correspond to integral cycles on the sym
plectic mirror\, multiplied by a certain transcendental characteristic cla
ss called the Gamma class. In the second part of the talk I will explain a
new geometric approach to the Gamma Conjecture\, which is based on the SY
Z viewpoint on mirror symmetry. We find that the appearance of zeta(k) in
the asymptotics of period integrals arises from the codimension-k singular
locus of the SYZ fibration.\n\nThis is based on joint work with Abouzaid\
, Ganatra\, and Iritani.\n
LOCATION:https://stable.researchseminars.org/talk/SMSMS-2021/2/
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SUMMARY:Du Pei (Harvard)
DTSTART:20210630T130000Z
DTEND:20210630T134500Z
DTSTAMP:20260404T094120Z
UID:SMSMS-2021/3
DESCRIPTION:Title: Verlinde Formula\, Brane Quantization\, and Mirror Symmetry\
nby Du Pei (Harvard) as part of SMSMS 2021 (School on Mirror Symmetry and
Moduli Spaces)\n\n\nAbstract\nIntroductory talk surveying some results abo
ut mirror symmetry of branes in the moduli space of Higgs bundles.\n
LOCATION:https://stable.researchseminars.org/talk/SMSMS-2021/3/
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SUMMARY:Anton Mellit (Viena)
DTSTART:20210630T140000Z
DTEND:20210630T144500Z
DTSTAMP:20260404T094120Z
UID:SMSMS-2021/4
DESCRIPTION:Title: Relations in cohomology rings via mirror symmetry\nby Anton
Mellit (Viena) as part of SMSMS 2021 (School on Mirror Symmetry and Moduli
Spaces)\n\n\nAbstract\nI will talk about Lefschets-type sl2 action on the
cohomology of the moduli space of stable GL_n-Higgs bundles. It turns out
\, the S matrix of this action interchanges the operators of multiplicatio
n by certain tautological classes with certain monodromy operators. In a j
oint project with Tamas Hausel we attempt to guess a complete list of rela
tions between these operators. This is then implies some relations in the
cohomology ring. Conjecturally\, we obtain all relations in ranks 2 and 3.
\n
LOCATION:https://stable.researchseminars.org/talk/SMSMS-2021/4/
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