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Abstracts for Motivic structures on quantum cohomology and pencils of Calabi-Yau motives. Final reports

Alternatively have a look at the program.

Talks tba. (Motivic structures on quantum cohomology and pencils of Calabi-Yau motives)

Posted in
Date: 
Sat, 2014-09-13 11:00 - 18:00
Location: 
MPIM Lecture Hall

Subjects: Fano manifolds and their mirror dual pencils, maximally mutable Laurent polynomials, the first and second structure connections, gamma conjectures and the gamma class, drops in the images of monodromies in Landau-Ginzburg models, congruence Galois reps and congruence sheaves, Bloch-Kato classes and numerator/denominator of L-values, GSp_4 - Galois representations and paramodular non-lifts, hypergeometric families and weighted projective spaces, hypergeometric motives and their L-functions, extensions of Picard-Fuchs equations and subcritical L-valu

Talks tba. (Motivic structures on quantum cohomology and pencils of Calabi-Yau motives)

Posted in
Date: 
Sun, 2014-09-14 11:00 - 18:00
Location: 
MPIM Lecture Hall

Subjects: Fano manifolds and their mirror dual pencils, maximally mutable Laurent polynomials, the first and second structure connections, gamma conjectures and the gamma class, drops in the images of monodromies in Landau-Ginzburg models, congruence Galois reps and congruence sheaves, Bloch-Kato classes and numerator/denominator of L-values, GSp_4 - Galois representations and paramodular non-lifts, hypergeometric families and weighted projective spaces, hypergeometric motives and their L-functions, extensions of Picard-Fuchs equations and subcritical L-valu

Reducibility of Galois representations and critical L-values: another mod 691 congruence

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Speaker: 
N. Dummigan
Date: 
Mon, 2014-09-15 10:30 - 11:30
Location: 
MPIM Lecture Hall

I will start with Ramanujan's famous mod 691 congruence, after a
brief discussion of rational torsion on elliptic curves, and the
Birch-Swinnerton-Dyer conjecture. Then I will look at an experimental mod
691 congruence of Bergstroem, Faber and van der Geer, involving the Hecke
eigenvalues of a genus 3 Siegel cusp form. This, like Ramanujan's congruence
and Harder's conjecture, is an example of an ``Eisenstein'' congruence. I
will then explain the coincidence of the moduli, visiting the Bloch-Kato
conjecture and Selmer groups along the way."

Amplitude in QFT and string theory, and the relation between them.

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Speaker: 
P. Vanhove
Date: 
Mon, 2014-09-15 11:30 - 12:30
Location: 
MPIM Lecture Hall

String theory amplitudes  are expressed as integral over a moduli
space of Riemann surface. The QFT is the degeneration limit of this.
I'll discuss how limitied Hodge structures are useful to bridge
between what we know in string theory and QFT.

Borcherds Products Everywhere Theorem

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Speaker: 
V. Gritsenko
Date: 
Mon, 2014-09-15 14:00 - 15:00
Location: 
MPIM Lecture Hall

This is a report on my joint results with Cris Poor and David Yuen about
Borcherds Products on groups that are simultaneously orthogonal and symplectic,
the paramodular groups  of degree two and the elementary divisors (1,t).
This work began as an attempt to make Siegel paramodular cusp forms
that are simultaneously Borcherds Products and additive Jacobi lifts
(or Gritsenko lifts). We prove the Borcherds Products Everywhere
Theorem, that constructs holomorphic Borcherds Products from all
Jacobi forms that are theta blocks without theta denominator.

New approach to Calabi-Yau operators

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Speaker: 
D. van Straten
Date: 
Mon, 2014-09-15 15:00 - 16:00
Location: 
MPIM Lecture Hall
Pencils of Calabi-Yau threefolds give rise to local systems and differential operators with very strong arithmetical properties. One interesting source of examples come from regularised quantum cohomology D-modules of Fano varieties. Although no classification is known, one may  hope to characerise and construct such operators  from  first principles.
I will describe joint work in progress with V. Golyshev and A.

Introduction to p-adic L-functions for group GL_2

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Speaker: 
Jeanine van Order
Date: 
Wed, 2014-09-17 10:30 - 11:00
Location: 
MPIM Lecture Hall
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