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DTSTART;TZID=America/New_York:20240404T103000
DTEND;TZID=America/New_York:20240404T113000
DTSTAMP:20260419T035521
CREATED:20240325T190117Z
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UID:10000885-1712226600-1712230200@cmsa.fas.harvard.edu
SUMMARY:Derived categories of genus one curves and torsors over abelian varieties
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Jonathan Rosenberg\, University of Maryland \n\nTitle: Derived categories of genus one curves and torsors over abelian varieties\n \nAbstract:  Studying orientifold string theories on elliptic curves or abelian\nvarieties motivates studying the derived category of coherent sheaves on\na genus one curve or a torsor over an abelian variety over the reals\n(as opposed to the complex numbers).\n\nIn joint work with Nirnajan Ramachandran (to appear in MRL)\, we show that\na genus one curve over a perfect field determines a class in the relative\nBrauer group of the Jacobian elliptic curve\, and that there is a natural\nMukai-type derived equivalence between the original genus one curve\nand the Jacobian twisted by the Brauer class.  The proof extends to\ntorsors over abelian varieties (of any dimension).
URL:https://cmsa.fas.harvard.edu/event/agst-4224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Algebraic-Geometry-in-String-Theory-04.04.24-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240411T103000
DTEND;TZID=America/New_York:20240411T113000
DTSTAMP:20260419T035521
CREATED:20240410T234504Z
LAST-MODIFIED:20240410T234742Z
UID:10000886-1712831400-1712835000@cmsa.fas.harvard.edu
SUMMARY:Mirror symmetry for fibrations and degenerations of K3 surfaces
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Alan Thompson (Loughborough University) \nTitle: Mirror symmetry for fibrations and degenerations of K3 surfaces \nAbstract: In 2016\, Doran\, Harder\, and I conjectured a mirror symmetric relationship between Tyurin degenerations and splittings of codimension 1 fibrations on Calabi-Yau manifolds. In this talk I will discuss recent work to make this conjecture rigorous in the case of K3 surfaces. I will give a precise definition of what it means for a Tyurin degeneration of K3’s to be mirror to a splitting of an elliptically fibred K3\, and show that this definition enjoys the following compatibilities with existing mirror symmetric theories: 1) The general fibre of the Tyurin degeneration is mirror to the elliptically fibred K3\, in the sense of Dolgachev-Nikulin. 2) Components of the Tyurin degeneration and pieces of the splitting satisfy a homological version of the (quasi-) Fano-LG correspondence. 3) Components of the Tyurin degeneration which are weak del Pezzo are mirror to pieces of the splitting that arise as restrictions of the corresponding lattice polarised LG models to discs. This is joint work with Luca Giovenzana.
URL:https://cmsa.fas.harvard.edu/event/agst-41124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-04.11.2024_Page_1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240418T101500
DTEND;TZID=America/New_York:20240418T113000
DTSTAMP:20260419T035521
CREATED:20240415T133328Z
LAST-MODIFIED:20240813T153315Z
UID:10000887-1713435300-1713439800@cmsa.fas.harvard.edu
SUMMARY:Geometric local systems on very general curves
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Aaron Landesman\, MIT \nTitle: Geometric local systems on very general curves \nAbstract: What is the smallest genus h of a non-isotrivial curve over the generic genus g curve? In joint work with Daniel Litt\, we show h is more than $\sqrt{g}$ by proving amore general result about variations of Hodge structure on sufficiently general curves. As a consequence\, we show that local systems on a sufficiently general curve of geometric origin are not Zariski dense in the character variety parameterizing such local systems. This gives counterexamples to conjectures of Esnault-Kerz and Budur-Wang.
URL:https://cmsa.fas.harvard.edu/event/agst-41824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Algebraic-Geometry-in-String-Theory-04.18.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240425T103000
DTEND;TZID=America/New_York:20240425T113000
DTSTAMP:20260419T035521
CREATED:20240416T133525Z
LAST-MODIFIED:20240422T185259Z
UID:10000888-1714041000-1714044600@cmsa.fas.harvard.edu
SUMMARY:The logarithmic double ramification locus
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Alessandro Chiodo\, IMJ-Paris Rive Gauche (Jussieu) \nTitle: The logarithmic double ramification locus \nAbstract: Given a family of smooth curves C -> S with a line bundle L on C\, it is natural to study the locus of points x in S where L_x is trivial on C_x. When the family is stable\, the definition can be extended\, not directly on the base scheme S\, but more naturally on a (logarithmic) blow-up S’ of S. The problem is in many ways analogue to the problem of defining a Néron model on the moduli space of stable curves (instead of a DVR). Over the past years\, David Holmes and his collaborators pioneered a new approach on a logarithmic modification of the entire moduli space of curves. In this talk\, we determine this logarithmic double ramification cycle and several variants and alternative presentations of it (work in collaboration with David Holmes).
URL:https://cmsa.fas.harvard.edu/event/agst-42524/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-04.25.2024.docx-2.png
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