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DTSTART;TZID=America/New_York:20240222T103000
DTEND;TZID=America/New_York:20240222T113000
DTSTAMP:20260627T025939
CREATED:20240215T152956Z
LAST-MODIFIED:20240216T164834Z
UID:10000879-1708597800-1708601400@cmsa.fas.harvard.edu
SUMMARY:Geometric origins of values of the Riemann Zeta functions at positive integers
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Yan Zhou\, Northeastern \nTitle: Geometric origins of values of the Riemann Zeta functions at positive integers \nAbstract: Given a Fano manifold\, Iritani proposed that the asymptotic behavior of solutions to the quantum differential equation of the Fano should be given by the so-called ‘Gamma class’ in its cohomology ring. Later\, Abouzaid-Ganatra-Iritani-Sheridan reformulated the ‘Gamma conjecture’ for Calabi-Yau manifolds via the tropical SYZ mirror symmetry and proposed that values of the Riemann Zeta function at positive integers have geometric origins in the tropical periods and singularities of the SYZ geometry. In this talk\, we will first review the content of the Gamma conjecture. Then\, we will discuss the first step of generalizing AGIS’ approach to Gamma conjecture for the Gross-Siebert mirror families of a Fano manifold in dimension 2 cases\, based on joint work with Bohan Fang and Junxiao Wang.
URL:https://cmsa.fas.harvard.edu/event/agst-22224/
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-02.22.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240229T103000
DTEND;TZID=America/New_York:20240229T113000
DTSTAMP:20260627T025939
CREATED:20240226T153440Z
LAST-MODIFIED:20240226T153514Z
UID:10000880-1709202600-1709206200@cmsa.fas.harvard.edu
SUMMARY:Classifying curves on Fano varieties
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Brian Lehmann (Boston College) \nTitle: Classifying curves on Fano varieties \nAbstract: How can we understand the set of curves on a Fano variety? One perspective is provided by Geometric Manin’s Conjecture\, a collection of conjectures with roots in arithmetic and topology.  While I will mention some recent progress\, the main focus will be developing a conceptual framework for thinking about our question.
URL:https://cmsa.fas.harvard.edu/event/agst-22924/
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-02.29.2024.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240307T103000
DTEND;TZID=America/New_York:20240307T113000
DTSTAMP:20260627T025939
CREATED:20240214T150457Z
LAST-MODIFIED:20240228T195719Z
UID:10000881-1709807400-1709811000@cmsa.fas.harvard.edu
SUMMARY:Geometric construction of toric NCRs
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Jesse Huang\, University of Alberta \nTitle: Geometric construction of toric NCRs \nAbstract: The Rouquier dimension of a toric variety is recently shown to be achieved by the Frobenius pushforward of O via coherent-constructible correspondence. From the perspective of noncommutative geometry\, this result leads to a geometric construction of toric NCR of the invariant ring of the Cox ring with respect to a multi-grading which also gives the information about its global dimension. From the perspective of mirror symmetry\, the same construction provides a universal “wall skeleton” capturing VGIT wall-crossings\, which contains a window for each chamber as a full subcategory. From the perspective of commutative algebra\, the same construction indicates the existence of virtual resolutions of the multigraded diagonal bimodule\, which agrees with a recent result of Hanlon-Hicks-Larzarev constructing one such resolution explicitly. In this talk\, I will survey these perspectives. The talk is based on joint works with P. Zhou\, joint works with D. Favero\, and work in progress with D. Favero. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/agst-3724/
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-03.07.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240321T103000
DTEND;TZID=America/New_York:20240321T113000
DTSTAMP:20260627T025939
CREATED:20240318T205345Z
LAST-MODIFIED:20240403T173032Z
UID:10000883-1711017000-1711020600@cmsa.fas.harvard.edu
SUMMARY:The KSBA moduli space of log Calabi-Yau surfaces
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Pierrick Bousseau\, University of Georgia \nTitle: The KSBA moduli space of log Calabi-Yau surfaces \nAbstract: The KSBA moduli space\, introduced by Kollár–Shepherd-Barron\, and Alexeev\, is a natural generalization of “the moduli space of stable curves” to higher dimensions. It parametrizes stable pairs (X\,B)\, where X is a projective algebraic variety satisfying certain conditions and B is a divisor such that K_X+B is ample. This moduli space is described concretely only in a handful of situations: for instance\, if X is a toric variety and B=D+\epsilon C\, where D is the toric boundary divisor and C is an ample divisor\, it is shown by Alexeev that the KSBA moduli space is a toric variety. Generally\, for a log Calabi-Yau variety (X\,D) consisting of a projective variety X and an anticanonical divisor D\, with B=D+\epsilon C where C is an ample divisor\, it was conjectured by Hacking–Keel–Yu that the KSBA moduli space is still toric (up to passing to a finite cover). In joint work with Alexeev and Argüz\, we prove this conjecture for all log Calabi-Yau surfaces. This uses tools from the minimal model program\, log smooth deformation theory and mirror symmetry. \n 
URL:https://cmsa.fas.harvard.edu/event/agst-32124/
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-03.21.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240404T103000
DTEND;TZID=America/New_York:20240404T113000
DTSTAMP:20260627T025939
CREATED:20240325T190117Z
LAST-MODIFIED:20240326T153652Z
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:20260627T025939
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:20260627T025939
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:20260627T025939
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
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240509T103000
DTEND;TZID=America/New_York:20240509T113000
DTSTAMP:20260627T025939
CREATED:20240416T133629Z
LAST-MODIFIED:20240507T152049Z
UID:10000890-1715250600-1715254200@cmsa.fas.harvard.edu
SUMMARY:Computing periods of hypersurfaces and elliptic surfaces via effective homology
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Eric Pichon-Pharabod\, Universite Paris-Saclay \nTitle: Computing periods of hypersurfaces and elliptic surfaces via effective homology \nAbstract: The period matrix of a smooth complex projective variety X encodes the isomorphism between its singular homology and its algebraic De Rham cohomology. Numerical approximations with sufficient precision of the entries of this matrix\, called periods\, allow to recover some algebraic invariants of the variety\, such as the Néron-Severi group in the case of surfaces. In this talk\, we will present a method relying on the computation of an effective description of the homology for obtaining such numerical approximations of the periods of hypersurfaces and elliptic surfaces.
URL:https://cmsa.fas.harvard.edu/event/agst-5924/
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-05.09.2024.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240516T103000
DTEND;TZID=America/New_York:20240516T113000
DTSTAMP:20260627T025939
CREATED:20240416T133753Z
LAST-MODIFIED:20240514T183407Z
UID:10003374-1715855400-1715859000@cmsa.fas.harvard.edu
SUMMARY:Mirror symmetry and log del Pezzo surfaces
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Franco Rota\, University of Glasgow \nTitle: Mirror symmetry and log del Pezzo surfaces \nAbstract: The homological mirror symmetry conjecture predicts a duality\, expressed in terms of categorical equivalences\, between the complex geometry of a variety X (the B side) and the symplectic geometry of its mirror object Y (the A side). Motivated by this\, we study a series of singular surfaces (called log del Pezzo). I will describe the category arising in the B side\, using the McKay correspondence and explicit birational geometry. I will discuss early results on the A side\, using the language of pseudolattices to focus on the special case of a smooth degree 2 del Pezzo surface. This is joint work with Giulia Gugiatti.
URL:https://cmsa.fas.harvard.edu/event/agist_51624/
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-05.16.2024.png
END:VEVENT
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