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DTSTART;TZID=America/New_York:20240516T103000
DTEND;TZID=America/New_York:20240516T113000
DTSTAMP:20260620T101607
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
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240509T103000
DTEND;TZID=America/New_York:20240509T113000
DTSTAMP:20260620T101607
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:20240425T103000
DTEND;TZID=America/New_York:20240425T113000
DTSTAMP:20260620T101607
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:20240418T101500
DTEND;TZID=America/New_York:20240418T113000
DTSTAMP:20260620T101607
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:20240411T103000
DTEND;TZID=America/New_York:20240411T113000
DTSTAMP:20260620T101607
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:20240404T103000
DTEND;TZID=America/New_York:20240404T113000
DTSTAMP:20260620T101607
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:20240321T103000
DTEND;TZID=America/New_York:20240321T113000
DTSTAMP:20260620T101607
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:20240307T103000
DTEND;TZID=America/New_York:20240307T113000
DTSTAMP:20260620T101607
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:20240229T103000
DTEND;TZID=America/New_York:20240229T113000
DTSTAMP:20260620T101607
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:20240222T103000
DTEND;TZID=America/New_York:20240222T113000
DTSTAMP:20260620T101607
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:20240208T103000
DTEND;TZID=America/New_York:20240208T113000
DTSTAMP:20260620T101607
CREATED:20240129T162946Z
LAST-MODIFIED:20240205T190443Z
UID:10000877-1707388200-1707391800@cmsa.fas.harvard.edu
SUMMARY:On (semi)stable reduction and KSBA moduli in positive characteristic
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Iacopo Brivio (Harvard CMSA) \nTitle: On (semi)stable reduction and KSBA moduli in positive characteristic \nAbstract: The moduli space M_g of genus g stable curves is perhaps the most studied of all algebraic varieties. Its higher-dimensional generalization is the moduli functor M_{n\,v} of n-dimension stable varieties of volume v. It was proven only recently\, and thanks to the joint effort of many over many years\, that such functors are represented by projective algebraic spaces when working over the complex numbers. In this talk I will give some examples showing that the same moduli functors in positive characteristic are not even proper and\, more in general\, that the MMP fails to be functorial even in very nice families. In the second part I am going to explore some possible generalizations of the notion of stable variety that could be used as a replacement in positive characteristic.
URL:https://cmsa.fas.harvard.edu/event/agst-2824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240201T103000
DTEND;TZID=America/New_York:20240201T113000
DTSTAMP:20260620T101607
CREATED:20240119T213407Z
LAST-MODIFIED:20240122T183212Z
UID:10000876-1706783400-1706787000@cmsa.fas.harvard.edu
SUMMARY:Algebraic billiards and dynamical degrees
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Max Weinreich (Harvard) \nTitle: Algebraic billiards and dynamical degrees \nAbstract: Billiards is one of the most-studied dynamical systems\, modeling the behavior of a point particle bouncing around some space. If the space is a plane region bounded by an algebraic curve\, then we may use techniques from algebraic geometry to study its billiards map. We explain how to view billiards as a complex algebraic correspondence\, and we prove upper and lower bounds on the dynamical degree\, the growth rate of the degrees of the iterates\, in terms of the degree of the boundary curve. These degree growth rates are studied in mathematical physics\, broadly speaking\, as a way to identify integrable (exactly solvable) physical models. In our setting\, this theory gives us an upper bound on the entropy\, or chaos\, of billiards in curves.
URL:https://cmsa.fas.harvard.edu/event/agst-2124/
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-02.01.2024_Page_1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231211T103000
DTEND;TZID=America/New_York:20231211T113000
DTSTAMP:20260620T101607
CREATED:20240221T112820Z
LAST-MODIFIED:20240221T112900Z
UID:10002782-1702290600-1702294200@cmsa.fas.harvard.edu
SUMMARY:M-theory on nodal Calabi-Yau 3-folds and torsion refined GV-invariants
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Thorsten Schimannek (Utrecht University) \n\nTitle: M-theory on nodal Calabi-Yau 3-folds and torsion refined GV-invariants \nAbstract: The physics of M-theory and Type IIA strings on a projective nodal CY 3-folds is determined by the geometry of a small resolution\, even if the latter is not Kähler. We will demonstrate this explicitly in the context of a family of Calabi-Yau double covers of P^3. Using conifold transitions\, we prove that the exceptional curves in any small resolution are torsion while M-theory develops a discrete gauge symmetry.This leads to a torsion refinement of the ordinary Gopakumar-Vafa invariants\, that is associated to the singular Calabi-Yau and captures the enumerative geometry of the non-Kähler resolutions. We further argue that twisted circle compactifications of the 5d theory are dual to IIA compactifications on the nodal CY 3-fold with a flat but topologically non-trivial B-field. As a result\, the torsion refined invariants are encoded in the topological string partition functions with different choices for the global topology of a flat B-field. \nThe talk is based on 2108.09311\, 2212.08655 (with S. Katz\, A. Klemm\, and E. Sharpe) and 2307.00047 (with S. Katz).
URL:https://cmsa.fas.harvard.edu/event/agst-121123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-12.11.2023-scaled.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231127T103000
DTEND;TZID=America/New_York:20231127T113000
DTSTAMP:20260620T101607
CREATED:20240221T113319Z
LAST-MODIFIED:20240221T113411Z
UID:10002783-1701081000-1701084600@cmsa.fas.harvard.edu
SUMMARY:A p-adic Laplacian on the Tate curve
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: An Huang (Brandeis) \nPre-talk Speaker: TBA: 10:00-10:30 am \n\n\nTitle: A p-adic Laplacian on the Tate curve \nAbstract: We shall first explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis. We then propose a genus one p-adic string worldsheet action. The key is the definition of a p-adic Laplacian operator on the Tate curve. We show that the genus one p-adic Green’s function exists\, is unique under some obvious constraints\, is locally constant off diagonal\, and has a reflection symmetry. It can also be numerically computed exactly off the diagonal\, thanks to some simplifications due to the p-adic setup. Numerics suggest that at least in some special cases\, the asymptotic behavior of the Green’s function near the diagonal is a direct p-adic counterpart of the familiar Archimedean case\, although the p-adic Laplacian is not a local operator. Joint work in progress with Rebecca Rohrlich.
URL:https://cmsa.fas.harvard.edu/event/agst-112723/
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-11.27.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231023T103000
DTEND;TZID=America/New_York:20231023T113000
DTSTAMP:20260620T101607
CREATED:20240222T073026Z
LAST-MODIFIED:20240222T073026Z
UID:10002789-1698057000-1698060600@cmsa.fas.harvard.edu
SUMMARY:Gauged Linear Sigma Models and Cohomological Field Theories
DESCRIPTION:Algebraic Geometry in String Theory Seminar \n\nSpeaker: David Favero\, University of Minnesota \n\nTitle: Gauged Linear Sigma Models and Cohomological Field Theories \nAbstract: This talk is dedicated to the memory of my friend and collaborator Bumsig Kim and based on joint work with Ciocan-Fontanine-Guere-Kim-Shoemaker.  Gauged Linear Sigma Models (GLSMs)  serve as a means of interpolating between Kahler geometry and singularity theory.  In enumerative geometry\, they should specialize to both Gromov-Witten and Fan-Jarvis-Ruan-Witten theory.   In joint work with Bumsig Kim (see arXiv:2006.12182)\, we constructed such enumerative invariants for GLSMs.  Furthermore\, we proved that these invariants form a Cohomological Field Theory.   In this lecture\, I will describe GLSMs and Cohomological Field Theories\, review the history of their development in enumerative geometry\, and discuss the construction of these general invariants.  Briefly\, the invariants are obtained by forming the analogue of a virtual fundamental class which lives in the twisted Hodge complex over a certain “moduli space of maps to the GLSM”.  This virtual fundamental class roughly comes as the Atiyah class of a “virtual matrix factorization” associated to the GLSM data.
URL:https://cmsa.fas.harvard.edu/event/agst-102323/
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-10.23.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231016T100000
DTEND;TZID=America/New_York:20231016T113000
DTSTAMP:20260620T101607
CREATED:20240222T075624Z
LAST-MODIFIED:20240222T075624Z
UID:10002790-1697450400-1697455800@cmsa.fas.harvard.edu
SUMMARY:Moduli of boundary polarized Calabi-Yau pairs
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nPre-talk Speaker: Rosie Shen (Harvard): 10:00-10:30 am \nPre-talk Title: Introduction to the singularities of the MMP \n\nSpeaker: Dori Bejleri (Harvard Math & CMSA) \nTitle: Moduli of boundary polarized Calabi-Yau pairs \nAbstract: The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However\, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau pairs which should interpolate between KSBA and K-stable moduli via wall-crossing.  I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work with K. Ascher\, H. Blum\, K. DeVleming\, G. Inchiostro\, Y. Liu\, X. Wang. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/agst-101623/
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-10.16.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231002T103000
DTEND;TZID=America/New_York:20231002T113000
DTSTAMP:20260620T101607
CREATED:20240222T084421Z
LAST-MODIFIED:20240222T084421Z
UID:10002791-1696242600-1696246200@cmsa.fas.harvard.edu
SUMMARY:Motivic decomposition of moduli space from brane dynamics
DESCRIPTION:Algebraic Geometry in String Theory Seminar \n\n\nPre-talk Speaker: Kai Xu (CMSA): 10:00-10:30 am \n\nSpeaker: Kai Xu (CMSA) \nTitle: Motivic decomposition of moduli space from brane dynamics \nAbstract: Supersymmetric gauge theories encode deep structures in algebraic geometry\, and geometric engineering gives a powerful way to understand the underlying structures by string/M theory. In this talk we will see how the dynamics of M5 branes tell us about the motivic and semiorthogonal decompositions of moduli of bundles on curves.
URL:https://cmsa.fas.harvard.edu/event/agst-10223/
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-10.02.2023.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230925T100000
DTEND;TZID=America/New_York:20230925T113000
DTSTAMP:20260620T101607
CREATED:20240222T090151Z
LAST-MODIFIED:20240222T090151Z
UID:10002792-1695636000-1695641400@cmsa.fas.harvard.edu
SUMMARY:Species Scale across String Moduli Spaces
DESCRIPTION:Algebraic Geometry in String Theory Seminar \n\nPre-talk Speaker: David Wu (Harvard Physics): 10:00-10:30 am \nSpeaker: Damian van de Heisteeg\, CMSA \n\nTitle: Species Scale across String Moduli Spaces \nAbstract: String theories feature a wide array of moduli spaces. We propose that the energy cutoff scale of these theories – the so-called species scale – can be determined through higher-curvature corrections. This species scale varies with the moduli; we use it both asymptotically to bound the diameter of the field space\, as well as in the interior to determine a “desert point” where it is maximized.
URL:https://cmsa.fas.harvard.edu/event/agst-92523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211123T093000
DTEND;TZID=America/New_York:20211123T103000
DTSTAMP:20260620T101607
CREATED:20240213T064610Z
LAST-MODIFIED:20240213T064610Z
UID:10002127-1637659800-1637663400@cmsa.fas.harvard.edu
SUMMARY:Wall crossing for moduli of stable log varieties
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/wall-crossing-for-moduli-of-stable-log-varieties/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211116T093000
DTEND;TZID=America/New_York:20211116T103000
DTSTAMP:20260620T101607
CREATED:20240214T051424Z
LAST-MODIFIED:20240304T061932Z
UID:10002537-1637055000-1637058600@cmsa.fas.harvard.edu
SUMMARY:Gromov-Witten theory of complete intersections
DESCRIPTION:Abstract: I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal Gromov-Witten invariants\, we introduce the new notion of nodal relative Gromov-Witten invariants. This is joint work with Hülya Argüz\, Rahul Pandharipande\, and Dimitri Zvonkine (arxiv:2109.13323).
URL:https://cmsa.fas.harvard.edu/event/gromov-witten-theory-of-complete-intersections/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-Seminar-11.16.21-1-1-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211109T103000
DTEND;TZID=America/New_York:20211109T223000
DTSTAMP:20260620T101607
CREATED:20240304T062554Z
LAST-MODIFIED:20240304T062554Z
UID:10002897-1636453800-1636497000@cmsa.fas.harvard.edu
SUMMARY:Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds
DESCRIPTION:Speaker: Michail Savvas\, UT Austin \nTitle: Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds \nAbstract: Localization by cosection\, first introduced by Kiem-Li in 2010\, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.\nIn this talk\, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence\, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application\, the stable pair invariants of hyperkähler fourfolds\, constructed by Maulik-Cao-Toda\, vanish\, as expected. \n\n\n\nevent\n\n\nOrganizer: Seminars
URL:https://cmsa.fas.harvard.edu/event/11-9-21-cmsa-algebraic-geometry-in-string-theory-seminar/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211109T103000
DTEND;TZID=America/New_York:20211109T113000
DTSTAMP:20260620T101607
CREATED:20240213T062822Z
LAST-MODIFIED:20240304T062818Z
UID:10002112-1636453800-1636457400@cmsa.fas.harvard.edu
SUMMARY:Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds
DESCRIPTION:Abstract: Localization by cosection\, first introduced by Kiem-Li in 2010\, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.\nIn this talk\, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence\, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application\, the stable pair invariants of hyperkähler fourfolds\, constructed by Maulik-Cao-Toda\, vanish\, as expected.
URL:https://cmsa.fas.harvard.edu/event/cosection-localization-for-virtual-fundamental-classes-of-d-manifolds-and-donaldson-thomas-invariants-of-calabi-yau-fourfolds/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-Seminar-11.09.21-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211102T130000
DTEND;TZID=America/New_York:20211102T140000
DTSTAMP:20260620T101607
CREATED:20240214T052811Z
LAST-MODIFIED:20240304T062921Z
UID:10002538-1635858000-1635861600@cmsa.fas.harvard.edu
SUMMARY:Gauss-Manin connection in disguise: Quasi Jacobi forms of index zero
DESCRIPTION:Abstract: We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields. This is a joint work with J. Cao and R. Villaflor. (arXiv:2109.00587)
URL:https://cmsa.fas.harvard.edu/event/gauss-manin-connection-in-disguise-quasi-jacobi-forms-of-index-zero/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211026T130000
DTEND;TZID=America/New_York:20211026T140000
DTSTAMP:20260620T101607
CREATED:20240214T062643Z
LAST-MODIFIED:20240304T063155Z
UID:10002549-1635253200-1635256800@cmsa.fas.harvard.edu
SUMMARY:On singular Hilbert schemes of points
DESCRIPTION:Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a conjecture of Wang-Zhou on the Euler characteristics of the tautological sheaves on Hilbert schemes of points.
URL:https://cmsa.fas.harvard.edu/event/on-singular-hilbert-schemes-of-points/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211019T130000
DTEND;TZID=America/New_York:20211019T140000
DTSTAMP:20260620T101607
CREATED:20240214T053044Z
LAST-MODIFIED:20240304T063307Z
UID:10002539-1634648400-1634652000@cmsa.fas.harvard.edu
SUMMARY:D-critical structure(s) on Quot schemes of points of Calabi-Yau 3-folds
DESCRIPTION:Abstract: D-critical schemes and Artin stacks were introduced by Joyce in 2015\, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes\, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry is wide open. We discuss this problem\, and new results in this direction\, when the moduli space is the Hilbert (or Quot) scheme of points on a Calabi-Yau 3-fold. Joint work with Michail Savvas.
URL:https://cmsa.fas.harvard.edu/event/d-critical-structures-on-quot-schemes-of-points-of-calabi-yau-3-folds/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211012T130000
DTEND;TZID=America/New_York:20211012T140000
DTSTAMP:20260620T101607
CREATED:20240214T053342Z
LAST-MODIFIED:20240304T063443Z
UID:10002540-1634043600-1634047200@cmsa.fas.harvard.edu
SUMMARY:Derived projectivizations of two-term complexes
DESCRIPTION:Abstract: For a given two-term complex of vector bundles on a derived scheme (or stack)\, there are three natural ways to define its “derived projectivizations”: (i) as the derived base-change of the classical projectivization of Grothendieck; (ii) as the derived moduli parametrizing one-dimensional locally free quotients; (iii) as the GIT quotient of the total space by $\mathbb{G}_m$-action. In this talk\, we first show that these three definitions are equivalent. Second\, we prove a structural theorem about the derived categories of derived projectivizations and study the corresponding mutation theory. Third\, we apply these results to various moduli situations\, including the moduli of certain stable pairs on curves and the Hecke correspondences of one-point modification of moduli of stable sheaves on surfaces. If time allowed\, we could also discuss the generalizations of these results to the derived Quot schemes of locally free quotients.
URL:https://cmsa.fas.harvard.edu/event/derived-projectivizations-of-two-term-complexes/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210928T130000
DTEND;TZID=America/New_York:20210928T140000
DTSTAMP:20260620T101607
CREATED:20240214T054256Z
LAST-MODIFIED:20240304T064006Z
UID:10002542-1632834000-1632837600@cmsa.fas.harvard.edu
SUMMARY:The Mirror Clemens-Schmid Sequence
DESCRIPTION:Abstract: I will present a four-term exact sequence relating the cohomology of a fibration to the cohomology of an open set obtained by removing the preimage of a general linear section of the base. This exact sequence respects three filtrations\, the Hodge\, weight\, and perverse Leray filtrations\, so that it is an exact sequence of mixed Hodge structures on the graded pieces of the perverse Leray filtration. I claim that this sequence should be thought of as a mirror to the Clemens-Schmid sequence describing the structure of a degeneration and formulate a “mirror P=W” conjecture relating the filtrations on each side. Finally\, I will present evidence for this conjecture coming from the K3 surface setting. This is joint work with Charles F. Doran.
URL:https://cmsa.fas.harvard.edu/event/the-mirror-clemens-schmid-sequence/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210921T130000
DTEND;TZID=America/New_York:20210921T140000
DTSTAMP:20260620T101607
CREATED:20240214T054755Z
LAST-MODIFIED:20240304T064114Z
UID:10002543-1632229200-1632232800@cmsa.fas.harvard.edu
SUMMARY:What do bounding chains look like\, and why are they related to linking numbers?
DESCRIPTION:Abstract: Gromov-Witten invariants count pseudo-holomorphic curves on a symplectic manifold passing through some fixed points and submanifolds. Similarly\, open Gromov-Witten invariants are supposed to count disks with boundary on a Lagrangian\, but in most cases such counts are not independent of some choices as we would wish. Motivated by Fukaya’11\, J. Solomon and S. Tukachinsky constructed open Gromov-Witten invariants in their 2016 papers from an algebraic perspective of $A_{\infty}$-algebras of differential forms\, utilizing the idea of bounding chains in Fukaya-Oh-Ohta-Ono’06. On the other hand\, Welschinger defined open invariants on sixfolds in 2012 that count multi-disks weighted by the linking numbers between their boundaries. We present a geometric translation of Solomon-Tukachinsky’s construction. From this geometric perspective\, their invariants readily reduce to Welschinger’s.
URL:https://cmsa.fas.harvard.edu/event/what-do-bounding-chains-look-like-and-why-are-they-related-to-linking-numbers/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210914T110200
DTEND;TZID=America/New_York:20210914T120200
DTSTAMP:20260620T101607
CREATED:20240214T055014Z
LAST-MODIFIED:20240304T064603Z
UID:10002544-1631617320-1631620920@cmsa.fas.harvard.edu
SUMMARY:Simplices in the Calabi–Yau web
DESCRIPTION:Abstract: Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds\, and for the associated string theories. In particular\, for 4-folds and beyond\, I will highlight certain simplices appearing in the web\, and identify corresponding derived category structures.
URL:https://cmsa.fas.harvard.edu/event/simplices-in-the-calabi-yau-web/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210907T093000
DTEND;TZID=America/New_York:20210907T103000
DTSTAMP:20260620T101607
CREATED:20240213T112149Z
LAST-MODIFIED:20240304T105626Z
UID:10002492-1631007000-1631010600@cmsa.fas.harvard.edu
SUMMARY:Derived categories of nodal quintic del Pezzo threefolds
DESCRIPTION:Abstract: Conifold transitions are important algebraic geometric constructions that have been of special interests in mirror symmetry\, transforming Calabi-Yau 3-folds between A- and B-models. In this talk\, I will discuss the change of the quintic del Pezzo 3-fold (Fano 3-fold of index 2 and degree 5) under the conifold transition at the level of the bounded derived category of coherent sheaves. The nodal quintic del Pezzo 3-fold X has at most 3 nodes. I will construct a semiorthogonal decomposition for D^b(X) and in the case of 1-nodal X\, detail the change of derived categories from its smoothing to its small resolution.
URL:https://cmsa.fas.harvard.edu/event/derived-categories-of-nodal-quintic-del-pezzo-threefolds/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
END:VCALENDAR