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DTSTART;TZID=America/New_York:20241003T100000
DTEND;TZID=America/New_York:20241003T110000
DTSTAMP:20260620T040305
CREATED:20240927T144416Z
LAST-MODIFIED:20240927T183006Z
UID:10003592-1727949600-1727953200@cmsa.fas.harvard.edu
SUMMARY:Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Chuck Doran\, Harvard CMSA \nTitle: Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds \nAbstract: Smooth $M_m$-polarized K3-fibered Calabi-Yau (CY) 3-folds have been classified in terms of the choice of a generalized functional invariant and\, in the case $m=1$\, a generalized homological invariant. The resulting geometries generally exhibit a small number of complex structure moduli greater or equal to two. A concrete choice of these invariants realizes (almost all of) the known Calabi-Yau geometries with exactly two moduli and allows us to describe completely the structure of the corresponding moduli spaces. The corresponding variations of Hodge structure are entirely determined by the regular periods\, for which we obtain a generic expression in terms of $m$ and three integers $i\,j\,s$. Using the form of this period and Batyrev-Borisov mirror symmetry we explicitly construct the corresponding mirror CY 3-folds with two Kaehler moduli and show consistency with the DHT conjecture. In the cases with $s=0$\, the mirror CY 3-folds are again K3-fibered but with the mirror $<2m>$-polarization. The generic form of the periods allows us to derive generic modular expressions for the A-model topological string free energies and we argue that those are a consequence of a Tyurin degeneration of the generalized functional invariant with the central fiber being an $M_m$-polarized K3. This is joint work with Boris Pioline and Thorsten Schimannek.
URL:https://cmsa.fas.harvard.edu/event/mathphys_10324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-10.3.2024.png
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DTSTART;TZID=America/New_York:20241024T100000
DTEND;TZID=America/New_York:20241024T110000
DTSTAMP:20260620T040305
CREATED:20241018T143428Z
LAST-MODIFIED:20241018T144254Z
UID:10003595-1729764000-1729767600@cmsa.fas.harvard.edu
SUMMARY:Heterotic Little String Theories and Inequivalent Genus-One Fibrations
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Hamza Ahmed\, Northeastern University \nTitle: Heterotic Little String Theories and Inequivalent Genus-One Fibrations \nAbstract: Little String Theories (LSTs) are 6D Supersymmetric quantum field theories (SQFTs) with an additional physical relation called T-duality. This enables us to arrange them into equivalence classes\, where each equivalence class has 6D LSTs that lead to the same 5D effective theory when compactified on a circle. The problem of finding T-dual LSTs can be mapped to the problem of finding inequivalent genus-one fibrations of the same non-compact Calabi-Yau (CY) threefold. For T-dual theories\, certain field theory data is expected to match\, which then implies certain invariants of inequivalent fibrations. Focusing on theories with 8 supercharges (Heterotic LSTs)\, we use this geometry-field theory equivalence to study the T-duality landscape\, particularly in the case where the genus-one fiber does not have a section\, leading to what are called twisted T-dual theories. Based on the excellent agreement we find between the geometry and field theory arguments\, we conjecture the existence of a new class of twisted T-duals for which no geometric construction is known. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_102424/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-10.24.2024.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241031T100000
DTEND;TZID=America/New_York:20241031T110000
DTSTAMP:20260620T040305
CREATED:20241022T175333Z
LAST-MODIFIED:20241022T180010Z
UID:10003596-1730368800-1730372400@cmsa.fas.harvard.edu
SUMMARY:Mirror Construction for Nakajima Quiver Varieties
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Ju Tan (Boston University) \nTitle: Mirror Construction for Nakajima Quiver Varieties \nAbstract: Quiver possesses a rich representation theory. On the one hand\, it exhibits a deep connection with instantons and coherent sheaves as illuminated by the ADHM construction and the works of many others. On the other hand\, quivers also capture the formal deformation space of a Lagrangian submanifold. In this talk\, we will discuss these relations more explicitly from the perspective of SYZ mirror symmetry. In particular\, we will introduce the notion of framed Lagrangian immersions\, the Maurer-Cartan deformation spaces of which are Nakajima quiver varieties/ stacks. Besides\, we will realize the ADHM construction as a mirror symmetry phenomenon. This is based on the joint work with Jiawei Hu and Siu-Cheong Lau. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_103124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-10.31.2024.docx.pdf
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