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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210907T093000
DTEND;TZID=America/New_York:20210907T103000
DTSTAMP:20260705T193834
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
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210914T110200
DTEND;TZID=America/New_York:20210914T120200
DTSTAMP:20260705T193834
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:20210921T130000
DTEND;TZID=America/New_York:20210921T140000
DTSTAMP:20260705T193834
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:20210928T130000
DTEND;TZID=America/New_York:20210928T140000
DTSTAMP:20260705T193834
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
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