Algebraic Geometry in String Theory

During the 2021-22 academic year, the CMSA will be hosting a seminar on Algebraic Geometry in String Theory, organized by Yun Shi and Tsung-Ju Lee. This seminar will take place on Tuesdays at 10:30am – 11:30am (Boston time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form, or contact the organizers Yun (yshi@cmsa.fas.harvard.edu) and Tsung-Ju (tjlee@cmsa.fas.harvard.edu).

The schedule below will be updated as talks are confirmed.

DateSpeakerTitle/Abstract
9/7/2021Fei Xie, University of EdinburghTitle: Derived categories of nodal quintic del Pezzo threefolds

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.
9/14/2021Will Donovan, Tsinghua UniversityTitle: Simplices in the Calabi–Yau web

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.
9/21/2021Xujia Chen, Harvard UniversityTitle: What do bounding chains look like, and why are they related to linking numbers?

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.
9/28/2021Alan Thompson, Loughborough UniversityTitle. The Mirror Clemens-Schmid Sequence

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.
10/5/2021

*Special Time: 1:00PM – 2:00PM (ET)*
Mark Shoemaker, Colorado State University
10/12/2021Qingyuan Jang, University of Edinburgh
10/19/2021Andrea Ricolfi, SISSA
10/26/2021Xiaowen Hu
11/2/2021Hossein Movasati, IMPA
11/9/2021Michail Savvas, UT Austin
11/16/2021Pierrick Bousseau, ETH
11/23/2021Dori Bejleri, Harvard
11/30/2021Charles Doran, University of Alberta

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