NCMW - Derived categories and semi-orthogonal decompositions (2024)

Speakers and Syllabus

Syllabus:

Name of the Speakers with their affiliation.	No. of Lectures	Detailed Syllabus
Suresh Nayak, ISI Bangalore	6	Derived categories and Semi-orthogonal decomposition Derived categories, semi-orthogonal decomposition, mutations examples: P^n, Homogeneous spaces, the intersection of quadrics.
V. Srinivas, IIT Bombay + Tanya Srivastava, IIT Gandhinagar	3+3	Fourier Mukai transforms and derived Torelli Fourier Mukai transforms, the equivalence of derived categories of an abelian variety and its dual, K3 surface
Manoj Kummini, CMI	6	Hochschild (co)homology Hochschild homology and kernel functors
Swarnava Mukhopadhyay, TIFR	6	Window techniques Basically the work of Halpern-Leistner on “Autoequivalences of derived categories and variation of GIT quotient” and related topics.
BSS Sreedhar, HRI	6	Combinatorial constructions Topics from Combinatorial constructions of derived equivalences.
Anand Sawant, TIFR	6	Homological Projective Duality Homological Projective duality and applications.

References:

D. Huybrechts, Fourier-Mukai transforms in algebraic geometry
Kai Xu and Shing-Tung Yau, Semiorthogonal decompositions of Db(Bun2L)
Richard P. Thomas, Notes on HPD.
Halpern-Leistner, Autoequivalences of derived categories and variation of GIT quotient.
Halpern-Leistner, Steven, Sam Combinatorial constructions of derived equivalences
Kuznetsov, A., Homological projective duality. Publ. Math. Inst. Hautes Etudes Sci. ´ 105, 157–220 (2007)
Kuznetsov, Alexander, Perry, Alexander, Homological projective duality for quadrics. J. Algebraic Geom.30(2021), no.3, 457–476.
Kuznetsov, Alexander. Height of exceptional collections and Hochschild cohomology of quasiphantom categories. J. Reine Angew. Math. 708 (2015), 213–243.
Kuznetsov, Alexander. Hochschild homology and semiorthogonal decompositions. arxiv: /0904.4330
Charles Weibel. An Introduction to Homological Algebra. Cambridge University Press.
Peter Newstead. Geometric Invariant Theory. 3rd cycle. Guanajuato (Mexique), 2006, pp.17. cel-00392098
Robin. Hartshorne. Algebraic Geometry. GTM Vol 52 Springer
Andrei Caldararu. The Mukai pairing, I: the Hochschild structure, arXiv: 0308079

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