Intercity Seminar

INTERCITY SEMINAR - The integral Hodge conjecture for two-dimensional Calabi-Yau categories after Perry
Fridays, February 23 (Amsterdam), March 8 (Leiden), April 5 (Utrecht) and May 24 (Antwerp), 2024.
Talk length 1 hour 15min including questions.

Logistics for Day 4: May 24, 2024
Venue: Campus Middelheim, Middelheimlaan 1, 2020 Antwerpen, BE. Building A, Rm. M.A.143.
The best way from the central station is to take metro line 15 (direction Boechout P+R Boechout) and step out in Berchem Koninklijkelaan. From there is like 2min walking.
Talk 1: 13:00 - 14:15.
Talk 2: 14:45 - 16:00.
Talk 3: 16:15 -17:30.

Overview
In [1] Perry formulates and proves the variational Hodge conjecture for a family of two dimensional Calabi--Yau 2 categories using K-theory and Hochschild Homologies. Of these, those that degenerate in family to the derived categories of K3 surfaces or abelian surfaces, helps estalish the integral Hodge conjecture for cubic threefolds (and Gushel-Mukai fourfolds). The goal of this seminar is to understand this formulation. As a preparation we will go through bounded derived categories of coherent sheaves, their semi-orthogonal decomposition using [2], K-theory and Hochschild Homologies for varieties and derived categories as in [3]. A detailed syllabus including dates and speakers can be found here .

References.

[1] The integral Hodge conjecture for two-dimensional Calabi-Yau categories, Perry, Compositio Mathematica. 2022;158(2):287-333. doi:10.1112/S0010437X22007266.
[2] Hochschild homology and semiorthogonal decompositions, Kuznetsov, arXiv:0904.4330[math.AG]
[3] Hodge theory and derived categories of cubic fourfolds, Addington, Thomas, Duke Math. J. 163, no. 10 (2014), 1885-1927.
For more references see here.

Organizers.
Ignacio (Antwerp), Emma (Leiden), Yagna (Leiden), Martijn (Utrecht) and Lenny (Amsterdam).