课程名称: Introduction to Donaldson-Thomas invariants on Calabi-Yau 4 folds
课程简介: Donaldson-Thomas theory on CY 3-folds is a complexification of Chern-Simons
theory on 3-manifolds, which virtually counts coherent sheaves on CY 3-folds. There are
many interesting studies in this direction, for example, there is a famous conjecture by
Maulik-Nekrasov-Okounkov-Pandharipande which relates DT3 invariants to Gromov-Witten
invariants.
In a series of talks, we will introduce a complexification of Donaldson theory, which can be
regarded as an extension of DT theory to CY 4-folds. We will mention analogue/extension of
several interesting conjectures in DT3 theory to CY 4-folds. More specifically, we will cover:
I. Motivation from DT3 theory and an overview of definition of DT4 invariants.
II. Zero dimensional DT4 invariants.
III. Gopakumar-Vafa type invariants and DT4 invariants of one dimensional stable sheaves.
IV. Curve counting via stable objects in derived categories of CY 4-folds.
V. Hilbert schemes of curves and DT/PT correspondence.
VI. Tautological stable pair invariants.
VII. Counting invariants of perverse coherent systems.
The research involved is partially supported by JSPS KAKENHI Grant Number JP19K23397
and Royal Society Newton International Fellowships Alumni 2019.

授课人简介：曹亚龙，东京大学Kavli IPMU研究所项目研究员。主要研究工作为发展了4维 Calabi-Yau流形上的Donaldson-Thomas理论。文章发表于Adv. Math., Comm. Math.
Phys., J. Eur. Math. Soc., Trans. Amer. Math. Soc. 等期刊。

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