A-infinity structures and moduli space

Monday, 5 March, 2018 to Monday, 28 May, 2018
A-infinity structures and moduli spaces

Alexander Polishchuk (University of Oregon) is spending the spring semester as a SwissMAP guest professor at ETH Zurich. In this context, he will give a course on A-infinity structures and moduli spaces. The first lecture will held on March 5th 2018.


The concept of an A-infinity algebra, originally motivated by homotopy theory (as a more flexible version of Massey products), more recently featured in symplectic geometry and algebraic geometry, due to groundbreaking ideas of Fukaya and Kontsevich’s homological mirror symmetry program.

In my lectures I will start with basics of A-infinity algebras. In particular, I will discuss their deformation theory and explain how to construct A-infinity enhancement of derived categories using homological perturbations. I will then consider some examples arising from algebraic geometry.

From the point of view of establishing equivalences of A-infinity algebras, needed for homological mirror symmetry, it is important to study all possible A-infinity structures extending a given graded associative algebra. I will introduce the corresponding moduli problem and will show that in some cases there exists a fine moduli space parametrizing A-infinity structures. I will consider in detail examples of moduli spaces of A-infinity structures related to moduli spaces of curves.


More information: https://www.math.ethz.ch/fim/lectures/nachdiplom-lectures/alexander-polishchuk.html

Event location: 

ETH - Room HG G 43

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