Lectures on

Variations of Hodge structures, special geometry,

and tt* geometry


Murad Alim

(Emmy Noether Research Group Leader, Hamburg University)

Waseda University

Nishi-Waseda Campus, Building 60, Room 303 A-B (third floor)

4-8 February 2019


This course will introduce some concepts of variations of Hodge structures guided by the example of families of elliptic curves. It will be shown how the Gauss Manin flat connection gives rise to an instance of the tt* equations and of special geometry in this case. The modularity of the solutions of the differential equations stemming from the Gauss Manin flat connection will be discussed. Furthermore a differential ring of special functions will be introduced, whose existence is related to the flatness of the Gauss Manin connection and which is, in the case of elliptic curves, related to the differential ring of quasi modular forms. Moreover, an enhanced moduli space of pairs of elliptic curves together with differential forms will be introduced, which connects in a natural way to modular forms.


Monday February 4,14:45-18:00

Tuesday February 5,14:45-18:00

Thursday February 7, 14:45-18:00

Friday February 8, 14:45-16:15

The course is an activity of the

Mathematics and Physics Unit "Multiscale Analysis, Modelling and Simulation" Top Global University Project, Waseda University

Students may register to obtain credit for this course (MATX72ZL Advanced Study of Nonlinear Mechanics).

These lectures are also supported by the Institute for Mathematical Science, Waseda University

Introductory lectures will be given by Martin Guest (Waseda University) as follows:

Monday January 21,14:45-18:00 Room 59-217

Tuesday January 22,14:45-18:00 Room: 51-18-06

Monday January 28,14:45-18:00 Room: 51-17-06

Tuesday January 29,14:45-18:00 Room: 51-18-06

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