Counting curves on K3 surfaces and modular forms
Rahul Pandharipande (Zürich)
What 


When 
May 28, 2015 from 03:15 pm to 04:15 pm 
Where  Mainz, 05432 (Hilbertraum) 
Contact Name  Duco van Straten 
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Abstract. I will discuss the enumeration of curves on K3 surfaces: both the classical roots in projective geometry and the modern successes (connected to modular forms). How many tritangent planes does a quartic surface have? The answer, when appropriately counted, is 3200  the q^2 coefficient of the Fourier expansion of the inverse of the discriminant modular form. This connection was first noticed by Yau and Zaslow in 1995. In the last two decades, all such counting question for K3 surfaces have been connected to modular forms. I will present both the results and the open directions in the subject.