Sai-Kee Yeung, Purdue U., USA

Classification and construction of fake projective planes and fake projective spaces

A fake projective plane is a complex surface different from but has the same Betti numbers as the complex projective plane. The first example was constructed by Mumford. Later on two more examples were found by Ishida and Kato.  Very recently a fourth possible one was proposed by Keum.  In this talk we present a joint work with Gopal Prasad on the classification of fake projective planes and their higher dimensional analogues.  Furthermore, new examples are constructed both in dimension two and higher dimensions, one corresponding to each class of our table of classification.