Abstract

We report on joint work with Tamás Darvas, in which we establish a Ross-Witt Nyström correspondence for weak geodesic lines in the (completed) space of Kähler metrics. Using this, we construct a wide range of weak geodesic lines on any projective Kähler manifold which are not generated by holomorphic vector fields, thus disproving a folklore conjecture popularized by Berndtsson. Remarkably, some of these weak geodesic lines turn out to be smooth. In the case of Riemann surfaces, our results can be significantly sharpened. Finally, we investigate the validity of Euclid's fifth postulate for the space of Kähler metrics.

Biography

Nicholas McCleerey is currently an assistant professor at Purdue University. He obtained his Ph.D. at Northwestern University in 2020, under the supervision of Valentino Tosatti. His research focuses on complex geometry.

Zoom meeting

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