Lines in the Space of K?hler Metrics
报告人：Nicholas McCleerey (Purdue University)
时间：2025-09-17 09:00-10:00
地点：online
【摘要】
We report on joint work with Tamás Darvas, in which we establish a Ross-Witt Nystr?m correspondence for weak geodesic lines in the (completed) space of K?hler metrics. Using this, we construct a wide range of weak geodesic lines on any projective K?hler 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 K?hler metrics.
【报告人介绍】
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.
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