Abstract: We introduce the trace operator for quasi-plurisubharmonic functions on compact Kähler manifolds, allowing us to study the singularities of such functions along submanifolds where their generic Lelong numbers vanish. Using this construction we obtain novel Ohsawa-Takegoshi extension theorems and give applications to restricted volumes of big line bundles (joint work with Mingchen Xia).

Biography: Dr. Darvas is currently a Full Professor at the University of Maryland. He graduated from Babeș-Bolyai University in 2009 with a degree in Mathematics and Computer Science. He received his PhD in Mathematics from Purdue University in 2014, where his thesis advisor was László Lempert. He has been at the University of Maryland since 2014. His research interests include complex differential geometry, Monge-Ampère type equations and infinite dimensional geometries.

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