Guest: Nikolaos Chalmoukis, University of Milano - Bicocca
Title: Potential Theory and Boundary Behavior in the Drury–Arveson Space (MATH)
Date/Time: April 16, 2025, 13:40
Location: FENS G032
Abstract: We introduce a notion of capacity in the Drury–Arveson space $H^2_d$ and study its connection to boundary behavior of functions in the space. In particular, we show that functions in $H^2_d$ admit Korányi limits outside sets of capacity zero, and that this condition is sharp. The notion of capacity is further shown to be equivalent to the concept of total nullity. We also present applications to cyclicity and invariant subspaces. This is a joint work with M. Hartz.
Bio: Nikolaos Chalmoukis is currently a type A Researcher (RTDA) at the University of Milano - Bicocca (2023–2025). He was previously an Alexander von Humboldt Postdoctoral Fellow at Saarland University (2022) and held a postdoctoral position at the University of Bologna (2021–2022). He earned his PhD in Mathematics from the University of Bologna under the supervision of Nicola Arcozzi, following a Master’s in Mathematics at Lund University and a Mathematics degree from Aristotle University of Thessaloniki. He also holds a degree in Classical Guitar from the State Conservatory of Thessaloniki. His research lies at the intersection of complex analysis, operator theory, and harmonic analysis, with particular focus on function theory in spaces of analytic functions such as Hardy, Dirichlet, and Bergman spaces. He is also interested in interpolation problems, Carleson measures, ergodic theory, and the geometry of reproducing kernel Hilbert spaces.