2025. 05. 23. 10:30 - 2025. 05. 23. 11:30
Nagyterem + Zoom
Előadó neve: László A. Koltai
Előadó affiliációja: ELTE
Esemény típusa: szeminárium
Szervezés: Intézeti
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Algebraic geometry and differential topology seminar

Leírás

Abstract: Let U ⊆ C^n be an open subset. The Bergman space A^2(U) is the 
Hilbert space of holomorphic functions on U which are square-integrable 
with respect to the Euclidean volume form dV. A theorem of Wiegerinck 
asserts that in dimension one the Bergman space of an open subset U ⊂ C 
is either infinite dimensional or trivial. Recently, this has been 
generalized to holomorphic vector bundles over the projective line by R. 
Szőke and later to vector bundles over any compact Riemann surface by A. 
Gallagher, P. Gupta, L. Vivas.
The topic of this talk will be to prove our even more recent result 
extending this dichotomy to the case of affine and projective algebraic 
curves. To do so I will recall the fundamentals of the theory of 
algebraic curves and introduce Bergman spaces. Then I discuss the 
extension of the results above to the case of certain singular volume 
forms on a Riemann surface associated to divisors and show how this 
yields versions of Wiegerinck’s theorem for algebraic curves.
Joint work with Alexander A. Kubasch and Róbert Szőke.

For Zoom access, please contact Viktória Földvári.