Matematični predavanji Rafaela Andrista in Daniela Smertniga
Na Oddelku za matematiko bomo v petek, 19. maja, v predavalnici 2.05 organizirali dve matematični predavanji, kjer bosta predavatelja Rafael Andrist (ob 10.15) in Daniel Smertnig (ob 12.15) predstavila svoje raziskovalno delo. Naslova in povzetka predavanj se nahajata spodaj.
Rafael Benedikt Andrist, FMF: Symmetries in complex Geometry
Symmetries are a fundamental concept of geometry. In complex-analytic geometry, the symmetries to be studied are the holomorphic automorphisms of complex manifolds. In this talk, we focus on Stein manifolds with the so-called density property. These are complex manifolds that enjoy having a very large group of holomorphic automorphisms, allowing for approximation and interpolation results. Among the examples discussed will be the spectral ball and Calogero-Moser spaces.
Daniel Smertnig, Univerza v Gradcu: Algebraic structures and arithmetical properties
I will discuss the interaction of algebraic structures and arithmetical properties in two aspects: (1) the study of non-unique factorizations of elements into irreducibles in (noncommutative) rings, and in a similar vein, the study of direct-sum decompositions of modules via the non-unique factorization theory of monoids; and (2) implications of arithmetical restrictions on coefficients of rational noncommutative power series on their structural decomposition. The talk will consist of a brief survey of results and current projects in (1), and then focus on (2). Here, I characterize noncommutative multivariate rational power series over a field K, whose coefficients are contained in a finite subgroup K (Pólya series). This extends a classical theorem of Pólya from the univariate to the noncommutative multivariate setting, and resolves a 1979 conjecture of Reutenauer. Further, I show how this leads to the resolution of an algorithmic decidability question concerning the determinizability of weighted finite automata.