Doctoral Defense in Mathematics - Álfheiður Edda Sigurðardóttir

Doctoral candidate:
Álfheiður Edda Sigurðardóttir

Title of thesis:
Polynomial Approximation and Pluripotential Theory

Opponents:
Dr. David Witt Nyström, Professor at the Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Sweden Prof. Dr. Barbara Drinovec Drnovšek, Professor at the Faculty of Mathematics and Physics, University of Ljubljana, Slovenia

Advisors:
Dr. Benedikt Steinar Magnússon, Associate Professor at the Faculty of Physical Sciences, University of Iceland Dr. Ragnar Sigurðsson, Professor at the Faculty of Physical Sciences, University of Icelandn

Also in the doctoral committee:
Dr. Séverine Biard, Associate professor at the Faculty of Mathematics, Université Polytechnique des Hauts-de-France, France Dr. Tyson Ritter, Associate Professor at the Department of Mathematics and Physics, Universitetet i Stavanger, Norway

Chair of Ceremony:
Dr. Snæbjörn Pálsson, Professor and Head of the Faculty of Life and Environmental Sciences, University of Iceland

Abstract:
We study the rings of polynomials in several complex variables whose exponents are restricted to the dilates of a compact convex set that contains the origin. We study the properties of weighted extremal functions associated to these polynomial rings, that are generalizations of the Siciak function and the pluricomplex Green function. We prove that these functions satisfy a Siciak-Zakharyuta Theorem. We also show versions of the Runge-Oka-Weil Theorem on the approximation of holomorphic functions by polynomials from these rings.

About the candidate:
Álfheiður Edda Sigurðardóttir was born and raised in Reykjavík. Her parents are Sigurður Ólafsson, engineer and Margrét Þorvaldsdóttir, sociologist. She finished her diploma from Reykjavík Junior College in 2016 and her bachelor studies from the University of Iceland in 2019. She graduated with a masters degree from the University of Cambridge the summer of 2020 and began doctoral studies at the University of Iceland the same year. After her doctorate she will move to Ljubljana for postdoctoral research