Finnur Lárusson Associate Professor of Pure Mathematics School of Mathematical Sciences University of Adelaide Adelaide SA 5005 Australia office: Ingkarni Wardli, room 649 tel.: +61 8 8303 3528 e-mail: myfirstname.mylastname[at]adelaide.edu.au

• Short CV and research information
• Mathematical publications
  • My papers as downloadable PDF files
  • Reviews of my papers on MathSciNet
• Exposition and course materials
  • Survey of Oka theory, September 2010
  • What is an Oka manifold? A survey article for the Notices of the American Mathematical Society, January 2010
  • Lecture notes for an honours course on differential geometry
  • Homotopy theory of equivalence relations
  • Notes for three lectures given at a Winter School on Geometry and Physics, July 2009: Ellipticity and hyperbolicity in geometric complex analysis
  • Slides for undergraduate seminar talks
    • The Limits of Proof
    • Infinite Numbers
• Mathematical links
• I participate in Mathematicians in Schools
• I was the director of the 2011 AMSI Summer School

I welcome enquiries from prospective honours or postgraduate students. Feel free to e-mail me or, if you are in Adelaide, stop by my office.

If you are interested in PhD or MPhil studies in Adelaide, I would be glad to discuss possible thesis topics with you. I mainly work in complex analysis and complex geometry, including pluripotential theory, and applications of abstract homotopy theory to these areas. Start by looking at my papers or read this to get an idea of what sorts of things I do. There are several other people in Adelaide working in related areas. We run an active seminar with talks by locals and visitors.

I am happy to supervise honours projects in complex analysis and the many areas of mathematics that interact with it. An honours topic that I particularly like is the theory of compact Riemann surfaces. It provides an opportunity to meet and apply important ideas from functional analysis, homological algebra, manifold theory, partial differential equations, and sheaf theory in an accessible geometric context. The first goal of a project in this area would be to get to the central theorem on compact Riemann surfaces, the Riemann-Roch Theorem. After that, the project could continue in various different directions.

There are many other options, including complex analysis in higher dimensions, algebraic geometry, differential geometry, topology, and category theory. In recent years I have supervised an honours project on wavelets, a newly developed area within real and functional analysis with applications to image compression; a project about the correspondence between planar trees and so-called Shabat polynomials, involving combinatorics, complex analysis, and topology; a project on one-dimensional complex tori, also known as elliptic curves; a project about category theory and toposes of graphs; a project on the so-called Oka principle, which mixes homotopy theory and complex geometry; and a project on Belyi's famous theorem, characterising the compact Riemann surfaces that can be defined over a number field.