## Finnur LárussonProfessor of Pure Mathematics
School of Mathematical
Sciences
office: Ingkarni Wardli, room 649 |

- In August-November 2016, I was a research fellow at the Centre for Advanced Study at the Norwegian Academy of Science and Letters in Oslo. Here is a photo from a seminar I gave at the Centre.
- Short CV
**Mathematical publications****Exposition and course materials**- Eight lectures on Oka manifolds given at the Chinese Academy of Sciences, May 2014
- 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

- I am an associate editor of the Journal of the Australian Mathematical Society
- A video of my lecture entitled The naked pure mathematician, given to a mixed audience of 265 people on 24 March 2015
- In 2010-2017, I was active in
Mathematicians in Schools

Here are the topics that I did with Year 4 and 5 students at Belair Primary School

And here are worksheets that I made for Year 1 and 2 students - I was the director of the 2011 AMSI Summer School
- Mathematical links

My book Lectures
on Real Analysis was published by Cambridge University Press in mid-2012.
Click on the title or the picture of the front cover, and you can have a look inside the book on the CUP website. The book is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The exposition is brisk and concise, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is intended for second-year undergraduates and for more advanced students who need a foundation in real analysis. I will be grateful for any comments from readers. Please e-mail me if you find misprints or mistakes in the book. |

**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; a project on Belyi's famous theorem, characterising the compact Riemann surfaces that can be defined over a number field; and a project on 20th century generalisations of the Riemann mapping theorem.