Finnur Lárusson Professor of Pure Mathematics Discipline of Mathematical Sciences School of Computer and Mathematical Sciences University of Adelaide Adelaide SA 5005 Australia tel.: +61 8 8313 3528 e-mail: myfirstname.mylastname[at]adelaide.edu.au

• Short CV
• My papers
• Exposition and course materials
  • Introduction to some of the pure mathematics underpinning deep learning. Notes for three lectures given in The Other Pure Seminar at the University of Adelaide, March 2024
  • Eight lectures on Oka manifolds given at the Chinese Academy of Sciences, May 2014
  • What is an Oka manifold? A survey article for the Notices of the American Mathematical Society, January 2010
  • Lecture notes for an honours/masters course on the basic theory of smooth manifolds
  • Homotopy theory of equivalence relations
  • Ellipticity and hyperbolicity in geometric complex analysis. Notes for three lectures given at a Winter School on Geometry and Physics, July 2009
  • Slides for undergraduate seminar talks
    • The Limits of Proof
    • Infinite Numbers
• I am an associate editor of the Journal of the Australian Mathematical Society
  • Guidelines for neophyte referees
• I co-organised a Virtual Conference on Complex Analysis and Complex Geometry, 4 May to 14 June 2020
  and the Second Virtual Conference on Complex Analysis and Complex Geometry, 10 May to 13 June 2021
• 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
• 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 the outreach program 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

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. 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.

Recent postgraduate students of mine

Elliot Herrington, PhD 2021, Highly symmetric homogeneous Kobayashi-hyperbolic manifolds
David Bowman, PhD 2016, Holomorphic flexibility properties of spaces of elliptic functions
Alexander Hanysz, PhD 2013, Holomorphic flexibility properties of complements and mapping spaces
Tyson Ritter, PhD 2011, Acyclic embeddings of open Riemann surfaces into elliptic manifolds

Wills Ton Minh Nguyen, MPhil 2023, The closing lemma for Riemann surfaces
Ryan Dye, MPhil 2022, Algebraic Oka theory for curves
Alexander Lai De Oliveira, MPhil 2022, Equivariant Oka theory for Riemann surfaces
Haripriya Sridharan, MPhil 2020, Spaces of holomorphic immersions of open Riemann surfaces into the complex plane
Matthew Ryan, MPhil 2019, The parametric Oka principle for Riemann surfaces
Daniel John, MPhil 2019, Holomorphic immersions of restricted growth from smooth affine algebraic curves into the complex plane
Brett Chenoweth, MPhil 2016, Deformation retractions from spaces of continuous maps onto spaces of holomorphic maps
William Crawford, MPhil 2014, Oka theory of Riemann surfaces

My book Lectures on Real Analysis was published by Cambridge University Press in 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.