Welcome to my website. I am a post-doc at the University of Münster.

I am a research mathematician with interests in the theory of building, large cardinals, and geometric group theory.

My CV- PhD thesis,
*Generalizations of the Fundamental Theorem of Projective Geometry*, University of New South Wales, Supervisor: Prof. Michael Cowling. - Prècis of PhD thesis in Bulletin of Australian Mathematical Society
- Andreas Čap, Michael G. Cowling, Filippo de Mari, Michael Eastwood, and Rupert McCallum,
*The Heisenberg Group, SL(3,R) and Rigidity*, in "Group Representations, Automorphic Forms, and Invariant Theory". - Rupert McCallum, Rigidity of the group topology for p-adic semisimple groups and automorphism groups of trees, submitted
- Rupert McCallum, A Local-to-Global Result for Topological Spherical Buildings, Advances in Geometry. Band 13, Heft 3, Seiten 435 - 448, July 2013
- Rupert McCallum, A Consistency Proof for Some Restrictions of Tait's Reflection Principles, Mathematical Logic Quarterly, Volume 59, Issue 1-2, pages 112-118
- Rupert McCallum, Rigidity of the group topology for closed Weyl transitive groups of automorphisms of a Bruhat-Tits tree and maximal Kac-Moody groups over a finite field, submitted

I also take a strong interest in the philosophy of mathematics, physics and its philosophy, normative ethics, and meta-ethics. On previous occasions I gave a talk at the University of Sydney to students about to embark on animal research projects about the philosophy of animal rights. I'm extremely interested in the work Penelope Maddy in the philosophy of set theory and the work of Peter Koellner and Hugh Woodin in set theory and its philosophy. Here is my entry to Sam Harris' Moral Landscape essay competition.

I submitted the following thesis in partial fulfilment for the requirements of my Honours degree in 2003. I was attempting to prove a result
about free subgroups of SL(3,*k*) for an algebraic number field *k* but only managed to obtain a special case using an argument suggested by my supervisor Professor Michael Cowling.
However since that time I have managed to prove a more general result. Tal Poznanski treated this problem in more detail in a PhD thesis of 2008
which I have not been able to find on-line. I have also become aware of related work by G. Soifer and S. Vishkautsan, in Theorem 1.4 of a paper entitled "Simultaneous Ping-Pong Partners in PSL_n(Z)", which includes the special case of my result where the ground field is equal to R.

Here is a draft of a new paper on the philosophy of large cardinals.

Here are some useful resources about effective altruism.