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mathematician, composer, photographer, fiddler

22 Jun 2012 | categories: Talks, Mathematics

Euler Calculus in Edinburgh

I’m looking forward to speaking about A New Approach to Euler Calculus for Continuous Integrands at ATMCS 5 in Edinburgh on Monday 2 July 2012.

I will generalize Euler calculus from constructible integrands to continuous integrands in a way which is additive & functorial, satisfies a Fubini theorem, and is defined within any O-minimal theory.

19 Nov 2011 | categories: Mathematics, Papers

The Cayley Plane and String Bordism

My new paper [published 2 Oct 2014]:

The Cayley Plane and String Bordism, Geometry & Topology 18-4 (2014), 2045–2078.

shows that an affinity between bordism rings and projective spaces extends further than previously known.

For those familiar with Milnor’s generators for the unoriented (respectively complex) bordism ring, namely degree-(1,1) hypersurfaces in products of projective spaces Pm×Pn over R (respectively C): I extend this construction to the String bordism ring MO⟨8⟩[1/6] using the Cayley Plane—the projective plane over the Octonions O. This involves showing that the arithmetic of Cayley plane bundle characteristic numbers arising in Borel–Hirzebruch Lie group-theoretic calculations correspond precisely to the arithmetic arising in the Hovey–Ravenel–Wilson BP Hopf ring-theoretic calculation of String bordism at primes greater than 3.

10 Oct 2007 | categories: Talks, Mathematics

How Twisted Is Infinity?


How Twisted Is Infinity?
McMenemy Seminar, Trinity Hall Cambridge
18:15 Wednesday 10 October 2007, Graham Storey Room
Carl McTague, PhD Candidate in Pure Mathematics

This talk will investigate the geometric nature of infinity. It will unfold, like a David Lynch film, in a sequence of increasingly surreal episodes populated by characters in split algebraic and geometric roles, filled with abstract symbols whose veiled meanings might at once confound and intrigue, and conveyed through graphic imagery and strong language which might at times discomfort. (Rest assured however that every effort will be made to make the talk broadly accessible.) The story begins with the disappearance of a point from a small Euclidean neighborhood. Tracing the point’s steps leads to a twisted reality at the outskirts of town where parallel lines meet and ultimately to a shadowy algebraic underworld where one plus one equals zero.

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