## Adam Logan's Professional Home Page

I am currently visiting the
Department of Mathematics at
McGill University as a guest of
Henri Darmon.
Recently I participated in the
special semester at
the Centre de Recherches
Mathematiques in Montreal.
My most recent academic position was at the
University of Waterloo, in the
Department of Pure Mathematics.
Previously, I received an AB degree from
Princeton in 1995, and
the PhD degree from Harvard
in 1999.

My main research interest is in rational points on curves and surfaces,
and especially using the Brauer-Manin obstruction to prove that there are none.
For reasons too complicated to explain here, I wrote my thesis in
algebraic geometry. Here are links to most of my papers:

- the main results of my dissertation (the version
submitted to the American Journal of Mathematics, now in print);
- a slightly revised
chapter
of my thesis, published separately in Communications in Algebra;
- a
paper on
deformation theory (the number-theory kind), now in Acta Arithmetica;
- a little
article giving
an improvement on the main result of my thesis (incorporated into the AJM
paper above);
- a paper with Henri
Darmon on computations related to his Stark-Heegner point conjecture,
now in IMRN;
- an article on del Pezzo surfaces of degree 4,
joint with Bright, Bruin, and Flynn, now published in the
LMS Journal of Computation
and Mathematics;
- a paper on del Pezzo surfaces of degree 2, with
accompanying programs. (Caution: the example
dealing with the surface S_4 is incorrect; there are actually rational points.
Here is a correction.)
A version of this paper has
appeared in Math. Proc. Camb. Phil. Soc.
Copyright 2008 Cambridge University Press;
- a brief note on solving polynomials of degree 3 and
4 using algebraic geometry;
- a preprint
on the geometry and Brauer obstruction
on forms of Kummer surfaces, joint with Ronald van Luijk, in Math. Comp.;
- a paper with Jordan Ellenberg on modules over
completed group rings, now in Math. Res. Lett.
- and an article on the relation between
two approaches to the Kummer surface of a curve of genus 2. See also
accompanying programs. Copyright owned by IMPAN;
paper to appear in Acta Arithmetica with a few minor changes.
- (My Richelot-isogeny paper has been removed for repairs.)

In addition, you may download my package for
computing the Brauer obstruction on del Pezzo surfaces of degree 4 over
the rational field. You might start by looking at the
readme file.
This new version fixes a few things that got broken somewhere between
Magma 2.11 and 2.13. Thanks to Anthony Varilly for pointing them out.

Return to my main page.