Adam Logan's Professional Home Page

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.)

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