Walter Gubler

Walter Bruno Gubler (* 1965 in Olten ) is a Swiss mathematician .

Gubler studied mathematics at the ETH Zurich , he was with a diploma in 1989. Then there was an assistant and in 1992 Gisbert Wüstholz (doctorate level theory ) as a post-graduate student he was at Princeton University at Enrico Bombieri and the Humboldt University of Berlin . In 2003 he completed his habilitation at the ETH Zurich (Basic properties of heights of subvarieties). He was a lecturer at TU Dortmund University and was a substitute professor at Humboldt University before becoming a professor at the University of Southampton in 2009 . In the same year he moved to the University of Tübingen and is currently a professor at the University of Regensburg .

Walter Gubler works in the field of arithmetic algebraic geometry and deals with number theory , in which there are some of the most important open problems in mathematics. In particular, it is about the solution behavior of Diophantine equations : there Bogomolov's conjecture (after Fyodor Alexejewitsch Bogomolow ) states that the solutions of such equations are discrete in certain cases . A DFG project by Gubler also applies to this question. The Bogomolov conjecture about number fields and for curves that are embedded in their Jacobi variety was proven by Emmanuel Ullmo and Shou-Wu Zhang in 1998. Gubler proved the assumption for closed sub- varieties of Abelian varieties (instead of the original assumption for embedding in Jacobi varieties), which meet an additional requirement. In his proof he applied tropical geometry .

In 2010 he received the Joseph L. Doob Prize for his book with Enrico Bombieri on height functions in Diophantine geometry.

Fonts

with Enrico Bombieri: Heights in Diophantine Geometry, Cambridge University Press 2006
The Bogomolov conjecture for totally degenerate abelian varieties, Inventiones mathematicae, Volume 169, 2007, pp. 377-400, Arxiv
Tropical varieties for non-archimedean analytic spaces, Inventiones mathematicae, Volume 169, 2007, pp. 321-376, Arxiv
A guide to tropicalizations; in Algebraic and Combinatorial Aspects of Tropical Geometry, Contemporary Mathematics, Volume 589, Amer. Math. Soc., 2013, pp. 125-189, Arxiv