Dr. Gebhard Martin (Bonn), TopMath graduate of the 11th cohort, will give a talk on "Automorphisms of Algebraic Surfaces" within the Alumni Speakers Series.
The talk will take place on Thursday May 23rd 2019 at 6 PM at TUM, departments of Mathematics and Informatics, Hörsaal 3. Anyone interested is welcome to attend.
As part of the TopMath Alumni Speakers Series, TopMath regularly invites graduates of its program to share their experiences with students and doctoral candidates. They present their current projects in research or industry, speak about their career path and are then available for an informal exchange.
For the first Alumnus Talk of the year 2019, Dr. Gebhard Martin could be won. Dr. Martin, a 2018 TopMath graduate, is currently a post-doctoral candidate at the Hausdorff Center for Mathematics (hcm), a cluster of excellence located at the University of Bonn.
Dr. Gebhard Martin (Bonn): Automorphisms of Algebraic Surphases
"It used to be said that while algebraic curves (already composed in a harmonic theory) are created by God, surfaces, instead, are the work of the devil. Now, on the contrary, it is clear that God chose to create for surfaces an order of more hidden harmonies, where a wonderful beauty shines forth." (Federigo Enriques)
Understanding the symmetries of geometric objects has been one of the driving forces for geometers since antiquity; for example, platonic solids arose during the search for the most regular convex polyhedra in real 3-space. The simplest objects in complex algebraic geometry, compact Riemann surfaces, have been introduced in the 19th century by Riemann and the structure of their groups of symmetries, also called automorphism groups, is also classically known: While the automorphisms of the projective line are exactly the Möbius transformations and the automorphism group of a torus is a finite extension of its group of translations, Riemann surfaces of higher genus have only finitely many symmetries and a theorem of Hurwitz even gives a bound on the size of the automorphism group depending only on the genus. All of these results have been extended to algebraic curves, the analogues of Riemann surfaces, over arbitrary fields in the course of the last century.
Even though a rough classification of algebraic surfaces has been achieved by Enriques and Kodaira over the complex numbers and by Bombieri and Mumford in arbitrary characteristic, we are still far away from a description of their automorphism groups as complete as the one for algebraic curves. In this talk, Dr. Martin will give a survey on the structure of automorphism groups of algebraic surfaces over the complex numbers and over fields of positive characteristic, including recent results on automorphisms of Enriques surfaces.