Detailed information about the course
Title | Graduate Lectures in Mathematics |
Dates | September 23 - December 16, 2020 |
Organizer(s) | |
Speakers | Prof. Peter Feller, ETHZ and Prof. Jeremy Blanc, UNIBAS |
Description | The purpose of these traditional lectures is to present recent important developments in mathematics two a large audience of graduate students and young researchers. The lecturers are experts in algebraic geometry and geometric topology, known for important contributions in their fields. |
Program | Jérémy Blanc: Birational geometry of surfaces and Cremona group
An algebraic variety is given by the zero locus of some polynomials. A rational map between two algebraic varieties is given by quotients of polynomials. It is defined on open sets of points and there are closed subset of indeterminacies. One can however compose these where they are defined and define birational maps as rational maps having a rational inverse. For curves, we may solve the indeterminacies and obtain maps defined everywhere by simply taking smooth projective curves. In dimension 2, this is no longer true, but birational maps are nicely describable via sequence of so-called blow-ups and their inverses. I will describe all this slowly and illustrate it via examples. I will then relate this to the Cremona group, which is the group of birational maps from the plane to itself. No specific knowledge of algebraic geometry is needed to follow the course, as everything will be introduced. Blanc: Birational geometry of surfaces and Cremona group
Peter Feller: Topics in knot theory with a view towards classical algebraic geometry
We cover topics in low-dimensional topology with a focus on knot theory---the study of circles and surfaces in 3-dimensional and 4-dimensional space. - How does topology help in distinguish singularities of zero-sets of polynomials (following Newton, Oldenburg, Artin, Brieskorn, Milnor ...)? With this focus, the lecture will allow for synergies with the graduate lecture by Jeremy Blanc at different points. |
Location | UNIBE |
Information | |
Places | 15 |
Deadline for registration | 23.09.2020 |