Vorträge in der Woche 25.07.2022 bis 31.07.2022

Montag, 25.07.2022: TBA

Daniel Walpert (Universität Kassel)

Mittwoch, 27.07.2022: Logarithmic double ramification cycles

Johannes Schmitt

Inside the moduli space of smooth genus g curves (C, p1, ..., pn) there is a natural locus, cut out by the condition that there exists a rational function on C with zeros and poles at the marked points pi of specified orders. The double ramification cycle DR is an algebraic cycle class extending the fundamental class of this locus to the moduli space Mbar of stable curves. However, from its construction one can see that DR naturally lives as a cycle on a blowup of Mbar. Hence it gives a class in the logarithmic Chow ring of Mbar, which describes the intersection theory of all (suitable) blowups of Mbar simultaneously. I will describe a recent result with Molcho, Holmes, Pandharipande and Pixton where we compute an explicit formula for this so-called logarithmic double ramification cycle. On the way, we will see how to describe classes in the logarithmic Chow ring using piecewise polynomials on the moduli space of tropical curves.

Donnerstag, 28.07.2022: Machine learning in algebraic geometry: some examples

Sara Veneziale (Imperial College London)

The use of machine learning in pure mathematics to help formulate conjectures has been a growing research area, with examples in knot theory and representation theory. In this talk, we go through two successful example applications of machine learning algorithms to problems in algebraic geometry where toric varieties are the central object of study. In the first, we study the quantum period of toric varieties, and see if we can learn their dimension from it. In the second, we construct a neural network that distinguishes between terminal and non-terminal toric varieties from their GIT data, which motivates a proposed mathematical solution to the problem.

Donnerstag, 28.07.2022: Principle of Relationalism and the accelerated expansion of the universe

Sahand Tokasi (Tübingen)

What is the time? What was the fight between Leibniz and Newton about? What is the principle of relationalism? In this talk, we will focus on some fundamental questions about the development of (more)sensible physical theories. First, we will introduce the principle of relationalism. Then, the direct application of this principle leads us to a new theory called the Modified Newtonian Theory. We will give its equations of motion and discuss one of its cosmological consequences. This talk focuses more on the physical and foundational aspects.