Vorträge in der Woche 01.07.2019 bis 07.07.2019

Dienstag, 02.07.2019: Spektralsequenzen und die Khovanov-Homologie als Unknoten-Detektor

Jonathan Walz (Universität Tübingen)

Dienstag, 02.07.2019: Mathematik draußen machen: mathematische Wanderpfade und ihre Auswirkungen auf die Lernleistung

Herr Jörg Zender, Hochschule RheinMain, Wiesbaden

Mathematische Wanderpfade (math trails) verknüpfen auf natürliche Weise das Lernen draußen mit lebensnahen Anwendungsaufgaben zur Mathematik. Durch die Smartphone-App MathCityMap werden seit 2016 auch mobile math trails möglich und so kommen die Wanderpfade auch in der Lebenswirklichkeit der Schülerinnen und Schüler an. Wie gut diese Wanderpfade ankommen wurde an der Goethe Universität Frankfurt am Main in einer Studie mit 25 Schulklassen untersucht. Die kurz- und langfristigen Auswirkungen auf die Lernleistung der Schülerinnen und Schüler werden im Vortrag ebenso präsentiert wie theoretische Hintergründe, praktische Beispiele und ein Ausblick auf die weitere Forschung. Im Anschluss gibt es die Möglichkeit selbst einen Wanderpfad in Tübingen abzulaufen.

Donnerstag, 04.07.2019: Tübingen-Zürich Meeting in Mathematical Physics

Stefan Teufel (Tübingen) et al.

Program see here: https://www.math.uni-tuebingen.de/de/forschung/maphy/personen/marcelloporta/tz_program.pdf

Donnerstag, 04.07.2019: Reduced Gromov-Witten invariants and singularities of genus one

Dr. Luca Battistella (MPI Bonn)

After recalling how the introduction of Kontsevich's stable maps has revitalised the interest in enumerative geometry, allowing mathematicians to answer many questions on rational curves in projective complete intersections, I will explain with an example how dealing with higher genus curves is more complicated. This problem has received considerable attention in genus one: on one hand, Li-Vakil-Zinger have produced a desingularisation of the main component of the moduli space of maps to projective space, defined reduced invariants for complete intersections, and compared them to ordinary invariants, providing the first mathematical proof of BCOV mirror symmetry predictions; on the other, Viscardi has produced irreducible compactifications by allowing the source curve to acquire a Gorenstein singularity of genus one (e.g. a cusp). In joint work with Carocci and Manolache, we relate the two approaches in the case of the quintic threefold. In the second part of the talk, I will hint at how log (and tropical) geometry allows us to study the relative problem, i.e. counts of curves with a tangency condition to a hyperplane, and how this can be used to interpolate between the theory of the ambient space and that of the hyperplane section, extending an algorithm due to Gathmann to the reduced genus one case. This is joint work in progress with Nabijou and Ranganathan, based on the work of Ranganathan, Santos-Parker, and Wise.

Donnerstag, 04.07.2019: Classical and Quantum Laws of Motion for Singularities of Spacetime

Shadi Tahvildar-Zadeh (Rutgers University)

In this talk I report on recent developments towards a relativistic quantum-mechanical theory of motion for a fixed, finite number of electrons, photons, and their anti-particles, as well as its possible generalizations to other particles and interactions. I will briefly explain the necessary conditions under which worldlines of charged particles can be identified with timelike singularities of spacetime and/or classical fields permeating the spacetime, and show examples of classical as well as quantum theories of motion for them when these conditions are satisfied. I will then show how one can define a quantum-mechanical wave function for a single photon, and use that to obtain a Lorenz-covariant system of multi-time wave equations for an interacting two-body system in one space dimension, comprised of one electron and one photon. I will demonstrate that the corresponding initial-boundary-value problem is well-posed, and that both electron and photon trajectories exist globally for typical initial particle positions. I will conclude by presenting preliminary results of numerical experiments that illustrate Compton scattering in this context, as well as a possible new phenomenon: photon capture and release by the electron. This talk is a summary of joint work with Michael Kiessling, Matthias Lienert, Annegret Burtscher, and others.

Freitag, 05.07.2019: Tübingen-Zürich Meeting in Mathematical Physics

Giovanna Marcelli (Tübingen) et al.

Program see here: https://www.math.uni-tuebingen.de/de/forschung/maphy/personen/marcelloporta/tz_program.pdf