This seminar centered loosely around algebraic dynamics, complex dynamics, and related topics. We meet weekly for a 90-minute talk, with the first 30 minutes aiming towards non-experts and graduate students. After the talk we will have 30 minutes of informal discussion.
More information:
https://ywfan-math.github.io/ADCD.html
Abstract
The problem of counting saddle connections and closed loops on Riemann surfaces with quadratic differential (equivalently: half-translation surfaces) can be, somewhat surprisingly, reformulated in terms of counting semistable objects in a 3-d Calabi-Yau category with stability condition. Here "counting" happens within the powerful framework of motivic Donaldson-Thomas theory as developed by Kontsevich-Soibelman, Joyce, and others. For meromorphic quadratic differentials with simple zeros, this reformulation is due to the work of Bridgeland-Smith. The case of quadratic differentials without higher order poles - in particular holomorphic ones - requires entirely different methods, based on deformation of A-infinity categories and transfer of stability conditions. As an application, counts of saddle connections and closed loops are related by the wall-crossing formula as one moves around in the moduli space. Based on 2104.06018 and 2303.18249.
About the speaker
Fabian Haiden is Assistant Professor at the Department of Mathematics and Computer Science (IMADA), University of Southern Denmark (SDU). Fabian obtained his PhD in Mathematics from the University of Vienna in 2015 under the supervision of Ludmil Katzarkov and Maxim Kontsevich. He obtained his MS degree in Mathematics in 2010 from the same institution. Before joining SDU, Dr. Haiden held the highly prestigious Titchmarsh Research Fellowship at University of Oxford since 2019. After his PhD he also held the equally prestigious Benjamin Peirce Fellowship at Harvard University from 2015-2018. In between Haiden has been both a senior postdoc at University of Vienna, invited researcher at Institut des Hautes Etudes Scientifiques (IHES) and visiting associate professor at University of Miami.
