Sun, 07/10/2018 (All day) to Thu, 11/10/2018 (All day)
Israel Institute for Advanced Studies, The Hebrew University of Jerusalem
In this workshop we intend to explore which methods and results can be extended from the realm of groups to stationary random graphs. In doing so we hope to gain better understanding of the factors that determine each random walk behavior, both on stationary random graphs and on Cayley graphs.
The moduli space of curves, first appearing in the work of Riemann in the 19th century, plays an important role in geometry. After an introduction to the moduli space, I will discuss recent directions in the study of tautological classes on the moduli space following ideas and conjectures of Mumford, Faber-Zagier, and Pixton. Cohomological Field Theories (CohFTs) play an important role. Read more about Zabrodsky Lecture 1: Geometry of the moduli space of curves
Cohomological Field Theories (CohFTs) were introduced to keep track of the classes on the moduli spaces of curves defined by Gromov-Witten theories and their cousins. I will define CohFTs (following Kontsevich-Manin), explain the classification in the semisimple case of Givental-Teleman, and discuss the application to Pixton's relations which appear in the first lecture.
I will explain how calculations of various natural classes on the moduli of curves fit into the CohFT framework. These include calculations related to Hilbert schemes of points, Verlinde bundles, and, if time permits, double ramification (DR) cycles.