☝️ Haniya Azam, one of the 12 laureates of the CIMPA-ICTP Research in Pairs programme, is an assistant professor at Lahore University of Management Sciences (Pakistan)
This course was filmed at CIMPA (Nice, France).
"An Introduction to Fukaya Categories from a Topological Viewpoint" (1/4)
Abstract: This course will be a gentle (and somewhat biased) introduction to Fukaya categories. Roughly speaking, Fukaya category associated to a symplectic manifold, is a category whose objects are Lagrangian submanifolds and whose morphisms are given by Floer chain complexes generated by intersections between these Lagrangian objects. These can be defined in various flavours depending on the geometric context at hand. The aim is to present as an example the topological Fukaya category of a closed surface of genus higher than one, using elementary geometry of curves on a surface, while suppressing the area form. Some familiarity with the language of categories may be helpful. In this course we will include an overview of categories, their equivalence, 
-categories and Floer theory. To make this beautiful yet intimidating area of mathematics interesting for a wider audience, and if time permits, we will present a categorification of the Burau representation of the Braid group by Bouchair, based on ideas from Khovanov-Seidel's categorification of the Braid group action on some derived category of modules.
Click on this link to access the playlist containing the other parts of this online course.