Elliptic Cohomology and Enumerative Geometry

Explore the fascinating intersection of elliptic cohomology and enumerative geometry in this 1-hour lecture by Andrei Okounkov at #ICBS2024. Delve into the popular practice of organizing counts into generating functions in enumerative geometry, and discover how these functions can satisfy differential or q-difference equations. Uncover the role of stable envelopes theory in providing a concrete geometric understanding of these q-difference equations and their solutions. Learn how this approach avoids direct enumeration and instead utilizes the language of elliptic cohomology. Gain insights into related phenomena, such as the emergence of elliptic quantum groups in enumerative settings. This introductory discussion offers a unique perspective on the connections between these complex mathematical concepts, suitable for those interested in advanced topics in geometry and cohomology theory.