Free Resolutions: Algebraic Geometry, Representation Theory, and Complexity Theory

Date: February 12, 2024

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Hang (Amy) Huang

Description: Abstract: The concept of free resolutions(syzygies), arising from linear algebra over commutative rings, has blossomed into a versatile tool with profound applications in diverse fields. In this talk, I will give a gentle introduction to free resolutions and showcase the invaluable role of representation theory in dissecting their structure. Then I will give a captivating glimpse into some of my results. These include using the representation theory of Lie superalgebra to unveil the hidden structure of some free resolutions, finding equations of nilpotent orbit closures, and some recent applications to complexity theory.