Jeffrey Ayers

Brief Bio

I recently defended my PhD in Mathematics at UNC Chapel Hill. My advisor was Andrey Smirnov. I recieved my B.S. in Math from UMass Amherst in May 2019. Starting February of 2025 I will be a Consultant at Beghou Consulting

My research was broadly within Geometric Representation Theory, Enumerative Geometry, and Mathematical Physics. My research concerns investigating objects originating in 3d N=4 SUSY Gauge Theories using enumerative and representation theoretic techniques. Specifically studying partition functions of Nakajima quiver varieties appearing as the Higgs branch of a moduli space of vacua. These partition functions are called vertex functions and encode important counts of quasimaps to the variety. A particular kind of vertex function called a capped vertex function, which is a merging of another vertex function, and an object coming from the study of quantum difference equations from representation theory.