Title: A tour of 3d mirror symmetry
 

Abstract: In the late 1990s, mathematicians and physicists started to observe connections between apparently unrelated algebraic varieties. These connections, now known as 3d mirror symmetry, interact with many areas of math, including geometry, topology, representation theory, and combinatorics. 3d mirror symmetry has proven to be a useful framework for interpreting and generalizing known results, as well as a mechanism for uncovering new ones. I will discuss the main ideas of 3d mirror symmetry and illustrate with examples some of the beautiful theorems and conjectures it has led to. Some of these ideas require modern mathematical tools, while others can be seen in properties of classical objects like hypergeometric functions, posets, and symmetric functions.

 

Bio: Hunter Dinkins works at the intersection of enumerative algebraic geometry and representation theory. He is interested in understanding invariants of moduli spaces appearing in algebraic geometry and using representation-theoretic tools to do so. He also enjoys exploring connections between these ideas and classical mathematical objects, including hypergeometric and q-hypergeometric functions. He received his PhD from UNC Chapel Hill in 2022 studying under the supervision of Andrey Smirnov. He was a Zelevinsky Postdoctoral Fellow at Northeastern University from 2022-2025, and is currently an NSF postdoctoral fellow at MIT.  Outside of math, he enjoys bicycling, cooking, and coffee.