Speaker: Nafiz Ishtiaque (SIMIS, Fudan)
Time: 2026-01-21 16:00-18:00
Location: 1710, SIMIS
Zoom Meeting ID: 859 8522 7039 Passcode: 152918
摘要：
Given a pair (Y,L) consisting of a toric Calabi-Yau 3-fold Y and a special Lagrangian submanifold L thereof, one can study various enumerative properties (e.g. Gromov-Witten/Donaldson-Thomas invariants) as well as construct a mirror Calabi-Yau uv=S(X,Z). S(X,Z)=0 is the so called mirror curve which partly parameterizes the Lagrangian L. I will discuss a gauge theoretic view of some of these ideas. In particular, I will discuss certain codimension-2 defects in 5d N=1 gauge theories in Omega background whose expectation values provide the generating function of refined (bigraded) open BPS invariants associated with (Y,L). Furthermore, these defects can also be used to define a gauge theory observable called a qq-character, which provides a “refinement” of the quantum mirror curve in the sense that forgetting one of the refinement parameters leads to a q-difference equation quantizing the mirror curve. In this unrefined limit the defect partition function provides a (partially) resummed solution to the quantum curve equation which coincides with Baxter’s TQ equation for some integrable system associated with the 5d theory providing an interesting connection between integrability and enumerative geometry.
About Speaker:
Nafiz Ishtiaque is currently an Associate Professor at SIMIS. He completed his PhD at Perimeter Institute for Theoretical Physics, University of Waterloo, in 2019. Prior to moving to Shanghai, he held postdoctoral positions at IAS (Princeton), and at IHES (Paris). His research primarily focuses on the study of integrability within gauge theory and string theory.
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