Junaid Hasan
Junaid Hasan
My research bridges algebraic combinatorics, potential theory, and tropical geometry by investigating discrete analogs of classical geometric structures. I am a PhD Candidate at the University of Washington working under the supervision of Farbod Shokrieh.
I investigate the link between graph divisor theory (chip-firing) and resistance curvature. My joint work introduces a discrete Foster energy and proves it is uniquely minimized by the canonical break divisor on "positively curved graphs".
This work establishes an explicit graded-ring isomorphism for a tropical Dolbeault theorem. By defining cup and cap products on singular (co)homology, we establish a tropical Poincaré formula used for computing volumes on tropical abelian varieties.
Extending classical tools to work with integral coefficients. We construct a full Beauville decomposition for the Chow ring and define an \(\mathfrak{sl}_2\) representation over controlled denominators.