Non-standard Hirzebruch-Riemann-Roch theorems

Christopher Eur, Harvard University

Online Talk 

A complex projective manifold carries two well-studied rings, namely, the cohomology ring and the Grothendieck K-ring of vector bundles.  For toric varieties, these have polyhedral descriptions, as the polytope algebra and the algebra of piecewise polynomials.  For special toric varieties, we show an exceptional isomorphism between these two rings, different from the classical Hirzebruch-Riemann-Roch theorem, and discuss its utility in combinatorial contexts. 

Joint works with Andrew Berget, Alex Fink, June Huh, Matt Larson, Hunter Spink, and Dennis Tseng.