Research
Research
My research interests lie primarily in tropical geometry and toric varieties. At present, I am especially interested in an important class of tropical cycles known as regular cycles. Briefly, a tropical k-cycle [F] is called regular if there exists a k-tuple of global PL convex functions (T_1, ..., T_k) such that the tropical intersection product has degree 1.
Regular tropical cycles are beautiful from several perspectives:
Fundamental examples arise from Esterov–Gusev's Mixed Volume 1 Classification Theorem.
Further fundamental examples come from Alex Fink's Classification Theorem.
The interplay between the underlying algebraic variety and its tropical compactification.
The ''Tropical Minimal Model Program'' — a conjectural framework for classifying such regular tuples.
The associated toric data and toric Chow ring.
...
Publications & Preprints:
Tropical fans supporting a reduced 0-dimensional complete intersection (arXiv).
another one is coming soon...