A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study of braid varieties and their Legendrian isotopy.
Research connects geometric structures to knot theory and algebraic combinatorics.
We show that the totally nonnegative part of a partial flag variety (in the sense of Lusztig) is a regular CW complex, confirming a conjecture of Williams. In particular, the closure of each positroid cell inside the totally nonnegative Grassmannian is homeomorphic to a ball, confirming a conjecture of Postnikov.
The paper connects knot theory and cluster algebras via dimer face polynomials.
Many interesting spaces --- including all positroid strata and wild character varieties --- are moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We show that the existence of cluster structures on these spaces may be deduced in a uniform, systematic fashion by constructing and taking…
Study links and quivers, proving polynomial equality conjecture.
We study Weinstein 4-manifolds which admit Lagrangian skeleta given by attaching disks to a surface along a collection of simple closed curves. In terms of the curves describing one such skeleton, we describe surgeries that preserve the ambient Weinstein manifold, but change the skeleton. The surgeries can be iterated …