We study the category of matrix factorizations for an isolated hypersurface singularity. We
compute the canonical bilinear form on the Hochschild homology of this category. We find …

We consider open symplectic manifolds which admit dilations (in the sense previously
introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian …

We define the Atiyah class for global matrix factorisations and use it to give a formula for the
categorical Chern character and the boundary-bulk map for matrix factorisations …

arXiv:2106.00435v1 [math.AG] 1 Jun 2021 Page 1 arXiv:2106.00435v1 [math.AG] 1 Jun 2021
HIRZEBRUCH-RIEMANN-ROCH FOR GLOBAL MATRIX FACTORIZATIONS BUMSIG KIM …

Let $ X $ be a smooth proper scheme over a field of characteristic 0. Following D. Shklyarov
[10], we construct a (non-degenerate) pairing on the Hochschild homology of $\per {X} …

We introduce the dimension matrix of a bimodule complex and the trace matrix of a chain
endomorphism of a bimodule complex, and give the Hirzebruch-Riemann-Roch (HRR) and …

Let X be a smooth projective complex variety. The Hochschild homology HH•(X) of X is an
important invariant of X, which is isomorphic to the Hodge cohomology of X via the …

Abstract Recall the classical Riemann-Roch theorem for curves: Given a smooth projective
complex curve and two holomorphic vector bundles E, F on it, the Euler form [special …

My research interests involve various aspects of algebraic geometry, noncommutative
geometry and homological algebra. During my post-doctoral appointment in the past two …