Papers
You can also find my preprints on arXiv
Published
Published in Journal of Algebra, 2026. DOI: 10.1016/j.jalgebra.2026.08.011 free access arXiv pdf
We establish a bijective correspondence between basic silting objects of \(\operatorname{per} A\), simple-minded collections of \(D_{\mathrm{fd}}(A)\), algebraic \(t\)-structures on \(D_{\mathrm{fd}}(A)\), and bounded co-\(t\)-structures on \(\operatorname{per} A\), for any locally finite non-positive dg algebra \(A\) over a field. More generally, we prove this correspondence in the abstract setting of ST-pairs inside an algebraic triangulated category, simultaneously generalizing the previously known cases where \(A\) is proper or homologically smooth with finite-dimensional zeroth cohomology.
Preprints
arXiv preprint, 2026. Link: arXiv:2609.10396 pdf
Fix an integer \(d\leq-2\). We characterize Hom-finite algebraic triangulated categories admitting a \((-d)\)-simple-minded system as stable categories \(\underline{\mathrm{CM}}(B)\) of proper \((-d)\)-self-injective non-positive dg algebras; equivalently, each admits a \(d\)-stable locally finite strictly positive dg model whose cosingular dg quotient recovers the chosen enhancement. Under a \(d\)-Calabi–Yau hypothesis, we give a characterization theorem for acyclic negative cluster categories in terms of the finite graded extension algebra of a simple-minded system. At chain level, Hochschild and reduced cyclic localization identify right \((d+1)\)-Calabi–Yau structures on the finite-dimensional part with normalized right \(d\)-Calabi–Yau structures on the cosingular quotient. Finally, when the Koszul dual is proper, the Brav–Dyckerhoff evaluation morphism is a quasi-isomorphism of mixed complexes, yielding left–right Calabi–Yau symmetry.
arXiv preprint, 2026. Link: arXiv:2606.15274 pdf
A finite-dimensional algebra is derived-discrete, in the sense of Vossieck, precisely when it is a piecewise hereditary algebra of Dynkin type or a gentle one-cycle algebra not satisfying the clock condition. Building on the discrete triangulated categories of Broomhead, Pauksztello, and Ploog, we study derived-discreteness for locally finite non-positively graded algebras, regarded as connective locally finite dg algebras with trivial differential. Our main result extends Vossieck's classification to this setting: such a graded algebra is derived-discrete if and only if it is graded Morita equivalent to a piecewise hereditary algebra of Dynkin type, or it is a graded gentle one-cycle algebra not satisfying the graded clock condition. Along the way, using surface models we prove the conjecture of Kalck and Yang that the graded clock condition is invariant under derived equivalence. We also establish a restriction on semi-orthogonal decompositions of the bounded derived category of a path algebra of Dynkin type.
arXiv preprint, 2026. Link: arXiv:2605.23704 pdf
We classify connected finite acyclic graded quivers \(Q\) for which the graded path algebra \(kQ\), regarded as a formal dg algebra, is silting-discrete. We prove that \(kQ\) is silting-discrete if and only if it is derived-discrete, and that both conditions are equivalent to the underlying graph of \(Q\) being of type ADE, or of type \(\widetilde{A}\) with unequal clockwise and counter-clockwise total degrees. The key ingredient is an explicit construction of an infinite pre-simple-minded collection in \(\operatorname{pvd} kQ\) in the non-discrete case.
arXiv preprint, 2026. Link: arXiv:2603.18790 pdf
We establish a bijection between silting complexes and simple-minded collections over a non-positive locally finitely generated dg algebra over a commutative complete local noetherian ring \((R, \mathfrak{m}, k)\), generalizing the classical result of Koenig–Yang over fields. As an application, we show that for any morphism \((R, \mathfrak{m}, k) \to (S, \mathfrak{n}, k)\) of complete local noetherian rings with a common residue field, the derived base change \(- \otimes^{\mathbf{L}}_R S\) induces a bijection on silting complexes.
arXiv preprint, 2024. Link: arXiv:2409.08842 pdf
We study contravariant Koszul duality between locally finite non-positive and locally finite positive dg algebras. We characterize locally finite positive dg algebras whose Koszul dual is locally finite (called pvd-finite), and show that the Koszul dual functor induces contravariant equivalences between the perfect derived category and the perfectly valued derived category. As applications, we establish an ST-correspondence between silting objects, simple-minded objects, algebraic \(t\)-structures, and bounded co-\(t\)-structures, and prove that every functorially finite bounded heart of the perfectly valued derived category of a locally finite non-positive dg algebra is a length category.