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Arkadij Bojko

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Papers by Arkadij Bojko

Research paper thumbnail of Virasoro constraints for moduli of sheaves and vertex algebras

Inventiones mathematicae, Feb 23, 2024

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Research paper thumbnail of Orientations for DT invariants on quasi-projective Calabi–Yau 4-folds

Advances in Mathematics, Sep 1, 2021

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Research paper thumbnail of A short proof of a new combinatorial identity

arXiv (Cornell University), Nov 18, 2021

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Research paper thumbnail of Wall-crossing for punctual Quot-schemes

arXiv (Cornell University), Nov 22, 2021

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Research paper thumbnail of Wall-crossing and orientations for invariants counting coherent sheaves on CY fourfolds

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Research paper thumbnail of Non-commutative counting and stability

arXiv (Cornell University), Oct 31, 2019

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Research paper thumbnail of Virasoro constraints on moduli of sheaves and vertex algebras

arXiv (Cornell University), Oct 11, 2022

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Research paper thumbnail of Application of Lagrange inversion to wall-crossing for Quot-schemes on surfaces

arXiv (Cornell University), Nov 18, 2021

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Research paper thumbnail of Stability conditions on quivers and semistable non-commutative curve counting

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Research paper thumbnail of Orientations on the moduli stack of compactly supported perfect complexes over a non-compact Calabi--Yau 4-fold

arXiv (Cornell University), Aug 19, 2020

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Research paper thumbnail of Wall-crossing for zero-dimensional sheaves and Hilbert schemes of points on Calabi--Yau 4-folds

arXiv (Cornell University), Feb 1, 2021

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Research paper thumbnail of Geometry of Twisted D-branes in Group Manifolds

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Research paper thumbnail of Equivariant Segre and Verlinde invariants for Quot schemes

arXiv (Cornell University), Mar 24, 2023

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Research paper thumbnail of Virasoro constraints on moduli of sheaves and vertex algebras

Cornell University - arXiv, Oct 11, 2022

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Research paper thumbnail of Application of Lagrange inversion to wall-crossing for Quot-schemes on surfaces

Cornell University - arXiv, Nov 18, 2021

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Research paper thumbnail of Wall-crossing and orientations for invariants counting coherent sheaves on CY fourfolds

University of Oxford, 2021

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Research paper thumbnail of Complex of the INTERLEUKIN-1 Receptor with the INTERLEUKIN-1 Receptor Antagonist (IL1RA)

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Research paper thumbnail of A short proof of a new combinatorial identity

While working with Grothendieck’s Quot-schemes and their virtual enumerative invariants, the auth... more While working with Grothendieck’s Quot-schemes and their virtual enumerative invariants, the author came across a combinatorial identity which would have followed as a consequence of a very general abstract machinery. We dedicate this short note to give a combinatorial proof of this identity which is closely related to the Lagrange inversion. A special case of the result was proved by Mathoverflow users “Alex Gavrilov” and “esg” answering our enquiry. In [2], we studied enumerative invariants of Grothendieck’s Quot-schemes on surfaces. Along the way we encountered a new combinatorial identity. We concluded there that it would have followed as a consequence of comparing two computations of the same enumerative invariants using different methods: 1. One relying on the wall-crossing framework of Joyce [6] and the methods developed in [3, 2]. 2. The second one used by [1] relying on virtual localization and additional geometric arguments. The statement of the above mentioned identity is...

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Research paper thumbnail of Geometry of Twisted D-branes in Group Manifolds

The main topic addressed in this work is the geometry of D-branes in the WZW model on a compact, ... more The main topic addressed in this work is the geometry of D-branes in the WZW model on a compact, simple, simply connected Lie group. At first, we recall some main ideas related to open strings in group manifolds and their gluing conditions. The D-branes given in terms of some special gluing conditions correspond to twisted conjugacy classes with respect to an automorphism of the Lie group. After setting up some mathematical machinery to allow us to work with them, we parametrize the space of twisted conjugacy classes using a rather explicit computation and comparing it with the abstract method. We also point out some(what we believe to be) errors in a previous work on this topic on which both of the methods we use agree. Finally, as stabilizer of the twisted conjugacy classes also fi t into the picture of D-branes, we compute them explicitly and again more abstractly for SU(4).

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Research paper thumbnail of Orientations for DT invariants on quasi-projective Calabi–Yau 4-folds

Advances in Mathematics, 2021

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Research paper thumbnail of Virasoro constraints for moduli of sheaves and vertex algebras

Inventiones mathematicae, Feb 23, 2024

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Research paper thumbnail of Orientations for DT invariants on quasi-projective Calabi–Yau 4-folds

Advances in Mathematics, Sep 1, 2021

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Research paper thumbnail of A short proof of a new combinatorial identity

arXiv (Cornell University), Nov 18, 2021

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Research paper thumbnail of Wall-crossing for punctual Quot-schemes

arXiv (Cornell University), Nov 22, 2021

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Research paper thumbnail of Wall-crossing and orientations for invariants counting coherent sheaves on CY fourfolds

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Non-commutative counting and stability

arXiv (Cornell University), Oct 31, 2019

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Research paper thumbnail of Virasoro constraints on moduli of sheaves and vertex algebras

arXiv (Cornell University), Oct 11, 2022

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Research paper thumbnail of Application of Lagrange inversion to wall-crossing for Quot-schemes on surfaces

arXiv (Cornell University), Nov 18, 2021

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Research paper thumbnail of Stability conditions on quivers and semistable non-commutative curve counting

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Research paper thumbnail of Orientations on the moduli stack of compactly supported perfect complexes over a non-compact Calabi--Yau 4-fold

arXiv (Cornell University), Aug 19, 2020

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Research paper thumbnail of Wall-crossing for zero-dimensional sheaves and Hilbert schemes of points on Calabi--Yau 4-folds

arXiv (Cornell University), Feb 1, 2021

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Research paper thumbnail of Geometry of Twisted D-branes in Group Manifolds

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Research paper thumbnail of Equivariant Segre and Verlinde invariants for Quot schemes

arXiv (Cornell University), Mar 24, 2023

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Research paper thumbnail of Virasoro constraints on moduli of sheaves and vertex algebras

Cornell University - arXiv, Oct 11, 2022

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Research paper thumbnail of Application of Lagrange inversion to wall-crossing for Quot-schemes on surfaces

Cornell University - arXiv, Nov 18, 2021

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Research paper thumbnail of Wall-crossing and orientations for invariants counting coherent sheaves on CY fourfolds

University of Oxford, 2021

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Research paper thumbnail of Complex of the INTERLEUKIN-1 Receptor with the INTERLEUKIN-1 Receptor Antagonist (IL1RA)

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Research paper thumbnail of A short proof of a new combinatorial identity

While working with Grothendieck’s Quot-schemes and their virtual enumerative invariants, the auth... more While working with Grothendieck’s Quot-schemes and their virtual enumerative invariants, the author came across a combinatorial identity which would have followed as a consequence of a very general abstract machinery. We dedicate this short note to give a combinatorial proof of this identity which is closely related to the Lagrange inversion. A special case of the result was proved by Mathoverflow users “Alex Gavrilov” and “esg” answering our enquiry. In [2], we studied enumerative invariants of Grothendieck’s Quot-schemes on surfaces. Along the way we encountered a new combinatorial identity. We concluded there that it would have followed as a consequence of comparing two computations of the same enumerative invariants using different methods: 1. One relying on the wall-crossing framework of Joyce [6] and the methods developed in [3, 2]. 2. The second one used by [1] relying on virtual localization and additional geometric arguments. The statement of the above mentioned identity is...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Geometry of Twisted D-branes in Group Manifolds

The main topic addressed in this work is the geometry of D-branes in the WZW model on a compact, ... more The main topic addressed in this work is the geometry of D-branes in the WZW model on a compact, simple, simply connected Lie group. At first, we recall some main ideas related to open strings in group manifolds and their gluing conditions. The D-branes given in terms of some special gluing conditions correspond to twisted conjugacy classes with respect to an automorphism of the Lie group. After setting up some mathematical machinery to allow us to work with them, we parametrize the space of twisted conjugacy classes using a rather explicit computation and comparing it with the abstract method. We also point out some(what we believe to be) errors in a previous work on this topic on which both of the methods we use agree. Finally, as stabilizer of the twisted conjugacy classes also fi t into the picture of D-branes, we compute them explicitly and again more abstractly for SU(4).

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Orientations for DT invariants on quasi-projective Calabi–Yau 4-folds

Advances in Mathematics, 2021

Bookmarks Related papers MentionsView impact

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