Arkadij Bojko - Academia.edu (original) (raw)
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Papers by Arkadij Bojko
Inventiones mathematicae, Feb 23, 2024
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Advances in Mathematics, Sep 1, 2021
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arXiv (Cornell University), Nov 18, 2021
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arXiv (Cornell University), Nov 22, 2021
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arXiv (Cornell University), Oct 31, 2019
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arXiv (Cornell University), Oct 11, 2022
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arXiv (Cornell University), Nov 18, 2021
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arXiv (Cornell University), Aug 19, 2020
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arXiv (Cornell University), Feb 1, 2021
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arXiv (Cornell University), Mar 24, 2023
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Cornell University - arXiv, Oct 11, 2022
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Cornell University - arXiv, Nov 18, 2021
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University of Oxford, 2021
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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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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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Advances in Mathematics, 2021
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Inventiones mathematicae, Feb 23, 2024
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Advances in Mathematics, Sep 1, 2021
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arXiv (Cornell University), Nov 18, 2021
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arXiv (Cornell University), Nov 22, 2021
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arXiv (Cornell University), Oct 31, 2019
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arXiv (Cornell University), Oct 11, 2022
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arXiv (Cornell University), Nov 18, 2021
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arXiv (Cornell University), Aug 19, 2020
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arXiv (Cornell University), Feb 1, 2021
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arXiv (Cornell University), Mar 24, 2023
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Cornell University - arXiv, Oct 11, 2022
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Cornell University - arXiv, Nov 18, 2021
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University of Oxford, 2021
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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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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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Advances in Mathematics, 2021
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