Azat M. Gainutdinov
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Azat M. Gainutdinov has a total of 25 co-authors. Here are the top co-authors by number of shared publications:
- Ingo Runkel
Universität Hamburg, Germany
10 shared publications - Bertrand Patureau-Mirand
Univ. Bretagne - Sud, UMR 6205, LMBA
3 shared publications - Jesper Lykke Jacobsen
Laboratoire de Physique de l'École Normale Supérieure ENS Université PSL CNRS Sorbonne Université Université Paris Cité F-75005 Paris France
3 shared publications - Johannes Berger
Fachbereich Mathematik Universität Hamburg Bundesstraße 55 20146 Hamburg Germany
3 shared publications - Marco De Renzi
Department of Mathematics, Faculty of Science and Engineering, Waseda University, Shinjuku-ku, Japan
3 shared publications - Anna Beliakova
Universität Zürich, Zürich, Switzerland
2 shared publications
Latest Publications
- 19 October 2026
- Published by Agence Bibliographique de l'Enseignement Supérieur
Synaptic and network mechanisms of the early sharp waves in the neonatal rodent hippocampus
Mécanismes synaptiques et de réseau des ondes aiguës précoces dans l'hippocampe du rongeur en periode néonatal: Dans l'hippocampe des rongeurs nouveau-nés, les ondes aigües précoces (« earlysharp waves, eSPWs ») représentent le premier patron d'activité organisée,apparaissant sous forme de bouffées d’activité récurrente de réseau neuronal. Cettethèse explore les mécanismes à l'origine de la génération des eSPWs, et leurs corrélatssynaptiques dans le contexte de la maturation développementale de l'inhibitionhippocampique.L'étude commence par examiner le rôle de la stimulation somatosensorielle dansl'induction des eSPWs. Les expériences ont démontré que la stimulation électriquesous-cutanée induit des eSPWs, avec des caractéristiques temporelles et spatialessimilaires à celles des événements spontanés. Les profils de densité des sources decourant (CSD) ont révélé l'implication des voies temporo-ammonique et perforante,reliant les entrées sensorielles externes à l'activité hippocampique.La dynamique temporelle des réponses synaptiques lors des eSPWs in vivo etpendant les réponses évoquées par la stimulation des voies temporo-ammonique etperforante dans les préparations in vitro a été analysée à l'aide d'enregistrements enpatch-clamp dans les régions CA1 et du gyrus denté (DG). L'analyse a montré que lescourants postsynaptiques excitateurs (EPSCs) précèdent les courants postsynaptiquesinhibiteurs (IPSCs) de plusieurs dizaines de millisecondes, créant une large fenêtred'intégration pour les entrées excitatrices. Ce décalage se réduit à mesure que lessynapses inhibitrices mûrissent, reflétant la progression développementale del'inhibition "feedforward".Enfin, une analyse immunohistochimique a cartographié la distribution et la mise enplace développementale des futures synapses inhibitrices à parvalbumine dans larégion CA1 de l'hippocampe. Les résultats de cette analyse suggèrent que les synapsesétablies par les interneurones à parvalbumin sur les dendrites se forment plusprécocement que les synapses périsomatiques.Dans l'ensemble, ces résultats indiquent un rôle clé des entrées excitatrices externesdans l'activation du réseau neuronal hippocampique immature et suggèrent égalementun développement tardif de l'inhibition dans l'hippocampe, ce qui, ensemble, crée lesconditions d'une activité en bouffée dans l'hippocampe au cours des premiers stades dudéveloppement.
- 19 October 2026
- Published by Agence Bibliographique de l'Enseignement Supérieur
Synaptic and network mechanisms of the early sharp waves in the neonatal rodent hippocampus
Mécanismes synaptiques et de réseau des ondes aiguës précoces dans l'hippocampe du rongeur en periode néonatal: Dans l'hippocampe des rongeurs nouveau-nés, les ondes aigües précoces (« earlysharp waves, eSPWs ») représentent le premier patron d'activité organisée,apparaissant sous forme de bouffées d’activité récurrente de réseau neuronal. Cettethèse explore les mécanismes à l'origine de la génération des eSPWs, et leurs corrélatssynaptiques dans le contexte de la maturation développementale de l'inhibitionhippocampique.L'étude commence par examiner le rôle de la stimulation somatosensorielle dansl'induction des eSPWs. Les expériences ont démontré que la stimulation électriquesous-cutanée induit des eSPWs, avec des caractéristiques temporelles et spatialessimilaires à celles des événements spontanés. Les profils de densité des sources decourant (CSD) ont révélé l'implication des voies temporo-ammonique et perforante,reliant les entrées sensorielles externes à l'activité hippocampique.La dynamique temporelle des réponses synaptiques lors des eSPWs in vivo etpendant les réponses évoquées par la stimulation des voies temporo-ammonique etperforante dans les préparations in vitro a été analysée à l'aide d'enregistrements enpatch-clamp dans les régions CA1 et du gyrus denté (DG). L'analyse a montré que lescourants postsynaptiques excitateurs (EPSCs) précèdent les courants postsynaptiquesinhibiteurs (IPSCs) de plusieurs dizaines de millisecondes, créant une large fenêtred'intégration pour les entrées excitatrices. Ce décalage se réduit à mesure que lessynapses inhibitrices mûrissent, reflétant la progression développementale del'inhibition "feedforward".Enfin, une analyse immunohistochimique a cartographié la distribution et la mise enplace développementale des futures synapses inhibitrices à parvalbumine dans larégion CA1 de l'hippocampe. Les résultats de cette analyse suggèrent que les synapsesétablies par les interneurones à parvalbumin sur les dendrites se forment plusprécocement que les synapses périsomatiques.Dans l'ensemble, ces résultats indiquent un rôle clé des entrées excitatrices externesdans l'activation du réseau neuronal hippocampique immature et suggèrent égalementun développement tardif de l'inhibition dans l'hippocampe, ce qui, ensemble, crée lesconditions d'une activité en bouffée dans l'hippocampe au cours des premiers stades dudéveloppement.
- 22 April 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH in Quantum Topology
Non-semisimple link and manifold invariants for symplectic fermions
We consider the link and three-manifold invariants in De Renzi et al. [Selecta Math. 28 (2022), article no. 42], which are defined in terms of certain non-semisimple ribbon categories \mathcal{C} (locally finite for link invariants, finite for manifold invariants) together with a choice of tensor ideal and modified trace. If the ideal is all of \mathcal{C} , these invariants agree with those defined by Lyubashenko in the 90’s. We show that in that case the invariants depend on the objects labelling the link only through their simple composition factors. In order to detect non-trivial extensions, one needs to pass to proper ideals. We compute examples of link and three-manifold invariants for \mathcal{C} being the category of N pairs of symplectic fermions. Using a quasi-Hopf algebra realisation of \mathcal{C} , we find that the Lyubashenko-invariant of a lens space is equal to the order of its first homology group to the power N , a relation we conjecture to hold for all three-manifolds with finite first homology group. For N \ge 2 , \mathcal{C} allows for tensor ideals \mathcal{I} with a modified trace which are different from all of \mathcal{C} and from the projective ideal. Using the theory of pullback traces and symmetrised cointegrals, we show that the link invariant obtained from \mathcal{I} can distinguish a continuum of indecomposable but reducible objects which all have the same composition series.
- 22 April 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH in Quantum Topology
Non-semisimple link and manifold invariants for symplectic fermions
We consider the link and three-manifold invariants in De Renzi et al. [Selecta Math. 28 (2022), article no. 42], which are defined in terms of certain non-semisimple ribbon categories \mathcal{C} (locally finite for link invariants, finite for manifold invariants) together with a choice of tensor ideal and modified trace. If the ideal is all of \mathcal{C} , these invariants agree with those defined by Lyubashenko in the 90’s. We show that in that case the invariants depend on the objects labelling the link only through their simple composition factors. In order to detect non-trivial extensions, one needs to pass to proper ideals. We compute examples of link and three-manifold invariants for \mathcal{C} being the category of N pairs of symplectic fermions. Using a quasi-Hopf algebra realisation of \mathcal{C} , we find that the Lyubashenko-invariant of a lens space is equal to the order of its first homology group to the power N , a relation we conjecture to hold for all three-manifolds with finite first homology group. For N \ge 2 , \mathcal{C} allows for tensor ideals \mathcal{I} with a modified trace which are different from all of \mathcal{C} and from the projective ideal. Using the theory of pullback traces and symmetrised cointegrals, we show that the link invariant obtained from \mathcal{I} can distinguish a continuum of indecomposable but reducible objects which all have the same composition series.
- Open Access
- 27 March 2026
- Published by Elsevier in Nuclear Physics B
- Vol. 1026
Universal TT- and TQ-relations via centrally extended q-Onsager algebra
- 27 March 2026
- Published by Elsevier in Nuclear Physics B
- Vol. 1026
Open AccessUniversal TT- and TQ-relations via centrally extended q-Onsager algebra
- Open Access
Davydov-Yetter cohomology and relative homological algebra
Davydov--Yetter (DY) cohomology classifies infinitesimal deformations of the monoidal structure of tensor functors and tensor categories. In this paper we provide new tools for the computation of the DY cohomology for finite tensor categories and exact functors between them. The key point is to realize DY cohomology as relative Ext groups. In particular, we prove that the infinitesimal deformations of a tensor category $\mathcal{C}$ are classified by the 3-rd self-extension group of the tensor unit of the Drinfeld center $\mathcal{Z}(\mathcal{C})$ relative to $\mathcal{C}$. From classical results on relative homological algebra we get a long exact sequence for DY cohomology and a Yoneda product for which we provide an explicit formula. Using the long exact sequence and duality, we obtain a dimension formula for the cohomology groups based solely on relatively projective covers which reduces a problem in homological algebra to a problem in representation theory, e.g. calculating the space of invariants in a certain object of $\mathcal{Z}(\mathcal{C})$. Thanks to the Yoneda product, we also develop a method for computing DY cocycles explicitly which are needed for applications in the deformation theory. We apply these tools to the category of finite-dimensional modules over a finite-dimensional Hopf algebra. We study in detail the examples of the bosonization of exterior algebras $\Lambda\mathbb{C}^k \rtimes \mathbb{C}[\mathbb{Z}_2]$, the Taft algebras and the small quantum group of $\mathfrak{sl}_2$ at a root of unity.Open AccessDavydov-Yetter cohomology and relative homological algebra
Davydov--Yetter (DY) cohomology classifies infinitesimal deformations of the monoidal structure of tensor functors and tensor categories. In this paper we provide new tools for the computation of the DY cohomology for finite tensor categories and exact functors between them. The key point is to realize DY cohomology as relative Ext groups. In particular, we prove that the infinitesimal deformations of a tensor category $\mathcal{C}$ are classified by the 3-rd self-extension group of the tensor unit of the Drinfeld center $\mathcal{Z}(\mathcal{C})$ relative to $\mathcal{C}$. From classical results on relative homological algebra we get a long exact sequence for DY cohomology and a Yoneda product for which we provide an explicit formula. Using the long exact sequence and duality, we obtain a dimension formula for the cohomology groups based solely on relatively projective covers which reduces a problem in homological algebra to a problem in representation theory, e.g. calculating the space of invariants in a certain object of $\mathcal{Z}(\mathcal{C})$. Thanks to the Yoneda product, we also develop a method for computing DY cocycles explicitly which are needed for applications in the deformation theory. We apply these tools to the category of finite-dimensional modules over a finite-dimensional Hopf algebra. We study in detail the examples of the bosonization of exterior algebras $\Lambda\mathbb{C}^k \rtimes \mathbb{C}[\mathbb{Z}_2]$, the Taft algebras and the small quantum group of $\mathfrak{sl}_2$ at a root of unity. - 21 February 2024
- Published by Springer Nature in Selecta Mathematica
- Vol. 30 (2) , 1-80
Davydov–Yetter cohomology and relative homological algebra
- 21 February 2024
- Published by Springer Nature in Selecta Mathematica
- Vol. 30 (2) , 1-80
Davydov–Yetter cohomology and relative homological algebra
- Open Access
- 4 November 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (11) , 1-65
$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $-invariant non-compact boundary conditions for the XXZ spin chainWe introduce new $$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $$ -invariant boundary conditions for the open XXZ spin chain. For generic values of $$ \mathfrak{q} $$ we couple the bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries of the spin chain, and for $$ \mathfrak{q}={e}^{\frac{i\pi}{p}} $$ a 2p-th root of unity — to its p-dimensional analogue. Both cases are parametrised by a continuous “spin” α ∈ ℂ.To motivate our construction, we first specialise to $$ \mathfrak{q} $$ = i, where we obtain a modified XX Hamiltonian with unrolled quantum group symmetry, whose spectrum and scaling limit is computed explicitly using free fermions. In the continuum, this model is identified with the (η, ξ) ghost CFT on the upper-half plane with a continuum of conformally invariant boundary conditions on the real axis. The different sectors of the Hamiltonian are identified with irreducible Virasoro representations.Going back to generic q we investigate the algebraic properties of the underlying lattice algebras. We show that if $$ \mathfrak{q} $$ α ∉± $$ \mathfrak{q} $$ ℤ, the new boundary coupling provides a faithful representation of the blob algebra which is Schur-Weyl dual to $$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $$ . Then, modifying the boundary conditions on both the left and the right, we obtain a representation of the universal two-boundary Temperley-Lieb algebra. The generators and parameters of these representations are computed explicitly in terms of $$ \mathfrak{q} $$ and α. Finally, we conjecture the general form of the Schur-Weyl duality in this case.This paper is the first in a series where we will study, at all values of the parameters, the spectrum and its continuum limit, the representation content of the relevant lattice algebras and the fusion properties of these new spin chains.- 4 November 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (11) , 1-65
Open Access$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $-invariant non-compact boundary conditions for the XXZ spin chainWe introduce new $$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $$ -invariant boundary conditions for the open XXZ spin chain. For generic values of $$ \mathfrak{q} $$ we couple the bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries of the spin chain, and for $$ \mathfrak{q}={e}^{\frac{i\pi}{p}} $$ a 2p-th root of unity — to its p-dimensional analogue. Both cases are parametrised by a continuous “spin” α ∈ ℂ.To motivate our construction, we first specialise to $$ \mathfrak{q} $$ = i, where we obtain a modified XX Hamiltonian with unrolled quantum group symmetry, whose spectrum and scaling limit is computed explicitly using free fermions. In the continuum, this model is identified with the (η, ξ) ghost CFT on the upper-half plane with a continuum of conformally invariant boundary conditions on the real axis. The different sectors of the Hamiltonian are identified with irreducible Virasoro representations.Going back to generic q we investigate the algebraic properties of the underlying lattice algebras. We show that if $$ \mathfrak{q} $$ α ∉± $$ \mathfrak{q} $$ ℤ, the new boundary coupling provides a faithful representation of the blob algebra which is Schur-Weyl dual to $$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $$ . Then, modifying the boundary conditions on both the left and the right, we obtain a representation of the universal two-boundary Temperley-Lieb algebra. The generators and parameters of these representations are computed explicitly in terms of $$ \mathfrak{q} $$ and α. Finally, we conjecture the general form of the Schur-Weyl duality in this case.This paper is the first in a series where we will study, at all values of the parameters, the spectrum and its continuum limit, the representation content of the relevant lattice algebras and the fusion properties of these new spin chains. - Open Access
- 15 April 2022
- Published by Elsevier in Nuclear Physics B
- Vol. 979
web models: Locality, phase diagram and geometrical defects- 15 April 2022
- Published by Elsevier in Nuclear Physics B
- Vol. 979
Open Accessweb models: Locality, phase diagram and geometrical defects - Open Access
The symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre
We introduce a family of factorisable ribbon quasi-Hopf algebras $Q(N)$ for $N$ a positive integer: as an algebra, $Q(N)$ is the semidirect product of $\mathbb{C}\mathbb{Z}_2$ with the direct sum of a Grassmann and a Clifford algebra in $2N$ generators. We show that $Rep Q(N)$ is ribbon equivalent to the symplectic fermion category $SF(N)$ that was computed by the third author from conformal blocks of the corresponding logarithmic conformal field theory. The latter category in turn is conjecturally ribbon equivalent to representations of $V_{ev}$, the even part of the symplectic fermion vertex operator super algebra. Using the formalism developed in our previous paper we compute the projective $SL(2,\mathbb{Z})$-action on the centre of $Q(N)$ as obtained from Lyubashenko's general theory of mapping class group actions for factorisable finite ribbon categories. This allows us to test a conjectural non-semisimple version of the modular Verlinde formula: we verify that the $SL(2,\mathbb{Z})$-action computed from $Q(N)$ agrees projectively with that on pseudo trace functions of $V_{ev}$.Open AccessThe symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre
We introduce a family of factorisable ribbon quasi-Hopf algebras $Q(N)$ for $N$ a positive integer: as an algebra, $Q(N)$ is the semidirect product of $\mathbb{C}\mathbb{Z}_2$ with the direct sum of a Grassmann and a Clifford algebra in $2N$ generators. We show that $Rep Q(N)$ is ribbon equivalent to the symplectic fermion category $SF(N)$ that was computed by the third author from conformal blocks of the corresponding logarithmic conformal field theory. The latter category in turn is conjecturally ribbon equivalent to representations of $V_{ev}$, the even part of the symplectic fermion vertex operator super algebra. Using the formalism developed in our previous paper we compute the projective $SL(2,\mathbb{Z})$-action on the centre of $Q(N)$ as obtained from Lyubashenko's general theory of mapping class group actions for factorisable finite ribbon categories. This allows us to test a conjectural non-semisimple version of the modular Verlinde formula: we verify that the $SL(2,\mathbb{Z})$-action computed from $Q(N)$ agrees projectively with that on pseudo trace functions of $V_{ev}$. - Top Cited Papers
- 25 January 2022
- Published by Springer Nature in Selecta Mathematica
- Vol. 28 (2) , 1-60
3-Dimensional TQFTs from non-semisimple modular categories
- 25 January 2022
- Published by Springer Nature in Selecta Mathematica
- Vol. 28 (2) , 1-60
Top Cited Papers3-Dimensional TQFTs from non-semisimple modular categories
- Open Access
3-Dimensional TQFTs From Non-Semisimple Modular Categories
We use modified traces to renormalize Lyubashenko's closed 3-manifold invariants coming from twist non-degenerate finite unimodular ribbon categories. Our construction produces new topological invariants which we upgrade to 2+1-TQFTs under the additional assumption of factorizability. The resulting functors provide monoidal extensions of Lyubashenko's mapping class group representations, as discussed in arXiv:2010.14852. This general framework encompasses important examples of non-semisimple modular categories coming from the representation theory of quasi-Hopf algebras, which were left out of previous non-semisimple TQFT constructions.
Open Access3-Dimensional TQFTs From Non-Semisimple Modular Categories
We use modified traces to renormalize Lyubashenko's closed 3-manifold invariants coming from twist non-degenerate finite unimodular ribbon categories. Our construction produces new topological invariants which we upgrade to 2+1-TQFTs under the additional assumption of factorizability. The resulting functors provide monoidal extensions of Lyubashenko's mapping class group representations, as discussed in arXiv:2010.14852. This general framework encompasses important examples of non-semisimple modular categories coming from the representation theory of quasi-Hopf algebras, which were left out of previous non-semisimple TQFT constructions.