November 2022 - Geometria_Pisa - Mailing list — Dipartimento di Matematica, UniPI

[Indico] James Lewis, The Complexity of Higher Chow Groups, 30/11/2022, 16:30 Europe/Rome
by francesco.sala＠unipi.it 28 Nov '22

28 Nov '22

Title: The Complexity of Higher Chow Groups, Speaker(s): James Lewis, University of Alberta, Date and time: 30 Nov 2022, 16:30 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Department of Mathematics (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/127 Abstract -------- Let $X/{\mathbb C}$ be a smooth projective variety. We consider two integral invariants, one of which is the level of the Hodge cohomology algebra $H^*(X,{\mathbb C})$ and the other involving the complexity of the higher Chow groups ${\rm CH}^*(X,m;{\mathbb Q})$ for $m\geq 0$. We conjecture that these two invariants are the same and accordingly provide some strong evidence in support of this. -- Indico :: Email Notifier https://events.dm.unipi.it/e/127

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[Indico] Antonella Grassi, A family of threefolds with remarkable properties (namely: the unreasonable effectiveness of the Schoens), 30/11/2022, 15:00 Europe/Rome
by francesco.sala＠unipi.it 28 Nov '22

28 Nov '22

Title: A family of threefolds with remarkable properties (namely: the unreasonable effectiveness of the Schoens), Speaker(s): Antonella Grassi, Università degli Studi di Bologna, Date and time: 30 Nov 2022, 15:00 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Department of Mathematics (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/115 Abstract -------- The fiber product of certain rational elliptic surfaces were first studied by Schoen in the 80s to answer questions from string theory. Over the decades the “Schoens” have provided evidence for various conjectures as well as counterexamples to others. I will discuss these conjectures, the unusual features of the Schoens, and present other open questions. -- Indico :: Email Notifier https://events.dm.unipi.it/e/115

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Seminario 27/10/2021
by Tamas Szamuely 25 Nov '22

25 Nov '22

Cari tutti, ecco il programma del prossimo seminario di geometria algebrica e aritmetica di Pisa: Mercoledì 27 ottobre 2021, Dipartimento di matematica, Aula Magna 15:00--16:00 Valerio Melani (Pisa): The Poisson structure on the affine Grassmannian via derived algebraic geometry Motivated by a conjecture of Kapranov-Ginzburg-Vasserot, we will explain how to reinterpret the classical Poisson structure on the affine Grassmannian using tools from derived symplectic (and Poisson) geometry. Our approach is based on the study of symplectic structures on derived stacks whose cotangent complex is not perfect, and therefore uses in a crucial way the formalism of Tate modules. The talk is based on joint work with Mauro Porta and Pavel Safronov. Homepage del seminario: http://pagine.dm.unipi.it/tamas/saga.html Migliori saluti, Tamás Szamuely

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[Indico] Anton Mellit, P=W via $H_2$, 24/11/2022, 16:00 Europe/Rome
by francesco.sala＠unipi.it 23 Nov '22

23 Nov '22

Title: P=W via $H_2$, Speaker(s): Anton Mellit, University of Vienna, Date and time: 24 Nov 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Combinatorics, Lie Theory, and Topology, Venue: Department of Mathematics (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/108 Abstract -------- By $H_2$ we denote the Lie algebra of polynomial hamiltonian vector fields on the plane. We consider the moduli space of stable twisted Higgs bundles on an algebraic curve of a given coprime rank and degree. De Cataldo, Hausel and Migliorini proved in the case of rank 2 and conjectured in arbitrary rank that two natural filtrations on the cohomology of the moduli space coincide. One is the weight filtration W coming from the Betti realization, and the other one is the perverse filtration P induced by the Hitchin map. Motivated by computations of the Khovanov-Rozansky homology of links by Gorsky, Hogancamp and myself, we look for an action of $H_2$ on the cohomology of the moduli space. We find it in the algebra generated by two kinds of natural operations: on the one hand, we have the operations of cup product by tautological classes, and on the other hand, we have the Hecke operators acting via certain correspondences. We then show that both P and W coincide with the filtration canonically associated to the $\mathfrak{sl}_2$ subalgebra of $H_2$.Based on joint work with Hausel, Minets and Schiffmann. -- Indico :: Email Notifier https://events.dm.unipi.it/e/108

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[Indico] Andrea Ricolfi, Quot schemes and their d-critical structure(s), 23/11/2022, 15:00 Europe/Rome
by francesco.sala＠unipi.it 21 Nov '22

21 Nov '22

Title: Quot schemes and their d-critical structure(s), Speaker(s): Andrea Ricolfi, SISSA, Trieste, Date and time: 23 Nov 2022, 15:00 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Department of Mathematics (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/116 Abstract -------- D-critical schemes and Artin stacks were introduced by Joyce in 2015, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry (which is hard) is wide open. We discuss this problem, and new results in this direction, when the moduli space is the Quot scheme of points on a Calabi-Yau 3-fold. Joint work with Michail Savvas. -- Indico :: Email Notifier https://events.dm.unipi.it/e/116

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[Indico] Anton Mellit, P=W via $H_2$, 24/11/2022, 16:00 Europe/Rome
by francesco.sala＠unipi.it 18 Nov '22

18 Nov '22

Title: P=W via $H_2$, Speaker(s): Anton Mellit, University of Vienna, Date and time: 24 Nov 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Combinatorics, Lie Theory, and Topology, Venue: Department of Mathematics (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/108 Abstract -------- By $H_2$ we denote the Lie algebra of polynomial hamiltonian vector fields on the plane. We consider the moduli space of stable twisted Higgs bundles on an algebraic curve of a given coprime rank and degree. De Cataldo, Hausel and Migliorini proved in the case of rank 2 and conjectured in arbitrary rank that two natural filtrations on the cohomology of the moduli space coincide. One is the weight filtration W coming from the Betti realization, and the other one is the perverse filtration P induced by the Hitchin map. Motivated by computations of the Khovanov-Rozansky homology of links by Gorsky, Hogancamp and myself, we look for an action of $H_2$ on the cohomology of the moduli space. We find it in the algebra generated by two kinds of natural operations: on the one hand, we have the operations of cup product by tautological classes, and on the other hand, we have the Hecke operators acting via certain correspondences. We then show that both P and W coincide with the filtration canonically associated to the $\mathfrak{sl}_2$ subalgebra of $H_2$.Based on joint work with Hausel, Minets and Schiffmann. -- Indico :: Email Notifier https://events.dm.unipi.it/e/108

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[Indico] Rouven Frassek, Baxter Q-operators, QQ-systems and the shifted Yangian, 17/11/2022, 16:00 Europe/Rome
by francesco.sala＠unipi.it 16 Nov '22

16 Nov '22

Title: Baxter Q-operators, QQ-systems and the shifted Yangian, Speaker(s): Rouven Frassek, Università di Modena e Reggio Emilia, Date and time: 17 Nov 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Combinatorics, Lie Theory, and Topology, Venue: Department of Mathematics (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/123 Abstract -------- I plan to discuss the construction of Baxter Q-operators within the framework of the Quantum Inverse Scattering Method. The method follows the standard procedure for the transfer matrix construction of spin chains that was developed by Faddeev and collaborators but employs Lax matrices with an infinite-dimensional auxiliary space. Those Lax matrices do not fit into the standard Yangian of Drinfeld but can be understood in the context of the shifted Yangian. The Q-operators satisfy a set of functional relations that are known as QQ-relations that can be seen as the successor of the famous Bethe equations. In the case of the Yangian of $\mathsf{su}(n)$, the full set of functional relations can be derived from the Q-operators. Beyond $\mathsf{su}(n)$ new obstacles arise in the construction of Q-operators which will be discussed in the example of $\mathsf{so}(2r)$. -- Indico :: Email Notifier https://events.dm.unipi.it/e/123

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[Indico] Rouven Frassek, Baxter Q-operators, QQ-systems and the shifted Yangian, 17/11/2022, 16:00 Europe/Rome
by francesco.sala＠unipi.it 11 Nov '22

11 Nov '22

Title: Baxter Q-operators, QQ-systems and the shifted Yangian, Speaker(s): Rouven Frassek, Università di Modena e Reggio Emilia, Date and time: 17 Nov 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Combinatorics, Lie Theory, and Topology, Venue: Department of Mathematics (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/123 Abstract -------- I plan to discuss the construction of Baxter Q-operators within the framework of the Quantum Inverse Scattering Method. The method follows the standard procedure for the transfer matrix construction of spin chains that was developed by Faddeev and collaborators but employs Lax matrices with an infinite-dimensional auxiliary space. Those Lax matrices do not fit into the standard Yangian of Drinfeld but can be understood in the context of the shifted Yangian. The Q-operators satisfy a set of functional relations that are known as QQ-relations that can be seen as the successor of the famous Bethe equations. In the case of the Yangian of $\mathsf{su}(n)$, the full set of functional relations can be derived from the Q-operators. Beyond $\mathsf{su}(n)$ new obstacles arise in the construction of Q-operators which will be discussed in the example of $\mathsf{so}(2r)$. -- Indico :: Email Notifier https://events.dm.unipi.it/e/123

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[Indico] David Harari, Arithmetic of homogeneous spaces over global fields of characteristic p, 09/11/2022, 15:00 Europe/Rome
by francesco.sala＠unipi.it 07 Nov '22

07 Nov '22

Title: Arithmetic of homogeneous spaces over global fields of characteristic p, Speaker(s): David Harari, Université de Paris-Saclay, Date and time: 9 Nov 2022, 15:00 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Department of Mathematics (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/110 Abstract -------- Let $K$ be the function field of a curve over a finite field. Let $X$ be a homogeneous space of a reductive group over $K$. We discuss cohomological obstructions to the local-global principle on $X$. Similar results for weak and strong approximation will also be provided (joint work with Cyril Demarche). -- Indico :: Email Notifier https://events.dm.unipi.it/e/110

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Fwd: annoucement - GEOMETRIC REPRESENTATION THEORY AND QUANTUM TOPOLOGY
by Francesco Sala 05 Nov '22

05 Nov '22

Da Olivier Schiffmann: --- Bonjour, un workshop intitulé GEOMETRIC REPRESENTATION THEORY AND QUANTUM TOPOLOGY aura lieu a l'université Paris-Cité du 12 au 16 Decembre prochain. Plus d'informations sont disponibles sur la page web http://georep22.imj-prg.fr Amicalement, Eric Vasserot --- Ciao, Francesco

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