- Geometria_Pisa - Mailing list — Dipartimento di Matematica, UniPI

[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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[Indico] Miroslav Rapcak, Coherent Sheaves, Quivers and Affine-Yangian Representations, 03/11/2022, 16:00 Europe/Rome
by francesco.sala＠unipi.it 02 Nov '22

02 Nov '22

Title: Coherent Sheaves, Quivers and Affine-Yangian Representations, Speaker(s): Miroslav Rapcak, CERN, Date and time: 3 Nov 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Combinatorics, Lie Theory, and Topology, Venue: Department of Mathematics (Aula Seminari`). You can access the full event here: https://events.dm.unipi.it/e/124 Abstract -------- According to the famous result of Schiffmann and Vasserot, the cohomology of the ADHM moduli space carries the structure of an affine-Yangian module. For the purpose of our talk, it is useful to view this moduli space from a three-dimensional perspective of the derived category of coherent sheaves on $\mathbb{C}^3$. More concretely, one can interpret the ADHM moduli space as parametrizing extensions of a coherent sheaf on $\mathbb{C^2}\subset \mathbb{C}^3$ by skyscraper sheaves. It is then natural to ask whether exchanging such a "framing" non-compact sheaf by a different one leads to other representations of the algebra. In this talk, I am going to give an overview of some of the developments in this direction and comment on various predictions originating from physics. -- Indico :: Email Notifier https://events.dm.unipi.it/e/124

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Seminario topologia mercoledì
by Bruno Martelli 31 Oct '22

31 Oct '22

Buondì, Scusandomi per lo scarsissimo preavviso, annuncio un seminario di geometria e topologia per mercoledì (dopodomani). Siete tutti invitati, Bruno ----- Orario e luogo: 2 Novembre 2022, 16:00 - 17:00, Aula Seminari Speaker: Francesco Costantino (Toulouse) Title: Stated skein algebras Abstract: In this talk I will recall the notion of skein algebra and skein module of surfaces and of three-manifolds and I will introduce the recent idea of stated skein algebra and module. After discussing the interest of these objects with respect to the « standard » ones, I will discuss some key examples and some applications. Most of the material I will present is joint work with Thang Le.

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Double conference: June 2023 in Pisa
by Enrico Le Donne 31 Oct '22

31 Oct '22

Dear colleagues, We cordially invite you to attend a double event held at the De Giorgi Center of the SNS Pisa in June 2023. a) workshop "subRiemannian geometry and beyond, III" from 19th - 23rd June, 2023. https://sites.google.com/view/srgb3pisa2023 b) conference "Geometry and analysis of groups and manifolds" from 26th - 30th June, 2023. https://sites.google.com/view/geometryandanalysis/ The first meeting is the 3rd organized within the ERC project GeoMeG (Geometry of Metric Groups). The general plan is to bring together international researchers working in various areas of mathematics with connections to sub-Riemannian geometry or, more generally, metric geometry. The idea for this meeting is to focus on the large-scale geometry of nilpotent groups, Heintze groups and their boundaries, and the geometry of solvable groups or, more generally, the large-scale geometry of Lie groups. There will be introductory courses in the first two days, and conference talks for the next 3 days. The second conference will bring together world-leading experts on Geometric Analysis, Analysis on Metric Spaces, and Geometric Group Theory. These fields have seen rapid progress in recent years, both individually and in interaction, solving major open questions and opening up exciting new avenues of inquiry. Informally, the conference will also celebrate the contributions of Bruce Kleiner to these areas. Further information about registration and potential funding for junior participants will be available on the webpages. On behalf of the organizers. -- Enrico Le Donne

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Fwd: Postdoc positions at IHES
by Bruno Martelli 31 Oct '22

31 Oct '22

Inizio messaggio inoltrato: *Da: *Fanny Kassel <kassel(a)ihes.fr> *Oggetto: **Postdoc positions at IHES* *Data: *28 ottobre 2022, 11:18:06 CEST *A: *Fanny Kassel <kassel(a)ihes.fr> Dear colleagues, I hope this email finds you well. I would like to advertize that this year we are hiring five postdocs in mathematics at IHES: https://www.ihes.fr/en/applications/#post-docs Excellent candidates working on groups, geometry, and dynamics are strongly encouraged to apply. Particular attention will be paid to candidates who already have some experience working on one of the following topics: discrete subgroups of Lie groups, Teichmüller or higher Teichmüller theory, dynamics on character varieties, geometric structures on manifolds (hyperbolic geometry, convex projective geometry, Lorentzian or more generally pseudo-Riemannian geometry, etc.). The application deadline is 29 November 2022. Please feel free to pass on the information to anyone who might be interested. Best regards, Fanny Kassel

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[Indico] Miroslav Rapcak, Coherent Sheaves, Quivers and Affine-Yangian Representations, 03/11/2022, 16:00 Europe/Rome
by francesco.sala＠unipi.it 28 Oct '22

28 Oct '22

Title: Coherent Sheaves, Quivers and Affine-Yangian Representations, Speaker(s): Miroslav Rapcak, CERN, Date and time: 3 Nov 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Combinatorics, Lie Theory, and Topology, Venue: Department of Mathematics (Aula Seminari`). You can access the full event here: https://events.dm.unipi.it/e/124 Abstract -------- According to the famous result of Schiffmann and Vasserot, the cohomology of the ADHM moduli space carries the structure of an affine-Yangian module. For the purpose of our talk, it is useful to view this moduli space from a three-dimensional perspective of the derived category of coherent sheaves on $\mathbb{C}^3$. More concretely, one can interpret the ADHM moduli space as parametrizing extensions of a coherent sheaf on $\mathbb{C^2}\subset \mathbb{C}^3$ by skyscraper sheaves. It is then natural to ask whether exchanging such a "framing" non-compact sheaf by a different one leads to other representations of the algebra. In this talk, I am going to give an overview of some of the developments in this direction and comment on various predictions originating from physics. -- Indico :: Email Notifier https://events.dm.unipi.it/e/124

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[Indico] Vijaylaxmi Trivedi, Hilbert-Kunz density function and its applications to some Hilbert-Kunz multiplicity conjectures, 26/10/2022, 16:30 Europe/Rome
by francesco.sala＠unipi.it 24 Oct '22

24 Oct '22

Title: Hilbert-Kunz density function and its applications to some Hilbert-Kunz multiplicity conjectures, Speaker(s): Vijaylaxmi Trivedi, Tata Institute of Fundamental Research, India, Date and time: 26 Oct 2022, 16:30 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Scuola Normale Superiore, Pisa (Aula Mancini). You can access the full event here: https://events.dm.unipi.it/e/106 Abstract -------- In this talk we introduce a compactly supported and real valued continuous function called Hilbert-Kunz (HK) density function. We briefly describe its properties and its applications to study characteristic p-invariants like HK multiplicity and F -thresholds.Further we discuss in more detail some long standing conjectures of Watanabe-Yoshida and Yoshida on the HK multiplicities of quadric hypersurfaces.Here, using the classification of ACM bundles on the smooth quadric via matrix factorizations, we describe the HK density functions of the quadrics. The structure of the function explains the difficulties in nailing down the computations of HK multiplicities of even such simple class of rings.As a corollary we prove a part of the Watanabe-Yoshida conjecture for all dimensions. Moreover, for large p, we give a closed formula for HK multiplicities of quadrics hypersurfaces and a proof of Yoshida’s conjecture. -- Indico :: Email Notifier https://events.dm.unipi.it/e/106

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