Geometria_Pisa

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2 participants
767 discussions

[Indico] Leonid Rybnikov, Kashiwara crystals and the moduli space of stable rational curves, 25/05/2022, 16:00 Europe/Rome
by francesco.sala＠unipi.it 24 May '22

24 May '22

Title: Kashiwara crystals and the moduli space of stable rational curves, Speaker(s): Leonid Rybnikov, HSE University, Faculty of Mathematics, Moscow, Date and time: 25 May 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Combinatorics, Lie Theory, and Topology, Venue: Aula Riunioni (Department of Mathematics). You can access the full event here: https://events.dm.unipi.it/e/92 Abstract -------- The category of Kashiwara crystals for a semisimple complex Lie algebra $\mathfrak{g}$ is a combinatorial model of the tensor category of finite-dimensional $\mathfrak{g}$-modules, where $\mathfrak{g}$-modules are represented by colored oriented graphs with the weight vectors being represented by points (marked by the weights of the representation), and the action of the Chevalley generators being represented by arrows (marked by simple roots). Kashiwara crystals form a monoidal category in which the tensor product is not symmetric, but the tensor products of two crystals in different orders are still connected by some functorial isomorphism called commuter. This structure is similar to braiding in the category of representations of the quantum group $U_q(\mathfrak{g})$ (and, in fact, comes from it), but the commutator do not satisfy the braid group relation. In particular, on the tensor power of a given crystal, all possible commutors generate not the action of the braid group $B_n$, but the action of another group $J_n$, called the cactus group -- the $S_n$-equivariant fundamental group of $\overline{M_{0 ,n+1}}(\mathbb{R})$, the Deligne-Mumford compactification of the moduli spaces of real stable rational curves with $n+1$ marked points. Such monoidal categories are called coboundary. I will describe a general construction of a coboundary monoidal category as a family of compatible coverings over real Deligne-Mumford spaces, thus explaining the appearance of the real Deligne-Mumford compactification in this context. This construction also explains how Kashiwara crystals arise in quantum integrable systems, such as the Gaudin magnet chain. This helps to compute some monodromy of solutions of Bethe ansatz equations for quantum magnet chains. I will show how this works in the example $\mathfrak{g}=\mathfrak{sl}_2$ which is already interesting and sufficiently general. (joint work with Joel Kamnitzer, Iva Halacheva, and Alex Weekes, arXiv:1708.05105) -- Indico :: Email Notifier https://events.dm.unipi.it/e/92

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[Indico] Siddharth Mathur, Searching for the impossible Azumaya algebra, 25/05/2022, 14:30 Europe/Rome
by francesco.sala＠unipi.it 24 May '22

24 May '22

Title: Searching for the impossible Azumaya algebra, Speaker(s): Siddharth Mathur, Orsay, Date and time: 25 May 2022, 14:30 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Scuola Normale Superiore (Aula Volterra). You can access the full event here: https://events.dm.unipi.it/e/72 Abstract -------- In two 1968 seminars, Grothendieck used the framework of etale cohomology to extend the definition of the Brauer group to all schemes. Over a field, the objects admit a well-known algebro-geometric description: they are represented by $\mathbb{P}^n$-bundles (equivalently: Azumaya algebras). Despite the utility and success of Grothendieck's definition, an important foundational aspect remains open: is every cohomological Brauer class over a scheme represented by a $\mathbb{P}^n$-bundle? It is not even known if smooth proper threefolds over the complex numbers have enough Azumaya algebras! In this talk, I will outline a strategy to construct a Brauer class that cannot be represented by an Azumaya algebra. Although the candidate is algebraic, the method will leave the category of schemes and use formal-analytic line bundles to create Brauer classes. I will then explain a strange criterion for the existence of a corresponding Azumaya algebra. At the end, I will reveal the unexpected conclusion of the experiment. -- Indico :: Email Notifier https://events.dm.unipi.it/e/72

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[Indico] Giulio Bresciani, Two results about Grothendieck's Section Conjecture, 18/05/2022, 14:30 Europe/Rome
by francesco.sala＠unipi.it 17 May '22

17 May '22

Title: Two results about Grothendieck's Section Conjecture, Speaker(s): Giulio Bresciani, SNS Pisa, Date and time: 18 May 2022, 14:30 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/73 Abstract -------- Grothendieck's Section Conjecture states that, if $X$ is an hyperbolic curve over a field $k$ finitely generated over $\mathbb{Q}$, every section of the map $\pi_1(X) \to \mathsf{Gal}(k)$ is associated with a rational point of the completion of $X$. After summarizing the main known facts concerning the conjecture, we will present two new results. First, we generalize to number fields a theorem which was proved over $\mathbb{Q}$ by Stix: we prove that if $k$ is a number field and the Weil restriction of $X$ to $\mathbb{Q}$ admits a rational map to a non-trivial Brauer-Severi variety, then $X$ satisfies the conjecture. Secondly, if $k$ is finitely generated over $\mathbb{Q}$, we prove that the conjecture holds for sections which satisfy a strong birationality assumption. In particular, this implies that the section conjecture is equivalent to Esnault and Hai's cuspidalization conjecture, which states that every Galois section of every hyperbolic curve $X$ lifts to every open subset of $X$. -- Indico :: Email Notifier https://events.dm.unipi.it/e/73

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Fwd: A postdoc position
by Stefano Riolo 07 May '22

07 May '22

Segnalo post-doc di 2 anni in Corea dal Sud, su (G,X)-strutture, senza insegnamento. La data d'inizio a settembre è indicativa: pare si possa rinviare di massimo mezzo anno. Eventualmente contattare Gye-Seon Lee (http://www.math.snu.ac.kr/~gyeseonlee/) all'indirizzo gyeseonlee(a)snu.ac.kr Buon finesettimana, Stefano -------- Messaggio Inoltrato -------- Hi Stefano, As I told you before, I'm looking for candidates for a two-year postdoc position at the Department of Mathematical Sciences of Seoul National University, starting from September 2022. The funding comes from my research grant "A study on convex real projective Dehn filling". The annual salary is approximately 65000000 Won (roughly 48000 Euro) before taxes. There is no teaching duty. I hope that candidates have good research potential with interests in geometric structures on manifolds and representation spaces. Best, Gye-Seon

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[Indico] Luca Schaffler, Boundary divisors in the stable pair compactification of the moduli space of Horikawa surfaces, 04/05/2022, 14:30 Europe/Rome
by francesco.sala＠unipi.it 03 May '22

03 May '22

Title: Boundary divisors in the stable pair compactification of the moduli space of Horikawa surfaces, Speaker(s): Luca Schaffler, Roma 3, Date and time: 4 May 2022, 14:30 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/71 Abstract -------- Smooth minimal surfaces of general type with $K^2=1$, $p_g=2$, and $q=0$ constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli space $M$ of their canonical models admits a geometric and modular compactification $\overline{M}$ by stable surfaces. Franciosi-Pardini-Rollenske classified the Gorenstein stable degenerations parametrized by it, and jointly with Rana they determined boundary divisors parametrizing irreducible stable surfaces with a unique T-singularity. In this talk, we continue with the investigation of the boundary of $\overline{M}$ constructing eight new irreducible boundary divisors parametrizing reducible surfaces. Additionally, we study the relation with the GIT compactification of $M$ and the Hodge theory of the degenerate surfaces that the eight divisors parametrize. This is joint work in progress with Patricio Gallardo, Gregory Pearlstein, and Zheng Zhang. -- Indico :: Email Notifier https://events.dm.unipi.it/e/71

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Fwd: Concorso RTDB trieste
by Bruno Martelli 02 May '22

02 May '22

Buondì, Segnalo un RTD-B in Geometria a Trieste A presto, Bruno Martelli ---------- Forwarded message --------- Cari colleghi, vi inoltro l'annuncio di un concorso da RTDB per Geometria a Trieste con scadenza 12/5 (https://web.units.it/node/44270/ricerca/pub) con la preghiera di diffondere la notizia tra chi potrebbe essere interessato. Grazie mille, Alessia

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Seminario mercoledì prossimo
by Bruno Martelli 29 Apr '22

29 Apr '22

Buondì, Segnalo un seminario di geometria per mercoledì prossimo. A presto, Bruno 04-May-2022 - 16:00 Sala Seminari (Dip. Matematica) Simplicial volume and aspherical manifolds Marco Moraschini Simplicial volume is a homotopy invariant for compact manifolds introduced by Gromov in the early 80s. It measures the complexity of a manifold in terms of singular simplices. Since simplicial volume behaves similarly to the Euler characteristic, a natural problem is to understand the relation between these two invariants. More precisely, a celebrated question by Gromov (~’90) asks whether all oriented closed connected aspherical manifolds with zero simplicial volume also have vanishing Euler characteristic. In this talk, we will describe the problem and we will show counterexamples to some variations of the previous question. Moreover, we will describe some new strategies to approach the problem as well as the relation between Gromov’s question and other classical problems in topology. This is part of a joint work with Clara Löh and George Raptis.

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Fwd: Postdoc position at Università di Firenze
by Bruno Martelli 27 Apr '22

27 Apr '22

---------- Forwarded message --------- From: Daniele Angella <daniele.angella(a)unifi.it> Date: Wed, Apr 27, 2022 at 5:47 PM Subject: Postdoc position at Università di Firenze To: geometriaglobale(a)lists.math.unifi.it < geometriaglobale(a)lists.math.unifi.it>, geometriaglobale-group(a)unifi.it < geometriaglobale-group(a)unifi.it> Cc: Fabio Podesta' <fabio.podesta(a)unifi.it> Dear all, We are looking for candidates for a Postdoc position at Università di Firenze, Italy, starting from July. The position is partially supported by the Project "Real and Complex Manifolds: Topology, Geometry and Holomorphic Dynamics". The call is open until the deadline May 29th, 2022: https://titulus.unifi.it/albo/viewer?view=files%2F004521290-UNFICLE-55ffded… The call is in Italian - feel free to contact us in case you need help on translation or if you want more information. Please forward the announcement to potential candidates! All the best,

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workshop on Recent advances in bounded cohomology
by Marco Moraschini 26 Apr '22

26 Apr '22

Dear all, We are pleased to announce a workshop on *Recent Advances in Bounded Cohomology* to be held at the University of Regensburg during *September 26-30, 2022*, funded by the SFB Higher Invariants of the University of Regensburg. The aim of this workshop is to bring together researchers in bounded cohomology theory and related fields and discuss recent developments. In addition to the invited talks, there will be opportunities for researchers to give contributed talks and ample time for discussions and collaboration. The workshop will be held in a hybrid format. Our speakers are: - Jonathan Bowden (University of Regensburg) - Michelle Bucher (University of Geneva) - Caterina Campagnolo (UAM Madrid) - Francesco Fournier-Facio (ETH Zürich) - Roberto Frigerio (University of Pisa) - Jean-François Lafont (Ohio State University) - Michał Marcinkowski (University of Wrocław) - Nicolas Monod (EPFL) - Sam Nariman (Purdue University) - Chricton Ogle (Ohio State University) - Roman Sauer (KIT) More information and the registration form are available on the conference website: https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/ind… If you have any questions, please do not hesitate to contact the organizers. We look forward to seeing you in September! Best regards, the organizers, Clara Löh, Marco Moraschini and George Raptis

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[Indico] Marco D'Addezio, Parabolicity conjecture of F-isocrystals, 27/04/2022, 14:30 Europe/Rome
by francesco.sala＠unipi.it 26 Apr '22

26 Apr '22

Title: Parabolicity conjecture of F-isocrystals, Speaker(s): Marco D'Addezio, Université de Paris, Date and time: 27 Apr 2022, 14:30 (Europe/Rome), Lecture series: Algebraic and Arithmetic Geometry Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/70 Abstract -------- In the last years the theory of crystalline cohomology and F-isocrystals had a great development. I will present a new result concerning the algebraic monodromy groups of F-isocrystals. I will start with a quick introduction on crystalline cohomology, F-isocrystals, and overconvergent F-isocrystals. Subsequently, I will recall the definition of monodromy groups of F-isocrystals (which uses the theory of Tannakian categories) and in the end I will explain the main theorem, the applications, and some ideas of the proof. -- Indico :: Email Notifier https://events.dm.unipi.it/e/70

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