Geometria_Pisa May 2022

geometria_pisa@lists.dm.unipi.it

5 participants
12 discussions

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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Seminario
by Andrea Tamburelli 31 May '22

31 May '22

Buongiorno, Vi segnalo un seminario questo pomeriggio in aula riunioni. Saluti, Andrea ______________________________________________________________________________________________ 31 Maggio 2022, 16:30 - 17:30, Aula Riunioni Nicholas Rungi (SISSA) Titolo: Pseudo-Kähler geometry of properly convex projective structures in a linear case Abstract: In this talk we will define a pseudo-Kähler structure on the deformation space of properly convex projective structures over the 2-dimensional torus. The symplectic form and the pseudo-Riemannian metric are both compatible with the complex structure inherited from the identification of this space with the total space of the holomorphic vector bundle of cubic differentials over Teichmuller space. I will also explain briefly what we expect in higher genus and the strategy to solve the problem. This is the first part of an ongoing PhD research project under the supervision of Dr. A. Tamburelli.

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Fwd: [gdrtresses] Post-doctoral position Leeds
by Bruno Martelli 30 May '22

30 May '22

Post-doc position in Leeds ---------- Forwarded message --------- From: wagner(a)imj-prg.fr <wagner(a)imj-prg.fr> Date: Mon, May 30, 2022 at 9:30 AM Subject: [gdrtresses] Post-doctoral position Leeds To: gdrtresses(a)listes.math.cnrs.fr <gdrtresses(a)listes.math.cnrs.fr> Dear all, Would you be able to help us advertise these two postdoctoral positions in the University of Leeds? (Or apply to them?) These positions will be supported by the EPSRC programme grant: "Combinatorial Representation Theory: Discovering the Interfaces of Algebra with Geometry and Topology" https://sites.google.com/view/crt-leeds There will be more positions opening in the future. So do keep us on the radar for future opportunities. Best wishes Joao Faria Martins http://www1.maths.leeds.ac.uk/~pmtjfa/

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Seminario di geometria
by Bruno Martelli 29 May '22

29 May '22

Buondì, Segnalo un seminario di geometria per il prossimo mercoledì. A presto, Bruno Martelli ---- 1 Giugno 2022, 16:00 - 17:00, Aula Seminari Francesco Lin (Columbia) Titolo: Equazioni di Seiberg-Witten e 3-varietà iperboliche Abstract: Un interessante problema aperto in topologia in dimensione bassa è quello di capire possibili interazioni fra l’omologia di Floer e gli invarianti geometrici di varietà iperboliche. Per esempio, un quesito base è quello di determinare si possano inferire o meno informazioni riguardo all’omologia di Floer da quantità come il volume, il raggio di iniettività e le lunghezze delle geodetiche. Nel seminario discuterò qualche risultato parziale in questa direzione ottenuto in una serie di lavori con M. Lipnowski.

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I: inizio minicorso di dottorato
by Tamas Szamuely 28 May '22

28 May '22

MINICORSO DI DOTTORATO SU UNA VERSIONE COMOLOGICA DELLA TEORIA DI HODGE NON ABELIANA Mark De Cataldo (Stony Brook) 4 lezioni Prima lezione lunedi` 30 maggio, ore 10, aula seminari, Dipartimento di Matematica. Una breve descrizione del programma la trovate nel file allegato. Prego tutti di inoltrare il messaggio a potenziali interessati e in particolare Luca Bruni di inoltrarlo alla mailing list dei perzionandi. Grazie.

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Seminario 31 maggio
by Andrea Tamburelli 26 May '22

26 May '22

Cari colleghi, Nicholas Rungi, un dottorando della SISSA che sto seguendo, e' qui in visita settimana prossima. Avevo pensato che potrebbe dare un seminario martedi pomeriggio, che mi pare essere libero da eventi. Volevo pero' prima essere sicuro che ci sara' un pubblico, visto che siamo vicini al ponte del 2 giugno ed e' stato organizzato all'ultimo momento. Vi prego di farmi sapere se potrete essere presenti. Trovate qui sotto titolo e abstract. Saluti, Andrea _______________________________________________________________________________________ *Title: Pseudo-Kähler geometry of properly convex projective structures in a linear case* *Abtract:* In this talk I will present a first result obtained in a joint work with A. Tamburelli. We define a pseudo-Kähler structure on the deformation space of properly convex projective structures over the 2-dimensional torus. The symplectic form and the pseudo-Riemannian metric are both compatible with the complex structure inherited from the identification of this space with the total space of the holomorphic vector bundle of cubic differentials over Teichmuller space. I will also explain briefly what we expect in higher genus and the strategy to solve the problem. This is the first part of an ongoing PhD research project under the supervision of Dr. A. Tamburelli.

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[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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Geometria_Pisa May 2022