fables
Différences
Ci-dessous, les différences entre deux révisions de la page.
Les deux révisions précédentesRévision précédenteProchaine révision | Révision précédenteProchaine révisionLes deux révisions suivantes | ||
fables [2018/11/17 15:40] – camilla | fables [2022/06/14 09:06] – kalinin0 | ||
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Ligne 3: | Ligne 3: | ||
The normal starting time of this seminar is 16.30 on Monday. | The normal starting time of this seminar is 16.30 on Monday. | ||
+ | |||
---- | ---- | ||
- | 2019, Monday, | + | |
+ | Thursday, June 16, 2022 | ||
+ | 16:00, room 1-07 | ||
+ | |||
+ | **Prof. | ||
+ | **“Topology of spaces of Legendrian knots via Algebraic K-theory”** | ||
+ | |||
+ | Abstract: The highly non-trivial stable homotopy groups of the Waldhausen’s | ||
+ | h-cobordism space inject into the homotopy groups of spaces of appropriate Legendrian submanifolds. For instance, | ||
+ | ---- | ||
+ | Monday, Dec, 20th, 16h15 - 18h15 | ||
+ | |||
+ | **On the asymptotics of Arakelov invariants** | ||
+ | |||
+ | We will discuss the asymptotics of invariants of Riemann | ||
+ | surfaces motivated by Arakelov theory. These invariants play a | ||
+ | fundamental role in bounds for the number of geometric torsion points on | ||
+ | curves. We will show that their asymptotic behaviour in families of | ||
+ | degenerating Riemann surfaces is controlled by their tropical counterparts. | ||
+ | ---- | ||
+ | Fri 17.12.2021, 13h30, room 6-13 | ||
+ | |||
+ | Andras Szenes | ||
+ | |||
+ | **Diagonal bases and wall-crossings in moduli spaces of vector bundle** | ||
+ | |||
+ | The idea of the calculation of the Hilbert function of the moduli spaces of vector bundles on Riemann surfaces goes back to the works of Michael Thaddeus in the early 90’s. | ||
+ | I describe joint work with Olga Trapeznikova where this plan is carried out in detail, which uses only basic tools of Geometric Invariant Theory and a combinatorial/ | ||
+ | ---- | ||
+ | Nov 1, 16h15. Room 06-13 | ||
+ | |||
+ | Vasily Golyshev (Moscow, Bures-sur-Yvette) | ||
+ | |||
+ | |||
+ | **Markov numbers in number theory, topology, algebraic geometry, and differential equations** | ||
+ | |||
+ | I will explain how the Markov numbers arise in different mathematical | ||
+ | disciplines, | ||
+ | |||
+ | ---- | ||
+ | |||
+ | 2020, Wednesday, May 20, 16:00 (CEST), Virtual seminar, Lionel Lang (Stockholm University) | ||
+ | |||
+ | https:// | ||
+ | Meeting ID: 592 872 9514 Password: (the number of lines on a cubic surface) | ||
+ | |||
+ | **Co-amoebas, | ||
+ | |||
+ | In this joint work in progress with J. Forsgård, we study the topology of maps P:(\C*)^2 \to \C given by Laurent polynomials P(z,w). | ||
+ | For specific P, we observed that the topology of the corresponding map can be described in terms of the co-amoeba of a generic fiber. When the latter co-amoeba is maximal, it contains a dimer (a particularly nice graph) whose fundamental cycles corresponds to the vanishing cycles of the map P. For general P, the existence of maximal co-amoebas is widely open. In the meantime, we can bypass co-amoebas, going directly to dimers using a construction of Goncharov-Kenyon and obtain a virtual correspondence between fundamental cycles and vanishing cycles. | ||
+ | In this talk, we will discuss how this (virtual) correspondence can be used to compute the monodromy of the map P. | ||
+ | |||
+ | ---- | ||
+ | |||
+ | |||
+ | 2020, Tuesday, April 7, 17:00, Virtual seminar (EDGE seminar) Grigory Mikhalkin (Geneva) | ||
+ | |||
+ | https:// | ||
+ | Meeting ID: 870 554 816 Password: 014504 | ||
+ | |||
+ | **Area in real K3-surfaces** | ||
+ | |||
+ | Real locus of a K3-surfaces is a multicomponent topological surface. The canonical class provides an area form on these components (well defined up to multiplication by a scalar). In the talk we'll explore inequalities on total areas of different components as well a link between such inequalities and a class of real algebraic curves called simple Harnack curves. Based on a joint work with Ilia Itenberg. | ||
+ | |||
+ | ---- | ||
+ | |||
+ | 2020, Monday, March 31, 17:00, Virtual seminar, Vladimir Fock (Strasbourg) | ||
+ | |||
+ | https:// | ||
+ | Meeting ID: 737 573 471 | ||
+ | |||
+ | **Higher measured laminations and tropical curves** | ||
+ | |||
+ | We shall define a notion of a higher lamination - a graph embedded | ||
+ | into a Riemann surface with edges coloured by generators of an affine | ||
+ | Weyl group. This notion generalises the notion of the ordinary | ||
+ | integral measured lamination and on the other hand of a tropical | ||
+ | curve and can be constructed out of a integral Lagrangian submanifold | ||
+ | of the cotangent bundle. | ||
+ | |||
+ | ---- | ||
+ | |||
+ | 2020, Monday, March 16, 16:30, Battelle, Alexander Veselov (Loughborough University)[POSTPONED] | ||
+ | |||
+ | **On integrability, | ||
+ | |||
+ | |||
+ | I will start with a short review of Liouville integrability in relation with Thurston’s geometrization programme, | ||
+ | using as the main example the geodesic flows on the 3-folds with SL(2, | ||
+ | |||
+ | A particular case of such 3-folds the modular quotient SL(2, | ||
+ | |||
+ | The talk is partly based on a recent joint work with Alexey Bolsinov and Yiru Ye. | ||
+ | |||
+ | ---- | ||
+ | |||
+ | 2020, Monday, February 17, 16:30, Battelle, Karim Adiprasito | ||
+ | (University of Copenhagen, Hebrew University of Jerusalem) | ||
+ | |||
+ | ** Algebraic geometry of the sphere at infinity, polyhedral de Rham theory and L^2 vanishing conjectures ** | ||
+ | |||
+ | |||
+ | I will discuss a conjecture of Singer concerning the vanishing of L^2 cohomology on non-positively curved manifolds, and relate it to Hodge theory on a Hilbert space that arises as the limit of Chow rings of certain complex varieties. | ||
+ | |||
+ | ---- | ||
+ | |||
+ | |||
+ | |||
+ | 2019, Friday, December 6, 15:00, Battelle, Tomasz Pelka (UniBe) | ||
+ | ** Q-homology planes satisfying the Negativity Conjecture ** | ||
+ | |||
+ | A smooth complex algebraic surface S is called a Q-homology plane if H_i(S,Q)=0 for i>0. This holds for example if S is a complement of a rational cuspidal curve in P^2. The geometry of such S is understood unless S is of log general type, in which case the log MMP applied to the log smooth completion (X,D) of S is insufficient. The idea of K. Palka was to study the pair (X,(1/2)D) instead. This approach gives much stronger constraints on the shape of D, and leads to the Negativity Conjecture, which asserts that the Kodaira dimension of K_X+(1/2)D is negative. It is a natural generalization e.g. of the Coolidge-Nagata conjecture about rational cuspidal curves, which was recently proved using these methods by M. Koras and K. Palka. | ||
+ | |||
+ | If this conjecture holds, all Q-homology planes of log general type can be classified. It turns out that, as expected by tom Dieck and Petrie, they are arranged in finitely many discrete families, each obtainable in a uniform way from certain arrangements of lines and conics on P^2. As a consequence, | ||
+ | |||
+ | |||
+ | ---- | ||
+ | |||
+ | 2019, Monday, November 25, 16:30, Battelle, Felix Schlenk (UniNe) | ||
+ | ** (Real) Lagrangian submanifolds ** | ||
+ | |||
+ | We start with describing how Lagrangian submanifolds of symplectic | ||
+ | manifolds naturally appear in many ways: In celestial mechanics, integrable systems, symplectic geometry, and algebraic geometry. | ||
+ | We then look at real Lagrangians, | ||
+ | of an anti-symplectic involution. How special is the property of being real? | ||
+ | While many of the examples discussed above are real, we explain why the | ||
+ | central fibres in toric symplectic manifolds are real only if the moment polytope | ||
+ | is centrally symmetric. | ||
+ | The talk is based on work of and with Joé Brendel, Yuri Chekanov, and Joontae Kim. | ||
+ | |||
+ | ---- | ||
+ | |||
+ | |||
+ | 2019, Friday, November 8, 14:00, Battelle, Johannes Rau (University of Tübingen) | ||
+ | ** The dimension of an amoeba ** | ||
+ | |||
+ | Amoebas are projections of algebraic varieties in logarithmic coordinates and were originally introduced by Gelfand, Kapranov and Zelevinsky in their influential book. Based on some computation, | ||
+ | |||
+ | |||
+ | ---- | ||
+ | 2019, Monday, | ||
+ | |||
+ | ** Quasimodular forms from Betti numbers** | ||
+ | |||
+ | This talk will be about refined curve counting on local P2, the noncompact Calabi-Yau 3-fold total space of the canonical line bundle of the projective plane. I will explain how to construct quasimodular forms starting from Betti numbers of moduli spaces of dimension 1 coherent sheaves on P2. This gives a proof of some stringy predictions about the refined topological string theory of local P2 in the Nekrasov-Shatashvili limit. Partly based on work in progress with Honglu Fan, Shuai Guo, and Longting Wu. | ||
+ | |||
+ | |||
+ | ---- | ||
+ | |||
+ | 2019, Monday, October 28, 16.30, Battelle, Ilia Itenberg, (Sorbonne University) | ||
+ | |||
+ | ** Planes in four-dimensional cubics ** | ||
+ | |||
+ | We discuss possible numbers of 2-planes in a smooth cubic hypersurface in the 5-dimensional projective space. | ||
+ | We show that, in the complex case, the maximal number of planes is 405, the maximum being realized by the Fermat cubic. | ||
+ | In the real case, the maximal number of planes is 357. | ||
+ | |||
+ | The proofs deal with the period spaces of cubic hypersurfaces in the 5-dimensional complex projective space | ||
+ | and are based on the global Torelli theorem and the surjectivity of the period map for these hypersurfaces, | ||
+ | as well as on Nikulin' | ||
+ | |||
+ | Joint work with Alex Degtyarev and John Christian Ottem. | ||
+ | |||
+ | |||
+ | ---- | ||
+ | |||
+ | 2019, Monday, October 14, 16:30, Battelle, Igor Krichever (Columbia University) | ||
+ | |||
+ | ** Degenerations of real normalized differentials ** | ||
+ | |||
+ | The behavior of real-normalized (RN) meromorphic differentials on Riemann surfaces under degeneration is studied. In particular, it is proved that the residues at the nodes are solutions of a suitable Kirchhoff problem on the dual graph of the curve. | ||
+ | Our main tool is a new method for constructing differentials | ||
+ | |||
+ | |||
+ | --- | ||
+ | 2019, Monday, October 7, 16:30, Battelle, Jérémy Blanc (University of Basel) | ||
+ | |||
+ | ** Quotients of higher dimensional Cremona groups ** | ||
+ | |||
+ | |||
+ | We study large groups of birational transformations $\mathrm{Bir}(X)$, | ||
+ | dimension at least $3$, defined over $\mathbb{C}$ or a subfield of $\mathbb{C}$.Two prominent cases are when $X$ is the projective space $\mathbb{P}^n$, | ||
+ | or when $X \subset \mathbb{P}^{n+1}$ is a smooth cubic hypersurface.In both cases, and more generally when $X$ is birational to a conic bundle, we produce infinitely many distinct group homomorphisms from | ||
+ | $\mathrm{Bir}(X)$ to $\mathbb{Z}/ | ||
+ | |||
+ | Joint work with Stéphane Lamy and Susanna Zimmermann | ||
+ | |||
+ | ---- | ||
+ | |||
+ | 2019, Monday, September 30,16:30, Battelle, | ||
+ | |||
+ | ** The wrapped Fukaya category of a Weinstein manifold is generated by the Lagrangian cocore discs** | ||
+ | |||
+ | In a joint work with B. Chantraine, G. Dimitroglou Rizell and P. Ghiggini, we decompose any object in the wrapped Fukaya category as a twisted complex built from the cocores of the critical (i.e. half-dimensional) handles in a Weinstein handle decomposition. The main tools used are the Floer homology theories of exact Lagrangian immersions, of exact Lagrangian cobordisms in the SFT sense (i.e. between Legendrians), | ||
+ | |||
+ | ---- | ||
+ | 2019, Wednesday, September | ||
+ | ** Two-dimensional local fields and integration on them** | ||
+ | |||
+ | Two-dimensional local fields include formal loop objects such as $R((t))$, $C((t))$, $Q_p((t))$ and also fields such as $F_p((t_1))((t_2))$, | ||
+ | ---- | ||
+ | |||
+ | 2019, Monday, September 16, 16:30, Battelle, Gleb Smirnov, (ETH Zurich) | ||
+ | |||
+ | **From flops to diffeomorphism groups** | ||
+ | |||
+ | Following a short introduction to the flop surgery, I will | ||
+ | explain how this surgery can be used to detect non-contractible | ||
+ | loops of diffeomorphisms for many algebraic surfaces. | ||
+ | |||
+ | |||
+ | ---- | ||
+ | 2019, Monday, May 20, 14:00, Battelle, Ziming Ma (Chinese University of Hong Kong) | ||
+ | |||
+ | **Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties** | ||
+ | |||
+ | In this talk, we construct a dgBV algebra PV^∗, | ||
+ | |||
+ | |||
+ | ---- | ||
+ | 2019, Monday, April 8, 16:00, Battelle, Michele Ancona (Institut Camille Jordan) | ||
+ | |||
+ | **Random sections of line bundles over real Riemann surfaces** | ||
+ | |||
+ | Given a line bundle L over a real Riemann surface, we study the number of real zeros of a random section of L. We prove a rarefaction result for sections whose number of real zeros deviates from the expected one. | ||
+ | |||
+ | ---- | ||
+ | 2019, Monday, April 1, 16:00, Battelle, Mikhail Shkolnikov (IST Austria) | ||
+ | |||
+ | **PSL-tropical limits** | ||
+ | |||
+ | The classical tropical limit is defined for families of varieties in the algebraic torus. One of the ways to generalize this framework is to consider non-commutative groups instead of algebraic tori. We describe tropical limits for subvarieties in PSL(2, | ||
+ | |||
+ | ---- | ||
+ | 2019, | ||
+ | |||
+ | **Berkovich approach to degenerations of hyper-Kähler varieties** | ||
+ | |||
+ | To a degeneration of varieties, we can associate the dual intersection complex, a topological space that encodes the combinatoric of the central fiber and reflects the geometry of the generic fiber. The points of the dual complex can be identified to valuations on the function field of the variety, hence the dual complex can be embedded in the Berkovich space of the variety. In this talk I will explain how this interpretation gives an insight in the study of the dual complexes. I will focus on some degenerations of hyper-Kähler varieties and show that we are able to determine the homeomorphism type of their dual complex using techniques of Berkovich geometry. The results are in accordance with the predictions of mirror symmetry, and the recent work about the rational homology of dual complexes of degenerations of hyper-Kähler varieties, due to Kollár, Laza, Saccà and Voisin. This is joint work with Morgan Brown. | ||
+ | |||
+ | ---- | ||
+ | 2019, Monday, March 18, 16:00, Battelle, Danilo Lewanski (Max Planck Institut für Mathematik) | ||
+ | |||
+ | **Refreshing Tropical Jucys curves** | ||
+ | |||
+ | We derive explicit formulae for the generating series of Grothendieck dessins d’enfant and monotone Hurwitz numbers via the semi-infinite wedge formalism, and from it we obtain bosonic Fock space expressions. This yields to a tropical geometric interpretation involving Gromov-Witten invariants as local multiplicities. | ||
+ | ---- | ||
+ | 2019, Monday, March 11, 16:00, Battelle, Anton Mellit (University of Vienna) | ||
+ | |||
+ | **Five-term relations** | ||
+ | |||
+ | I will review how the five term relation for the Fadeev-Kashaev' | ||
+ | ---- | ||
+ | 2019, Monday, March 4, 16:00, Battelle, Andras Stipsicz (Budapest University) | ||
+ | |||
+ | **Knot Floer homology and double branched covers** | ||
+ | |||
+ | We will review the basic constructions of (various versions of) | ||
+ | knot Floer homologies, show some applications and extensions of the | ||
+ | definitions to the double branched cover, also using the covering | ||
+ | transformation. | ||
+ | |||
+ | ---- | ||
+ | 2019, Monday, February 25, 16:00, Battelle, Erwan Brugallé (Université de Nantes) | ||
+ | |||
+ | **On the invariance of Welschinger invariants** | ||
+ | |||
+ | Welshinger invariants are real analogs of Gromov-Witten invariants for symplectic 4-manifolds X. In this talk, I will strengthen the original Welschinger' | ||
+ | This result follows easily from a formula relating Welschinger invariants of two real symplectic manifolds differing by a surgery along a real Lagrangian sphere. As an application, | ||
---- | ---- | ||
2018, Monday, December 10, 16:00, Battelle, Arthur Renaudineau (Lille) | 2018, Monday, December 10, 16:00, Battelle, Arthur Renaudineau (Lille) | ||
- | ***Lefschetz hyperplane section theorem for tropical hypersurfaces*** | + | **Lefschetz hyperplane section theorem for tropical hypersurfaces** |
+ | |||
+ | We will discuss variants of the Lefschetz hyperplane section theorem | ||
+ | for the integral tropical homology groups of non-singular tropical | ||
+ | hypersurfaces of toric varieties. As an application, | ||
+ | integral tropical homology groups of non-singular tropical hypersurfaces | ||
+ | are torsion free. This is a joint work with Charles Arnal and Kristin Shaw. | ||
- | We will discuss variants of the Lefschetz hyperplane section theorem | ||
- | for the integral tropical homology groups of non-singular tropical | ||
- | | ||
- | | ||
- | are torsion free. This is a joint work with Charles Arnal and Kristin Shaw. | ||
---- | ---- | ||
- | 2018, Monday, November 26, 16:00, Battelle, Vladimir Fock (Strasbourg) | + | |
- | ***Higher complex structures on surfaces*** | + | **Higher complex structures on surfaces** |
We suggest a definition of a differential geometric structures on | We suggest a definition of a differential geometric structures on | ||
Ligne 28: | Ligne 299: | ||
representation of the fundamental group to PGL(2)). Joint work with | representation of the fundamental group to PGL(2)). Joint work with | ||
A.Thomas. | A.Thomas. | ||
- | |||
---- | ---- | ||
2018, Monday, November 19, 16:15, Battelle, Stepan Orevkov (Moscow, Toulouse) | 2018, Monday, November 19, 16:15, Battelle, Stepan Orevkov (Moscow, Toulouse) | ||
- | ***Orthogonal polynomials in two variables*** | + | **Orthogonal polynomials in two variables** |
A natural generalization of classical systems of (one-variable) | A natural generalization of classical systems of (one-variable) | ||
Ligne 47: | Ligne 317: | ||
---- | ---- | ||
- | 2018, Monday, October 8, 16:30, Battelle, Sione Ma'u (Auckland) | + | |
| | ||
**Polynomial degree via pluripotential theory** | **Polynomial degree via pluripotential theory** |
fables.txt · Dernière modification : 2023/12/05 11:54 de slavitya_gmail.com