fables

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fables [2019/10/27 16:58] weronika |
fables [2020/05/10 17:37] (Version actuelle) weronika |
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The normal starting time of this seminar is 16.30 on Monday. | The normal starting time of this seminar is 16.30 on Monday. | ||

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+ | 2020, Wednesday, May 20, 16:00 (CEST), Virtual seminar, Lionel Lang (Stockholm University) | ||

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+ | https:// | ||

+ | Meeting ID: 592 872 9514 Password: (the number of lines on a cubic surface) | ||

+ | | ||

+ | **Co-amoebas, | ||

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+ | 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, | ||

+ | 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. | ||

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+ | ---- | ||

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+ | 2020, Tuesday, April 7, 17:00, Virtual seminar (EDGE seminar) Grigory Mikhalkin (Geneva) | ||

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+ | https:// | ||

+ | Meeting ID: 870 554 816 Password: 014504 | ||

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+ | **Area in real K3-surfaces** | ||

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+ | 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. | ||

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+ | ---- | ||

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+ | 2020, Monday, March 31, 17:00, Virtual seminar, Vladimir Fock (Strasbourg) | ||

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+ | https:// | ||

+ | Meeting ID: 737 573 471 | ||

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+ | **Higher measured laminations and tropical curves** | ||

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+ | 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. | ||

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+ | ---- | ||

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+ | 2020, Monday, March 16, 16:30, Battelle, Alexander Veselov (Loughborough University)[POSTPONED] | ||

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+ | **On integrability, | ||

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+ | 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, | ||

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+ | A particular case of such 3-folds the modular quotient SL(2, | ||

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+ | The talk is partly based on a recent joint work with Alexey Bolsinov and Yiru Ye. | ||

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+ | ---- | ||

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+ | 2020, Monday, February 17, 16:30, Battelle, Karim Adiprasito | ||

+ | (University of Copenhagen, Hebrew University of Jerusalem) | ||

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+ | ** Algebraic geometry of the sphere at infinity, polyhedral de Rham theory and L^2 vanishing conjectures ** | ||

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+ | 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. | ||

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+ | ---- | ||

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+ | 2019, Friday, December 6, 15:00, Battelle, Tomasz Pelka (UniBe) | ||

+ | ** Q-homology planes satisfying the Negativity Conjecture ** | ||

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+ | 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. | ||

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+ | 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, | ||

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+ | ---- | ||

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+ | 2019, Monday, November 25, 16:30, Battelle, Felix Schlenk (UniNe) | ||

+ | ** (Real) Lagrangian submanifolds ** | ||

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+ | 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. | ||

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+ | ---- | ||

fables.1572191935.txt.gz · Dernière modification: 2019/10/27 16:58 de weronika