Seminari de Geometria Algebraica de Barcelona
 UB UPC UAB
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 Seminari de Geometria Algebraica 2018/2019 Conferenciant Títol Data i hora ARCADES Doctoral School II and ESR Days 3 a 7 de setembre, IMUB Constantin Shramov Steklov Math Inst & NRU HSE Moscou, Rússia Contact: ignasi.mundet at ub.edu Automorphisms of Kaehler manifolds I will survey various results about finite groups acting by automorphisms and birational automorphisms of Kaehler manifolds. I will show that in many cases such groups enjoy the Jordan property, similar to subgroups of general linear groups. The talk is based on joint works with Yu. Prokhorov. Divendres 7 de setembre, 15h, Aula T2, FMI-UB Martín Sombra ICREA - UB The zero set of the independence polynomial of a graph In statistical mechanics, the independence polynomial of a graph G arises as the partition function of the hardcore lattice gas model on G. The distribution of the zeros of these polynomials when G→∞ is relevant for the study of this model and, in particular, to the determination of its phase transitions. In this talk, I will review the known results on the location of these zeros, with emphasis on the case of rooted regular trees of fixed degree and varying depth k ≥ 0. Our main result states that for these graphs, the zero sets of their independence polynomials converge as k→∞ to the bifurcation measure, in the sense of DeMarco, of a certain family of dynamical systems on the Riemann sphere. This is ongoing work with Juan Rivera-Letelier (Rochester) Divendres 28 de setembre, 15h, Aula T2, FMI-UB Alberto F. Boix Ben-Gurion U. of the Negev Beer-Sheva, Israel Contact: szarzuela at ub.edu A Characteristic Free Approach to Finite Determinacy Finite determinacy for mappings has been classically thoroughly studied in numerous scenarios in the real and complex-analytic category and in the differentiable case. It means that the map-germ is determined, up to a given equivalence relation, by a finite part of its Taylor expansion. The equivalence relation is usually given by a group action and the first step is always to reduce the determinacy question to an “infinitesimal determinacy”, i.e. to the tangent spaces at the orbits of the group action. The goal of this talk is to formulate a universal approach to finite determinacy in arbitrary characteristic, not necessarily over a field, for a large class of group actions; along the way, we introduce the notion of “pairs of (weak) Lie type”, which are groups together with a substitute for the tangent space at the unit element, such that the group is locally approximated by its tangent space, in a precise sense. This construction may be regarded as a sort of replacement of the exponential/logarithmic maps and is of independent interest. In this generality we establish the “determinacy versus infinitesimal determinacy” criteria, a far reaching generalization of numerous classical and recent results, together with some new applications. The content of this talk is based on joint work with Gert–Martin Greuel (Universität Kaiserslautern, Germany) and Dmitry Kerner (Ben–Gurion University of the Negev, Israel) Divendres 5 d'octubre, 15h, Aula T2, FMI-UB Roberto Gualdi U. Bordeaux - UB - CRM Contact: sombra at ub.edu Height of cycles in toric varieties We present in this talk some relations between suitable heights of cycles in toric varieties and the combinatorics of the defining Laurent polynomials. To do this, we associate to any Laurent polynomial f with coefficients in an adelic field two families of concave functions on a certain real vector space: the upper functions and the Ronkin functions of f. For the choice of an adelic semipositive toric metrized divisor D, we give upper bounds for the D-height of a complete intersection in a toric variety in terms of the upper functions of the defining Laurent polynomials. In the one-codimensional case, we prove an exact formula relating the D-height of a hypersurface to the Ronkin function of the associated Laurent polynomial, generalizing the well-known equality for the canonical case. Our approach involves mixed integrals, Legendre-Fenchel duality and other notions from convex geometry. Divendres 19 d'octubre, 15h, Aula T2, FMI-UB Francisco Presas ICMAT, Madrid Contact: ignasi.mundet at ub.edu Homotopy type of the space of smooth embeddings of $$\Large{\mathbb{S}}^1$$ in $$\Large{\mathbb{R}}^4$$ via Engel geometry. We introduce the space of horizontal embeddings for the standard Engel distribution in the Euclidean 4-space. We prove that the space of smooth embeddings of the circle into R⁴ is simply connected (classical result), by checking that the space of horizontal embeddings has homotopy type very related to the space of smooth embeddings (they are related by an h-principle). We extend the method to sketch the computation of the $$\pi_2$$ of that space showing that is Z$$\oplus$$Z (more modern result). We finally comment on work in progress further generalizing the techniques by using Manifold calculus to try to compute the whole homotopy type of this space. This is joint work with E. Fernández and X. Martínez-Aguinaga. Divendres 26 d'octubre, 15h, Aula T2, FMI-UB Pedro González Pérez UCM, Madrid Contact: TBA Divendres 9 de novembre, 15h, Aula T2, FMI-UB Joana Cirici UB TBA Divendres 16 de novembre, 15h, Aula T2, FMI-UB Diletta Martinelli School of Mathematics Edinburgh, Escòcia (UK) Contact: marti.lahoz at ub.edu TBA Divendres 23 de novembre, 15h, Aula T2, FMI-UB Bernd Sturmfels Max Plank Institut Leipzig (Alemanya) Contact: cdandrea at ub.edu Moment Varieties of Polytopes The moments of the uniform distribution on a convex polytope are rational functions in its vertex coordinates. We study the projective varieties parametrized by these moments. This is work with Kathlen Kohn and Boris Shapiro. On our journey, we encounter Hankel determinantal ideals, splines, cumulants, multisymmetric functions, and invariants of nonreductive groups. While moment varieties are complicated, they offer many nice open problems. Article Dilluns 26 de novembre, 15h, aula T1, FMI-UB Vincenzo Antonelli Politecnico di Torino, Itàlia Contact: miro at ub.edu TBA Divendres 30 de novembre, 15h, Aula T2, FMI-UB Enrico Carlini Politecnico di Torino Itàlia Contact: alessandro.oneto at upc.edu TBA Divendres 30 de novembre, 16h, Aula T2, FMI-UB

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