


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, FMIUB

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 RiveraLetelier (Rochester)

Divendres 28 de setembre, 15h, Aula T2, FMIUB

Alberto F. Boix
BenGurion U. of the Negev
BeerSheva, 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 complexanalytic category and in the differentiable
case. It means that the mapgerm 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, FMIUB

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 Dheight of a complete intersection in a toric variety
in terms of the upper functions of the defining Laurent polynomials.
In the onecodimensional case, we prove an exact formula relating the Dheight of a hypersurface to the Ronkin function of the associated Laurent
polynomial, generalizing the wellknown equality for the canonical case.
Our approach involves mixed integrals, LegendreFenchel duality and other
notions from convex geometry.

Divendres 19 d'octubre, 15h, Aula T2, FMIUB

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 4space. 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 hprinciple). 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. MartínezAguinaga.

Divendres 26 d'octubre, 15h, Aula T2, FMIUB

Pedro González Pérez
UCM, Madrid
Contact:

TBA

Divendres 9 de novembre, 15h, Aula T2, FMIUB

Joana Cirici
UB

TBA

Divendres 16 de novembre, 15h, Aula T2, FMIUB

Diletta Martinelli
School of Mathematics
Edinburgh, Escòcia (UK)
Contact:
marti.lahoz at ub.edu

TBA

Divendres 23 de novembre, 15h, Aula T2, FMIUB

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, FMIUB

Vincenzo Antonelli
Politecnico di Torino, Itàlia
Contact:
miro at ub.edu

TBA

Divendres 30 de novembre, 15h, Aula T2, FMIUB

Enrico Carlini
Politecnico di Torino
Itàlia
Contact:
alessandro.oneto at upc.edu

TBA

Divendres 30 de novembre, 16h, Aula T2, FMIUB



