Sala Seminari (Dip. Matematica)

Liouville-type problems on compact surfaces: a variational approach

Abstract. A class of Liouville equations and systems on compact surfaces is considered: we focus on the Toda system which is motivated in mathematical physics by the study of models in non-abelian Chern-Simons theory and in geometry in the description of holomorphic curves. We discuss its variational aspects which yield existence results.
Data Seminario: 
Wednesday, October 25, 2017
Relatore: 
Aleks Jevnikar
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Backward error analysis for polynomial rootfinders

Relatore: 
Leonardo Robol

The most common methods to compute roots of polynomials is to rephrase the problem in linear algebra terms: one constructs a companion matrix (or pencil) that has the roots of the polynomial as eigenvalues.
However, even when the eigenvalue method used is backward stable, it's non-trivial to map the backward error back on the polynomial. This problem has been studied extensively in the past and it has been shown that relying on the QR method does not provide a normwise backward-stable rootfinder. For this reason, one needs to rely on QZ + appropriate scaling.

Data Seminario: 
Tuesday, October 17, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
ISTI--CNR Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Morfismo traccia e deformazioni di coppie (varieta', fascio coerente).

Tipo Seminario: 
Relatore: 
Marco Manetti

Dato un fascio coerente F su una varieta' liscia proiettiva X, viene determinata l'algebra di Lie differenziale graduata che controlla le deformazioni della coppia (X,F). Viene poi introdotto un morfismo di traccia tra opportuni fasci di operatori differenziali mediante il quale viene esteso un classico risultato di Artamkin sulle deformazioni di fasci.

Data Seminario: 
Wednesday, October 18, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
Universita' di Roma "La Sapienza"
Ora Inizio: 
Saturday, January 1, 0000 - 14:00

Equivariant hyperbolization and applications

Tipo Seminario: 
Relatore: 
Danny Ruberman

Given a closed 3-manifold Y with the action of a finite group G, we show how to find a closely related hyperbolic G-manifold Y’. The two manifolds are related by an invertible equivariant homology cobordism; a cobordism from Y to Y’ is invertible if there is a second cobordism from Y’ to Y such that the union of the two along Y’ is a product cobordism.  I will give a collection of applications in 3 and 4-dimensional topology. (Joint work with Dave Auckly, Hee Jung Kim, and Paul Melvin.)

Data Seminario: 
Thursday, November 23, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 17:00
Affiliazione: 
Brandeis University
Ora Inizio: 
Saturday, January 1, 0000 - 16:00

The compressible Euler equations: Riemann problems and non-uniqueness

Tipo Seminario: 
Relatore: 
Elisabetta Chiodaroli
Abstract. In this talk we discuss some applications of the method of convex integration to the compressible Euler system of gas dynamics in two space dimensions. This leads to the construction of infinitely many non-standard solutions even in the case of classical Riemann data. We also show some recent studies meant at visualizing numerically such non-standard solutions.
Data Seminario: 
Wednesday, October 11, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di isa
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Rohlin’s theorem and non-simply connected 4-manifolds

Tipo Seminario: 
Relatore: 
Danny Ruberman

Most applications of gauge theory in 4-dimensional topology are concerned with simply-connected manifolds with non-trivial second homology. I will discuss the opposite situation, first describing the classical Rohlin invariant for manifolds with first homology = Z and vanishing second homology. I will give an interpretation in terms of a Seiberg-Witten theory, with an unusual index-theoretic correction term. I will discuss recent work with Jianfeng Lin and Nikolai Saveliev giving a new formula for this invariant in terms of monopole homology.

Data Seminario: 
Thursday, October 5, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Brandeis University
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

A weak universality result for the parabolic Anderson model

Relatore: 
Nicolas Perkowski

Abstract: We consider a class of nonlinear population models on a two-dimensional lattice which are influenced by a small random potential, and we show that on large temporal and spatial scales the population density is well described by the continuous parabolic Anderson model, a linear but singular stochastic PDE. The proof is based on a discrete formulation of paracontrolled distributions on unbounded lattices which is of independent interest because it can be applied to prove the convergence of a wide range of lattice models. This is joint work with Jörg Martin.

Data Seminario: 
Tuesday, September 26, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 09:15
Affiliazione: 
Humboldt-Universität zu Berlin
Ora Inizio: 
Saturday, January 1, 0000 - 08:15

On corks with low shadow-complexity

Tipo Seminario: 
Relatore: 
Hironobu Naoe

A cork is a contractible Stein domain that gives arise to exotic pairs of 4-manifolds. The first example was found by Akbulut. It is known that any two exotic, simply-connected, closed 4-manifolds are related by a cork twist. We show that there are no corks having shadow-complexity zero. We also show that there are infinitely many corks having shadow-conplexity 1 and 2. 

Data Seminario: 
Thursday, October 12, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Tohoku University, Japan
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

Binomial edge ideals

Relatore: 
Dott.Francesco Strazzanti

ABSTRACT:

In the last decades the connections between commutative algebra and combinatorics have been extensively explored. It is interesting to study classes of ideals in a polynomial ring associating with them combinatorial objects, such as simplicial complexes, graphs, clutters or polytopes.

In this talk we are interested in the so-called binomial edge ideals, which are ideals generated by binomials corresponding to the edges of a finite simple graph G. They can be viewed as a generalization of the ideal of 2-minors of a generic matrix with two rows.

Data Seminario: 
Monday, September 11, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
University of Sevilla
Ora Inizio: 
Saturday, January 1, 0000 - 14:00

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