SEMINARI DI CALCOLO DELLE VARIAZIONI

When does optimal transport branch?

Relatore: 
Mircea Petrache

Abstract. Consider the problem of transporting some objects
between N distinct locations. Depending on how we package
together different objects and on how the transport cost (per
unit of distance traveled) depends on the package that we are
moving, we may cook up a minimum-cost transport strategy.
Is it always the best option to let our objects travel independently
of each other, or is it sometimes more cost-efficient to merge/split
packages along the way, following a branched, tree-like, global
network?

Data Seminario: 
Wednesday, June 20, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Pontificia Universidad Católica de Chile
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

The Kakeya needle problem for rectifiable sets

Relatore: 
Alan Chang

Abstract. We show that the classical results about rotating
a line segment in arbitrarily small area, and the existence
of a Besicovitch and a Nikodym set hold if we replace the
line segment by an arbitrary rectifiable set.
This is joint work with Marianna Csörnyei.

Data Seminario: 
Wednesday, June 20, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 19:00
Affiliazione: 
University of Chicago
Ora Inizio: 
Saturday, January 1, 0000 - 18:00

Generalized Sadowsky Theory For Ribbons From Three-Dimensional Nonlinear Elasticity

Relatore: 
Roberto Paroni

Abstract. In the 1930s Sadowsky derived an asymptotic theory for narrow ribbons. We here provide a rigorous derivation of the generalized Sadowsky theory starting from nonlinear three-dimensional elasticity by means of Γ-convergence. On a technical level, this involves capturing a contribution to the asymptotic energy functional generated by a nonlinear constraint which is satisfied only approximately. It also involves the construction of fine-scale ‘corrugations’ capable of reaching a bending energy regime that is strictly below that of the original Sadowsky functional.

Data Seminario: 
Wednesday, May 30, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 19:00
Affiliazione: 
Universita' di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 18:00

Properties of Convex sets in Wiener spaces

Relatore: 
Michele Miranda

Abstract. We show some recent results on convex sets in Wiener spaces. We characterize the essential and reduced boundary of open convex sets and investigate integration by parts formulae. Of particular interest is the investigation of trace theorems for functions of bouned variation on boundaries of subsets in Wiener spaces.

Data Seminario: 
Wednesday, May 30, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Ferrara
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

A nonlocal isoperimetric problem with dipolar repulsion

Abstract. 

We study a functional in which perimeter and regularized dipolar repulsion compete under a volume constraint.

In contrast to previously studied similar problems, the nonlocal term contributes to the perimeter term to leading order for small regularization parameters.

Data Seminario: 
Wednesday, June 6, 2018
Relatore: 
Simon Thilo
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

A new gluing phenomenon for metrics of prescribed Q-curvature in dimension 6

Relatore: 
Luca Martinazzi
Abstract. Contrary to the Yamabe case, metric of prescribed Q-curvature (which we will briefly discuss) in dimension 4 and higher, can blow-up both on isolated points and on higher dimensional submanifolds, as discovered by Adimurthi, F. Robert and M. Struwe. We will show, in a radially symmetric situation, that both kind of blow-up behaviour can happen at the same time. This is based on a joint work with A. Hyder.
Data Seminario: 
Wednesday, May 23, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
University of Basel
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Purely unrectifiable metric spaces and perturbations of Lipschitz functions

Relatore: 
David Bate
Abstract. We give characterisations of purely $n$-unrectifiable subsets $S$ of a complete metric space $X$ with finite Hausdorff $n$-measure by studying arbitrarily small perturbations of Lipschitz functions $f\colon X \to R^m$. In one such characterisation it is shown that, if $S$ has positive lower density almost everywhere, a typical $f$ (with respect to the supremum norm) has ${\mathcal H}^n(f(S))=0$. Conversely, if $E\subset X$ is $n$-rectifiable with ${\mathcal H}^n(E)>0$, a typical $f$ has ${\mathcal H}^n(f(E))>0$.
Data Seminario: 
Wednesday, May 16, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Helsinki
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Structured deformations of continua: theory and applications

Relatore: 
Marco Morandotti
Abstract. Structured deformations provide a multiscale geometry that captures the contributions at the microlevel of both smooth geometrical changes and disarrangements at submicroscopic levels. Due to this versatility, they turn out to be a powerful tool to describe the deformations of bodies in a variety of settings. In this seminar, I will present the basic theory of structured deformations, alongside with some applications.
Data Seminario: 
Wednesday, April 18, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
TUM Monaco
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Limiting behaviour of rescaled nonlocal perimeters and of their first variations.

Abstract. We introduce a class of integral functionals known as nonlocal perimeters, which can be thought as interactions between a set and its complement that are weighted by a positive kernel. In the first part of the talk, we summarise the main features of these functionals and then we study the asymptotic behaviour of the family associated with mass-preserving rescalings of a given kernel. Namely, we prove that when the scaling parameter approaches $0$, the rescaled non local perimeters $Gamma$-converge to De Giorgi's perimeter, up to a multiplicative
Data Seminario: 
Wednesday, March 28, 2018
Relatore: 
Valerio Pagliari
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Uniqueness of solutions to singular Liouville equations

Relatore: 
Aleks Jevnikar
Abstract. We deduce new uniqueness results for solutions to singular Liouville equations both on spheres and on bounded domains, as well as a new self-contained proof of previously known results. To this end, we derive a singular Sphere Covering Inequality based on the Alexandrov-Bol isoperimetric inequality and symmetric rearrangements. Joint project with D. Bartolucci, C. Gui and A. Moradifam.
Data Seminario: 
Wednesday, March 21, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

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