Aula Magna (Dip. Matematica)

COLLOQUIUM di DIPARTIMENTO - Ergodic Ramsey Theory: the Meeting point of Dynamics and Combinatorics

Relatore: 
Vitaly Bergelson

Abstract:
The goal of this talk is to demonstrate the dynamical underpinning of some old and new results in combinatorics and number theory. 

The results to be discussed include Schur's theorem on Fermat equation over finite fields, theorems of van der Waerden and Szemeredi on arithmetic progressions and some of modern developments involving multiple recurrence along polynomials
and applications to the patterns in primes.

Data Seminario: 
Thursday, June 9, 2016
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:30
Affiliazione: 
Ohio State University
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

A brief introduction to rough paths theory - II

Relatore: 
Giovanni Zanco

We will introduce basic concepts and tools from rough paths theory, motivated by the need to establish a solution theory for differential equations driven by irregular signals. In particular we will discuss controlled rough paths, integration against rough paths, we will compare it to stochastic integration theories and show how classical results can be extended to the rough paths framework.

Data Seminario: 
Thursday, April 21, 2016
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 12:00
Affiliazione: 
IST Austria
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Flux-tube patterns in the Ginzburg-Landau model of type-I superconductors

Tipo Seminario: 
Relatore: 
Sergio Conti
We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields. We determine the optimal scaling law of the minimal energy in terms of the parameters of the problem, when the applied magnetic field is sufficiently small and the sample sufficiently thick. We show that, in an appropriate asymptotic regime, flux patterns may be described by a simplified branched transportation functional. We derive the simplified functional from the full Ginzburg-Landau model rigorously via Gamma-convergence.
Data Seminario: 
Thursday, February 11, 2016
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:00
Affiliazione: 
Bonn Universitat
Ora Inizio: 
Saturday, January 1, 0000 - 14:00

Mechanics of biological and bio-inspired locomotion: some case studies

Tipo Seminario: 
Relatore: 
Antonio De Simone
We will report on some recent case studies on biological and bio-inspired locomotion.
Starting from the observation of a motile organism (unicellular swimmers, earthworms, snakes), we model them as deformable rods and surfaces interacting with either the surrounding fluid or with the solid surface on which they rest.
Our  aim is to distill some of the key mechanisms at work in the biological templates in order to reproduce them in artificial bio-inspired prototypes based on the use of active materials.

References
Data Seminario: 
Friday, February 12, 2016
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:30
Affiliazione: 
SISSA
Ora Inizio: 
Saturday, January 1, 0000 - 10:30

Optimal distribution of oppositely charged phases: Screening, charge neutrality and regularity

Tipo Seminario: 
Relatore: 
Hans Knupfer
We study the minimum energy configuration of a uniform distribution of negative charge subject to Coulomb repulsive self-interaction and attractive interaction with a fixed positively charged domain.
After having established existence and uniqueness of a minimizing configuration, we prove charge neutrality and the complete screening of the Coulomb potential exerted by the positive charge, and we discuss the regularity properties of the solution.
Data Seminario: 
Friday, February 12, 2016
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 10:00
Affiliazione: 
Heidelberg Universitat
Ora Inizio: 
Saturday, January 1, 0000 - 09:00

Periodic striped ground states in Ising models with competing interactions

Tipo Seminario: 
Relatore: 
Alessandro Giuliani

We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa.

Data Seminario: 
Thursday, February 11, 2016
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:30
Affiliazione: 
Universita' di Roma Tre
Ora Inizio: 
Saturday, January 1, 0000 - 10:30

Carbon geometries as minimizers

Tipo Seminario: 
Relatore: 
Ulisse Stefanelli

Carbon nanostructures are identified with configurations of atoms interacting via empirical potentials.
The specific geometry of covalent bonding in carbon is phenomenologically described by the combination of an attractive-repulsive two-body interaction and a three-body bond-orientation part.
We investigate the strict local and global minimality of specific carbon configurations under general assumptions on the interaction potentials. In particular, we discuss the stability of carbyne, graphene, some fullerenes, and diamond.

Data Seminario: 
Thursday, February 11, 2016
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 10:00
Affiliazione: 
Wien Universitat
Ora Inizio: 
Saturday, January 1, 0000 - 09:00

Crystallization Results for Optimal Location Problems

Tipo Seminario: 
Relatore: 
David Bourne

While it is believed that many particle systems have periodic ground states, there are few rigorous crystallization results in two and more dimensions.
In this talk I will show how results by the Hungarian geometer László Fejes Tóth can be used to prove that an idealised block copolymer energy is minimised by the triangular lattice. I will also discuss a numerical method for a broader class of optimal location problems and some conjectures about minimisers in three dimensions.
This is joint work with Mark Peletier, Steven Roper and Florian Theil. 

Data Seminario: 
Wednesday, February 10, 2016
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 17:00
Affiliazione: 
Durham University
Ora Inizio: 
Saturday, January 1, 0000 - 16:00

Variational analysis of material defects and crystal plasticity

Tipo Seminario: 
Relatore: 
Adriana Garroni
Dislocations are line defects in the crystalline structure of metals. They are considered the main mechanism for plastic deformation and their interaction at the microscopic scale are relevant to understand complex phenomena as yielding and hardening.
Data Seminario: 
Wednesday, February 10, 2016
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:30
Affiliazione: 
Universita' di Roma La Sapienza
Ora Inizio: 
Saturday, January 1, 0000 - 14:30

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