Sala Seminari (Dip. Matematica)

Lagrangian mean curvature flow of Whitney spheres

Relatore: 
Andreas Savas-Halilaj
Abstract. We investigate the evolution under the mean curvature flow of an equivariant Lagrangian sphere. It is shown that under a convexity assumption on the Ricci curvature, the flow develops a type-II singularity that rescales to the product of a grim reaper with a flat Lagrangian space. In particular this result applies to the Whitney sphere. This is joint work with K. Smoczyk.
Data Seminario: 
Wednesday, December 19, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
University of Ioannina
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

The Yamabe problem on stratified spaces

Relatore: 
Ilaria Mondello
Abstract. The Yamabe problem on compact smooth manifolds has been one of the starting point of geometric analysis. It consists in showing, with both geometric and analytic tools, that there always exists a Riemmanian metric with constant scalar curvature in the conformal class of a given metric (N. Trudinger, T. Aubin, R. Schoen). When considering a manifold with singularities, it is not always possible to find such a metric. In this talk, we will focus on manifolds with conical singularities, isolated or not, and we will underline the
Data Seminario: 
Wednesday, December 5, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
LAMA, Université de Paris-Est Créteil
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Why do we care about multicomplexes?

Relatore: 
Marco Moraschini

Abstract: Il volume simpliciale è un invariante omotopico per varietà compatte introdotto da Gromov nel 1982 nel suo articolo pionieristico "Volume and bounded cohomology". In parole povere, il volume simpliciale misura la complessità di una varietà in termini delle sue catene singolari reali. L'obiettivo di questo seminario è di descrivere l'idea originaria di Gromov su come affrontare lo studio di questo invariante, ossia attraverso la teoria dei multicomplessi (e la più nota coomologia limitata).

Data Seminario: 
Thursday, November 22, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Università di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 16:30

Alcune osservazioni sulla coomologia di DX e QX

Relatore: 
Lorenzo Guerra

Abstract: Lo spazio dei lacci di uno spazio topologico X dotato di un punto base x_0 è lo spazio ΩX delle mappe [0,1]→X il cui valore agli estremi è x_0. Uno spazio di lacci di ordine k è il risultato di k applicazioni consecutive del funtore Ω; uno di ordine infinito è uno spazio che, per ogni k, è omotopicamente equivalente a un certo Ω^kX. Questi oggetti si sono rivelati estremamente importanti negli sviluppi della matematica a partire circa dalla metà del secolo scorso.

Data Seminario: 
Thursday, November 29, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 17:30
Affiliazione: 
SNS Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 16:30

Perimeter with densities: an energy for epitaxial growth

Abstract. In this talk I will introduce a free energy, first studied by Ratz and Voigt, defined as the integration over the reduced boundary of a crystal E of a suitable psi(u(x)) where psi is a convex function and u denotes the adatom density (the density of atoms not attached to the crystal and free to move on the surface). This energy leads the surface diffusion evolution in absence of the elastic stress and for small adatom densities. We treat the variational point of view, by analyzing the semicontinuity issues and the relaxad functional.
Data Seminario: 
Wednesday, November 28, 2018
Relatore: 
Marco Caroccia
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

On the positive definite solution of the nonlinear matrix equation X^p=A+M^T(X#B)M

Relatore: 
Jie Meng

The nonlinear matrix equation X^p = A + M^T (X # B)M is considered, where p ≥ 1 is a positive integer, M is an n × n nonsingular matrix, A is a positive semidefinite matrix and B is a positive definite matrix. We call C # D the geometric mean of positive definite matrices C and D. 

Data Seminario: 
Thursday, November 22, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
Pusan National University
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Dirac-harmonic maps and "supersymmetric" nonlinear sigma models

Relatore: 
Ruijun Wu
Abstract. In these models we deal with coupled pairs consisting of a map between manifolds and a spinorial field along this map. Originated from supersymmetric sigma models and supermanifold theory, they are recently analysed using the tools in nonlinear analysis. The Euler-Lagrangian system contains both a second order(Laplacian type) and a first order (Dirac type) elliptic equations. Some basic properties will be given as well as some example of the Dirac-harmonic maps.
Data Seminario: 
Wednesday, November 21, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 17:00
Affiliazione: 
Scuola Normale Superiore di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 16:00

On the 1/H flow via p-Laplace approximation under Ricci lower bounds

Relatore: 
Luciano Mari
Abstract. In this talk, we consider the existence problem for weak solutions of the Inverse Mean Curvature Flow on a complete manifold with only a Ricci lower bound. Solutions either issue from a point or from the boundary of a relatively compact open set. To prove their existence in the sense of Huisken-Ilmanen, we follow the strategy pioneered by J. Moser that uses approximation by p-Laplacian kernels. In particular, we prove new and sharp gradient estimates for the kernel of the p-Laplacian on M via the study of the fake distance associated to it.
Data Seminario: 
Wednesday, November 21, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Scuola Normale Superiore di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

The amenability conjecture for Gromov-hyperbolic groups

Tipo Seminario: 
Relatore: 
Andrea Sambusetti

We will present a classical conjecture on amenability for groups related
to growth. The original result, which is due to Cohen and,
independently, Grigorchuk, dates back to the 80's: a group Q finitely
presented as F/N, where F is a free group, is amenable if and only if
the exponential growth rates  (or _entropies)_ \omega(N) and \omega(F)
of N and F coincide.

Data Seminario: 
Thursday, December 6, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 17:00
Affiliazione: 
Università di Roma
Ora Inizio: 
Saturday, January 1, 0000 - 16:00

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