Sala Seminari (Dip. Matematica)

Dal locale al globale

Relatore: 
Andrea Marino

Spesso in matematica capita che alcuni oggetti siano costruiti incollando un modello locale più semplice; ad esempio, le varietà lisce sono localmente R^n, e gli schemi sono localmente spettri di un anello. 

Nella prima parte descriveremo il processo che porta dal modello locale all'oggetto globale per una categoria qualsiasi, in modo preciso. Mostreremo che ogni funtore (co)continuo si estende in maniera unica agli oggetti incollati. Questo ci permetterà di dimostrare dei teoremi non banali sulla rappresentabilita' di certi funtori.

Data Seminario: 
Wednesday, July 4, 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

Oper con monodromia banale e con due punti singolari

Relatore: 
Andrea Maffei

Nel seminario verranno introdotte alcune congetture e risultati di Frenkel e Gaitsgory sul legame che esiste tra alcune classi di equazioni differenziali sul disco, eventualmente con una singolarita' nell'origine e le rappresentazioni del gruppo di lacci di SL(2). Verranno inoltre esposti alcuni risultati ottenuti insieme a Giorgia Fortuna nel quale vengono introdotti Oper con due punti singolari e studiamo cosa succede quando i due punti collidono.

Data Seminario: 
Tuesday, July 17, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 12:30
Affiliazione: 
Universita' di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 10:30

The AJ conjecture for SU(2) and SL(2,C)

Tipo Seminario: 
Relatore: 
Alessandro Malusà

Given a knot K in S^3, one can consider as invariants the A-polynomial and the coloured Jones polynomial. After illustrating the original AJ conjecture, as formulated by Garoufalidis, I will specify its motivation from quantum SU(2)-Chern-Simons theory, and attempt to make sense of the statement that the two invariants mentioned above are classical and quantum in nature, respectively. This opens the question as of whether one can formulate an analogous conjecture for different Lie groups.

Data Seminario: 
Thursday, June 21, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
Aarhus University
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

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

Legendrian cobordisms

Relatore: 
Maylis Limouzineau

Abstract: Our framework here is low dimensional topology, and the main protagonists are Legendrian submanifolds, i.e. those which remains obediently tangent to the contact hyperplane distribution. We will see the subtleties brought by Legendrian knots in comparison with classical smooth knots, and understand the natural cobordism notion coming out, initiated by Arnol'd in the early 80's:

"What is a Legendrian surface between two Legendrian knots?"

There will be infinitely many trivial knots, some bow ties, one swallow tail... and a lot of drawings.

Data Seminario: 
Friday, May 25, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Università di Colonia
Ora Inizio: 
Saturday, January 1, 0000 - 16:30

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

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