REMINDER - 3 ICTP Mathematics Seminar this week (Stasi room)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2018


1)TOMORROW - Tuesday 3 July, at 16.00 hrs.

David Beltran (Basque Center for Applied Mathematics)


Title: Regularity of spherical maximal functions



Abstract:
Fractional integrals and the classical fractional maximal function are 
smoothing operators, in the sense that they map Lebesgue spaces into 
first order Sobolev spaces. We show that this phenomenon continues to 
hold for the fractional spherical maximal function when the dimension of 
the ambient space is greater than or equal to 5. A key element in the 
proof is a local smoothing estimate for the wave equation.
This is joint work with Joao P. G. Ramos and Olli Saari.


***


2) Wednesday 4 July, at 16.00 hrs.


Edgard A. Pimentel  (PUC- Rio)


Title:
Geometric regularity for (nonlinear) PDEs


Abstract:
In this talk we examine the regularity theory of the solutions to a few 
examples of (nonlinear) PDEs. Arguing through a genuinely geometrical 
method, we produce regularity results in Sobolev and Hölder spaces, 
including some borderline cases. Our techniques relate a problem of 
interest to another one - for which a richer theory is available - by 
means of a geometric structure, e.g., a path. Ideally, information is 
transported along such a path, giving access to finer properties of the 
original equation. Our examples include elliptic and parabolic fully 
nonlinear problems, the Isaacs equation, degenerate examples and a 
double divergence model. We close the talk with a discussion on open 
problems and further directions of work.


***


3)Thursday 5 July, at 14:30 hrs.


Hammed Praise Adeyemo (University of Ibadan)


Title:
Geometric Computation of Betti numbers of Springer varieties



Abstract:
There are quite a number of subvarieties which can be defined to sit 
inside flag varieties. One of such is the family of Hessenberg 
varieties. In this talk, I will give combinatorial and geometric 
descriptions of the computation of the one of the class members of the 
family known as Springer varieties and discuss the current problem at hand.





VENUE for all seminars:  Stasi Seminar Room (ICTP Leonardo da Vinci 
Building, first floor)