ICTP Mathematics Seminar (in two parts) - Thursday 13 July 2017 at 14:30

[Math Section]

M A T H E M A T I C S   S E M I N A R S   2017


Thursday 13 July, at 14.30 hrs.


Part 1
Time: 14:30 – 15:10

Speaker: Ana Cristina Moreira de Freitas  (Universidade do Porto)

Title: Introduction to extreme value theory for dynamical systems

Abstract: In this talk, we start by presenting some notions of extreme 
value theory, namely the notions of extreme value laws and extremal 
index, which is a parameter that quantifies the intensity of clustering 
of exceedances. Then, we consider discrete time dynamical systems and 
stochastic processes arising by evaluating an observable function along 
the orbits of such systems. We show the connection between extreme value 
laws and hitting time statistics and exploit it both in the absence and 
presence of clustering. We associate the occurrence of periodic 
phenomena to the existence of an extremal index less than 1.




Part 2
Time: 15:15 – 15:55

Speaker: Jorge Milhazes Freitas (Universidade do Porto)

Title:Rare events point processes and periodicity

Abstract: We consider time series corresponding to the evaluation of 
given potential along the orbits of systems with `nice' first return 
induced maps. Nice, here, means good memory loss properties. We are 
particularly interested in events corresponding to exceedances of high 
thresholds, i.e. instants at which the potential reaches abnormally high 
values, and, more specifically, when these exceedances have a tendency 
to appear in clusters. We will see the consequences of clustering in the 
convergence of conveniently normalised point processes that count the 
number of exceedances in a certain time frame.





VENUE:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)