

201718/
Seminari A.A. 20172018 

I Seminari si svolgono il martedì alle 14:30 nell'aula 311
del Dipartimento di Matematica
(salvo diversa indicazione)



Relatore 
Titolo 
Data 



Michele Correggi
Università Sapienza 

22 Maggio 2018 



Serena Cenatiempo
GSSI L'Aquila 

15 Maggio 2018 



Margherita Disertori
University of Bonn 

8 Maggio 2018 



Vieri Mastropietro
Università di Milano 

17 Aprile 2018 



Alfonso Sorrentino
Università Tor Vergata 

12 Aprile 2018 (giovedì) 



Martin Tassy
University of California 

06 Febbraio 2018 



Monia Capanna
Università dell'Aquila 

31 Gennaio 2018 (mercoledì ore 11:30 Aula 211) 



In [1], the author introduces a reactiondiffusion system to model the
pattern formation phenomenon present in morphogenesis. Under the
assumption that the reaction part of the system is stable around an
equilibrium point, he finds condiditions over the diffusion
coefficients under which the hole system is unstable due to the
amplification of nonzero Fourier modes. This phenomenon is known as
Turing instability.
In this talk, we introduce an interacting particle system at which
the latter phenomenon is present. The system is a continuoustime
Markov process that has two coupled discrete toruses with Ising spins
as statespace. The evolution in each torus responds to macroscopic
ferromagnetic Kac's potentials, while the spins in different toruses
interact in a local attractiverepulsive way. About this model, we
prove hydrodynamic limit, and find conditions that guarantee the
occurence of Turing instability.
In the Turing instability regime, we analyze the fluctuations of the
density fields around the equilibrium point (0,0) by studying the
limiting behaviour of the discrete Fourier modes of the system. More
precisely, we prove that, at a time at which the process is
infinitesimal, and under the proper spatial scaling, the unstable
Fourier modes converge to a normal distribution while the rest of the
modes vanish. We finally give a result about pattern formation at a
time that converges to the critical one at which the process starts to
be finite.
[1] A. M. Turing, The chemical basis of morphogenesis.




Alexandre Efremov
École Polytechnique Palaiseau 

30 Gennaio 2018 



Yinon Spinka
Tel Aviv University 

26 Gennaio 2018 (venerdì) 



Eric Ossami Endo
Universidade de Sao Paulo 

23 Gennaio 2018 



N.J.B. Aza
Universidade de Sao Paulo 

22 Gennaio 2018 (lunedì ore 11:30) 



Clément Erignoux
IMPA 

9 Gennaio 2018 



Domenico Monaco
Università Roma Tre 

21 Novembre 2017 



Eris Runa
Max Planck Institut 

14 Novembre 2017 



Hugo DuminilCopin
IHES 

7 Novembre 2017 



Fabio Toninelli
Université Lyon 1 

17 Ottobre 2017 



Suren Pogosian
Armenian Academy of Sciences 

04 Ottobre 2017 (mercoledì aula 211) 




