BASIC NOTIONS SEMINAR at ICTP - Wednesday, 22 May, at 14:30 (Stefano LUZZATTO)

[ICTP Math Section]

BASIC  NOTIONS  SEMINAR SERIES   2019


Wednesday 22 May, at 14.30 hrs.


Stefano Luzzatto (ICTP)


Title: Fractal Dimensions in Nature and Mathematics


Abstract: The notion of a one-dimensional, a two-dimensional, or a 
three-dimensional geometric object is fairly intuitive. A natural way to 
think of dimensions makes it relatively easy to define, though not 
necessarily easy to visualise, geometric objects also in four or five 
dimensions or indeed in n dimension for any positive integer n. It is 
however much harder to make sense of the notion of a geometric object 
with a non-integer (fractal) dimension, such as 1.5 for example, and to 
imagine what such an object might look like.

In this introductory talk I will give an elementary alternative 
definition of the dimension of a geometric object and show how this 
definition extends easily to fractal dimensions. I will also give some 
simple examples of geometric objects with fractal dimensions. I will 
discuss the way in which the geometry of many (in fact, most) objects in 
nature can arguably be modelled by geometric shapes with fractal 
dimension rather than the regular shapes familiar in classical Euclidean 
geometry. Finally, I will describe how objects with fractal dimensions 
occur naturally in certain areas of mathematics such as Dynamical Systems.


VENUE: Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, 1st floor)

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Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

For to be free is not merely to cast off one's chains, but to live in a way
that respects and enhances the freedom of others. Nelson Mandela