Colloquia Mathematica: Limiting cases

Martedì 21 Gennaio 2014, ore 16:00 - Aula 1A150 - C. Ciliberto



Martedì 21 Gennaio 2014 alle ore 16:00 in aula 1A150 della Torre Archimede, Ciro Ciliberto ( terrà una conferenza della serie Colloquia Mathematica dal titolo "Limiting cases".

A classical tool, used by the algebraic geometers of the so-called ''Italian school'' (in particular by Guido Castelnuovo and Federigo Enriques) was the study of the so-called ''limiting cases''. The idea is to consider geometric objects varying in a family and ''degenerating'', in the limit, to very particular configurations. These can be on one side very complicated, on the other may be simpler than the objects one started with. The point is to deduce properties of the general object of the family from those, hopefuly simpler, of the ''limit''. This technique, classically proved to be very fruitful, but was also very much criticized from the viewpoint of mathematical rigour. However in recent times it was revived and put on a firm basis, and it is today an essential tool for the resolution of difficult problems. In this talk I intend to start from very simple and concrete examples, at the level of secondary school, and, as such, already considered by Emma Castelnuovo (who inherited them from her father and uncle). These examples will illustrate the usefulness of these methods, but also the conceptual difficulties which they present. I will then try to illustrate some open research problems which can be attacked with these techniques and the interesting results which is possible to prove using them.

La Commissione Colloquia
F. Ancona, C. Bonotto, M. Conti, F. Marcuzzi

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