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Olivier Debarre, Sorbonne Université - Université de Paris
When can solutions of polynomial equations be algebraically parametrized?
http://www.mate.polimi.it/smf/index.php?settore=home&id_link...id_link=25
Monday, February 01 2021, at 10:30
https://polimi-it.zoom.us/j/83674264668 |
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Abstract
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The description of all the solutions of the equation $x^2+y^2=z^2$ in integral numbers (a.k.a. Pythagorean triples) is a very ancient problem: a Babylonian clay tablet from about 1800BC may contain some solutions, Pythagoras (about 500BC) seems to have known one infinite family of solutions, and so did Plato... This gives a first example of a rational variety: the rational points on the circle with equation $x^2+y^2=1$ can be algebraically parametrized by one rational parameter. More generally, one says that a variety, defined by a system of polynomial equations, is rational if its points (the solutions of the system) can be algebraically parametrized, in a one-to-one fashion, by independent parameters. I will begin with easy standard examples, then explain and apply some (not-so-recent) techniques that can be used to prove that some varieties (such as the set of rational solutions of the equation $x^3+y^3+z^3+t^3=1$) are not rational. |
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Sarah Zerbes, University College London
The mysteries of L-values
Tuesday, December 10 2019, at 14:00
Sala di Rappresentanza, Dipartimento di Matematica, Via C. Saldini 50 | |
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Piermarco Cannarsa, Università di Roma Tor Vergata
Propagation of singularities for solutions to Hamilton-Jacobi equations
Monday, December 02 2019, at 15:30
Sala Consiglio del 7 piano, Dipartimento di Matematica, Via Ponzio 31-33, Milano | |
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George Willis, University of Newcastle, Australia
Zero-dimensional symmetry, or locally profinite groups
Thursday, November 21 2019, at 16:00
Aula U5-3014 (Edificio 5, terzo piano) del Dipartimento di Matematica e Applicazioni dell'Università di Milano-Bicocca, in Via Cozzi 55 | |
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John Barrow, University of Cambridge
One Hunderd Years of Universes
Tuesday, October 29 2019, at 11:30
Palazzo di Brera, Via Brera 28, Milano, Sala Maria Teresa | |
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