Barry Simon, California Institute of Technology
SPECTRAL THEORY, SUM RULES AND LARGE DEVIATIONS
Lunedì 28 Maggio 2018, ore 16:30
Aula Chisini, Diparimento di Matematica, Via C. Saldini 50 | |
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Grigory Mikhalkin, Université de Genève
Maximally writhed real algebraic knots and links
Giovedì 17 Maggio 2018, ore 17:00 precise
Sala di Rappresentanza, Università di Milano, Via C. Saldini 50, Milano |
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Abstract
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The Alexander-Briggs tabulation of knots in R^3 (started almost
a century ago, and considered as one of the most traditional ones
in classical Knot Theory) is based on the minimal number of crossings
for a knot diagram. From the point of view of Real Algebraic Geometry
it is more natural to consider knots in RP^3 rather than R^3, and use
a different number also serving as a measure of complexity of a knot:
the minimal degree of a real algebraic curve representing this knot.
As it was noticed by Oleg Viro about 20 years ago, the writhe of a knot
diagram becomes an invariant of a knot in the real algebraic set-up,
and corresponds to a Vassiliev invariant of degree 1. In the talk we’ll
survey these notions, and consider the knots with the maximal possible
writhe for its degree. Surprisingly, it turns out that there is a unique
maximally writhed knot in RP^3 for every degree d. Furthermore, this
real algebraic knot type has a number of characteristic properties, from
the minimal number of diagram crossing points (equal to d(d-3)/2) to
the minimal number of transverse intersections with a plane (equal to
d-2). Based on a series of joint works with Stepan Orevkov.
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Arnaud Beauville, Université de Nice
Recent progress on rationality problems
Lunedì 14 Maggio 2018, ore 15:30
Sala di Rappresentanza, Università di Milano, Via C. Saldini 50, Milano | |
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Gilles Carron, Laboratoire de Mathématiques Jean Leray (UMR 6629), Université de Nantes, CNRS
The constant scalar curvature equation in some singular spaces
Mercoledì 14 Marzo 2018, ore 16:30
Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9 | |
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Alessandra Lunardi, Università di Parma
Sobolev and BV functions in infinite dimension
Venerdì 23 Febbraio 2018, ore 10:30 precise
Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9 | |
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