Shigefumi Mori, Kyoto University Institute of Advanced Study
BIRATIONAL EQUIVALENCE OF ALGEBRAIC VARIETIES
Monday, November 26 2018, at 16:30
Aula Chisini, Diparimento di Matematica, Via C. Saldini 50 | |
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Terence Tao, University of California, Los Angeles
VAPORIZING AND FREEZING THE RIEMANN ZETA FUNCTION
Friday, June 22 2018, at 14:30
Edificio U4, P.zza della Scienza, 4, Aula Luisella Sironi | |
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Zeljko Cuckovic, University of Toledo
The essential norm estimates of Hankel and the $\overline\partial$-Neumann operators
Friday, June 01 2018, at 11:00
Sala di Rappresentanza, Università di Milano, Via C. Saldini 50, Milano | |
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Barry Simon, California Institute of Technology
Tales of Our Forefathers
Tuesday, May 29 2018, at 11:00
Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9 | |
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Barry Simon, California Institute of Technology
SPECTRAL THEORY, SUM RULES AND LARGE DEVIATIONS
Monday, May 28 2018, at 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
Thursday, May 17 2018, at 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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