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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