Dear Colleagues and Students,<\/p>\n
You are cordially invited to the ODTU-Bilkent Algebraic Geometry Seminar:<\/p>\n
Speaker: Muhammed Uluda\u011f (Galatasaray)<\/p>\n
\u201cJimm, a fundamental involution\u201d<\/p>\n
Abstract: Dyer\u2019s outer automorphism of PGL(2,Z) induces an involution of the real line, which behaves very much like a kind of modular function. It has some striking properties: it preserves the set of quadratic irrationals sending them to each other in a non-trivial way and commutes with the Galois action on this set. It restricts to an highly non-trivial involution of the set unit of norm +1 of quadratic number fields. It conjugates the Gauss continued fraction map to the so-called Fibonacci map. It preserves harmonic pairs of numbers inducing a duality of Beatty partitions of N. It induces a subtle symmetry of Lebesgue\u2019s measure on the unit interval.<\/p>\n
On the other hand, it has jump discontinuities at rationals though its derivative exists almost everywhere and vanishes almost everywhere. In the talks, I plan to show how this involution arises from a special automorphism of the infinite trivalent tree and how it relates to the Minkowski question mark function.<\/p>\n
Date: 8 November 2019, Friday
\nTime: 15:40
\nPlace: Mathematics Seminar Room, SA \u2013 141<\/p>\n","protected":false},"excerpt":{"rendered":"
Dear Colleagues and Students, You are cordially invited to the ODTU-Bilkent Algebraic Geometry Seminar: Speaker: Muhammed Uluda\u011f (Galatasaray) \u201cJimm, a fundamental involution\u201d Abstract: Dyer\u2019s outer automorphism of PGL(2,Z) induces an involution of the real line, which behaves very much like a kind of modular function. It has some striking properties: [\u2026] <\/p>\n