BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news615@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190119T205152 DTSTART;TZID=Europe/Zurich:20131129T171500 SUMMARY:BZ Seminar in Analysis: Pekka Pankka (Jyväskylä) DESCRIPTION:One of the classical theorems in complex analysis is the Picard 's theorem stating that a non-constant entire holomorphic map from the c omplex plane to the Riemann sphere omits at most two points. In the late 1960's and early 1970's\, results of Reshetnyak and Martio-Rickman-Väis älä showed that mappings of bounded distortion\, also called as quasire gular mappings\, can be viewed as a counterpart for holomorphic mappings in quasiconformal geometry. One of the natural goals from the very beginn ing in this theory was obtain Picard-type results. In 1980\, Rickman show ed that a non-constant quasiregular mapping from the Euclidean n-space to the n-sphere omits only finitely many points\, where the number depends only on the dimension and distortion. The sharpness of Rickman's theorem was not as simple issue as in the classical Picard theorem. In 1984\, Ric kman showed by a surprising and elaborate construction that given any fin ite set in the 3-sphere there exists a quasiregular from the Euclidean 3- space into the 3-sphere omitting exactly that set. In this talk\, I will discuss joint work with David Drasin on the sharpness of Rickman's Picar d theorem in all dimensions. Especially\, I will discuss the role of bili pschitz geometry in the proof which leads to a stronger stament on the me tric properties of the map and is a crucial ingredient in dimensions n > 3. X-ALT-DESC: One of the classical theorems in complex analysis is the Picard 's theorem stating that a non-constant entire holomorphic map from the c omplex plane to the Riemann sphere omits at most two points.
In the late 1960's and early 1970's\, results of Reshetnyak and Martio-Rickman- Väisälä showed that mappings of bounded distortion\, also called as qu asiregular mappings\, can be viewed as a counterpart for holomorphic mapp ings in quasiconformal geometry. One of the natural goals from the very b eginning in this theory was obtain Picard-type results. In 1980\, Rickman showed that a non-constant quasiregular mapping from the Euclidean n-spa ce to the n-sphere omits only finitely many points\, where the number dep ends only on the dimension and distortion. The sharpness of Rickman's the orem was not as simple issue as in the classical Picard theorem. In 1984\ , Rickman showed by a surprising and elaborate construction that given an y finite set in the 3-sphere there exists a quasiregular from the Euclide an 3-space into the 3-sphere omitting exactly that set.
In this ta lk\, I will discuss joint work with David Drasin on the sharpness of Rick man's Picard theorem in all dimensions. Especially\, I will discuss the r ole of bilipschitz geometry in the proof which leads to a stronger stamen t on the metric properties of the map and is a crucial ingredient in dime nsions n >\; 3. DTEND;TZID=Europe/Zurich:20131129T181500 END:VEVENT END:VCALENDAR