BEGIN:VCALENDAR VERSION:2.0 METHOD:PUBLISH PRODID:-//Missouri State University/Calendar of Events//EN CALSCALE:GREGORIAN X-WR-TIMEZONE:America/Chicago BEGIN:VTIMEZONE TZID:America/Chicago BEGIN:DAYLIGHT TZOFFSETFROM:-0600 TZOFFSETTO:-0500 DTSTART:20070311T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU TZNAME:CDT END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0500 TZOFFSETTO:-0600 DTSTART:20071104T020000 RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU TZNAME:CST END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:dc1a60ce-116b-4d4a-b9ac-b973c33962c5.179792@calendar.missouristate.edu CREATED:20170329T172340Z LAST-MODIFIED:20170329T172340Z LOCATION:Cheek Hall 175 SUMMARY:Mathematics Lecture Series: Radon Transforms for a Pair of Grassma nnians DESCRIPTION:Abstract. The term Radon transform is commonly used for an int egral operator that assigns to a function on a set X a collection of inte grals of that function over certain subsets of X. For example\, one can i ntegrate a function on the plane over straight lines in that plane\, or a function on the 2-sphere over great circles in that sphere. One of the b asic problems is to reconstruct a function from such integrals.In his 191 1 thesis\, Paul Funk\, who studied the case of great circles on the spher e\, suggested a remarkable method that reduces the reconstruction problem to solution of a simple Abel integral equation connecting the correspond ing mean values. This method was later employed by Radon for lines on the plane and extended by Helgason to arbitrary constant curvature spaces.Dr . Rubin is planning to explain Funk’s approach in the n-dimensional setti ng and show its generalizationto the higher-rank case\, when the source s pace is the real Grassmann manifold of k-dimensional linear subspaces of Rn and the target space is a similar manifold of higher dimension. It tur ns out that Funk’s ideas extend nicely to this more general situation if theone-dimensional Abel integrals are replaced by the corresponding G°ard ing-Gindikin integrals over the cone of positive definite matrices.The ta lk is accessible to the audience with standard prerequisites in analysis and linear algebra. It is a joint work with Eric Grinberg. X-ALT-DESC;FMTTYPE=text/html:<html><head><title></title></head><body><p>Ab stract. The term Radon transform is commonly used for an integral operato r that assigns to a function on a set X a collection of integrals of that function over certain subsets of X. For example\, one can integrate a fu nction on the plane over straight lines in that plane\, or a function on the 2-sphere over great circles in that sphere. One of the basic problems is to reconstruct a function from such integrals.<br />In his 1911 thesi s\, Paul Funk\, who studied the case of great circles on the sphere\, sug gested a remarkable method that reduces the reconstruction problem to sol ution of a simple Abel integral equation connecting the corresponding mea n values. This method was later employed by Radon for lines on the plane and extended by Helgason to arbitrary constant curvature spaces.<br />Dr. Rubin is planning to explain Funk&rsquo\;s approach in the n-dimensional setting and show its generalization<br />to the higher-rank case\, when the source space is the real Grassmann manifold of k-dimensional linear s ubspaces of Rn and the target space is a similar manifold of higher dimen sion. It turns out that Funk&rsquo\;s ideas extend nicely to this more ge neral situation if the<br />one-dimensional Abel integrals are replaced b y the corresponding G&deg\;arding-Gindikin integrals over the cone of pos itive definite matrices.<br />The talk is accessible to the audience with standard prerequisites in analysis and linear algebra. It is a joint wor k with Eric Grinberg.</p></body></html> DTSTART;TZID=America/Chicago:20170411T150000 DTEND;TZID=America/Chicago:20170411T155000 SEQUENCE:0 URL:http://math.missouristate.edu/ CATEGORIES:Alumni,Current Students,Faculty,Future Students,Staff END:VEVENT END:VCALENDAR