SeminarTitle[20040930]= "Basic Notions";
Location[20040930]= "509LA";
Title[20040930]= "The determinant";
Abstract[20040930]= "The determinant of an <i>n</i>x<i>n</i> matrix was introduced by Leibniz as a tool that allows one to determine whether a system of linear equations is uniquely solvable. I will review different definitions and applications of the determinant. My main goal is to discuss how the notion of the determinant can be extended to operators in infinite dimensional spaces. Some generalizations (Fredholm determinants) were made in the first part of the 20th century. In 1974, Ray and Singer introduced the determinant of an elliptic differential operator. I will discuss properties of these determinants and their applications.";
Speaker[20040930]= "Leonid Friedlander";
SpeakerLink[20040930]= "http://math.arizona.edu/people/profile.php?n=friedlan";
PictureLink[20040930]= "http://math.arizona.edu/~people_photos/friedlan_color_150x210.jpg";
University[20040930]= "University of Arizona";
UniversityLink[20040930]= " http://math.arizona.edu/";
SecondUniversity[20040930]= " ";
SecondUniversityLink[20040930]= " ";
DateOfTalk[20040930]= "September 30, 2004";
DayOfWeek[20040930]= "Thursday";
TimeOfTalk[20040930]= "1:15";
IsTimeDefault[20040930]= "1";
IsDateDefault[20040930]= "1";
Entry[20040930]= "1";
Comments[20040930]= " ";

SeminarTitle[20040930]= "Basic Notions";
Location[20040930]= "509LA";
Title[20040930]= "The determinant";
Abstract[20040930]= "The determinant of an <i>n</i><font size=\"2\">x</font><i>n</i> matrix was introduced by Leibniz as a tool that allows one to determine whether a system of linear equations is uniquely solvable. I will review different definitions and applications of the determinant. My main goal is to discuss how the notion of the determinant can be extended to operators in infinite dimensional spaces. Some generalizations (Fredholm determinants) were made in the first part of the 20th century. In 1974, Ray and Singer introduced the determinant of an elliptic differential operator. I will discuss properties of these determinants and their applications.";
Speaker[20040930]= "Leonid Friedlander";
SpeakerLink[20040930]= "http://math.arizona.edu/people/profile.php?n=friedlan";
PictureLink[20040930]= "http://math.arizona.edu/~people_photos/friedlan_color_150x210.jpg";
University[20040930]= "University of Arizona";
UniversityLink[20040930]= " http://math.arizona.edu/";
SecondUniversity[20040930]= " ";
SecondUniversityLink[20040930]= " ";
DateOfTalk[20040930]= "September 30, 2004";
DayOfWeek[20040930]= "Thursday";
TimeOfTalk[20040930]= "1:15";
IsTimeDefault[20040930]= "1";
IsDateDefault[20040930]= "1";
Entry[20040930]= "1";
Comments[20040930]= " ";

SeminarTitle[20041021]= "Basic Notions";
Location[20041021]= "509LA";
Title[20041021]= "Haar measures";
Abstract[20041021]= "The Haar measure on a group is a measure which is invariant with respect to the group translations.<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; I will explain  Hermann Weyl\'s (1930\'s) and Hua Loo Keng\'s (1950\'s) ways of constructive work with the Haar measure and describe its relatively recent infinite-dimensional analogs:<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -- &quot;Chinese restaurant process&quot;, i.e. inverse  (sic!) limit of symmetric groups S<sub>n</sub> that was discovered in population genetics in 1970\'s;<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; -- inverse limits of unitary groups.";
Speaker[20041021]= "Yuri Neretin";
SpeakerLink[20041021]= " ";
PictureLink[20041021]= " ";
University[20041021]= "Institute of Theoretical and Experimental Physics, Moscow, Russia";
UniversityLink[20041021]= " http://heron.itep.ru/";
SecondUniversity[20041021]= " ";
SecondUniversityLink[20041021]= " ";
DateOfTalk[20041021]= "October 21, 2004";
DayOfWeek[20041021]= "Thursday";
TimeOfTalk[20041021]= "1:15";
IsTimeDefault[20041021]= "1";
IsDateDefault[20041021]= "1";
Entry[20041021]= "1";
Comments[20041021]= "  ";