Basic Notions Seminar

The current organizer of the seminar is Mikhail Shubin
 

Upcoming Talks:

• September 30, 2004
  Speaker:  Leonid Friedlander (University of Arizona)
  Title: The determinant
  Abstract: The determinant of an nxn 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.
   
• October 21, 2004
  Speaker:  Yuri Neretin (Institute of Theoretical and Experimental Physics, Moscow, Russia)
  Title: Haar measures
  Abstract: The Haar measure on a group is a measure which is invariant with respect to the group translations.
        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:
           -- "Chinese restaurant process", i.e. inverse (sic!) limit of symmetric groups S_n that was discovered in population genetics in 1970's;
           -- inverse limits of unitary groups.
   
• September 22, 2005
  Speaker: Ari Belenkiy (Bar-Ilan University, Israel)
  Title: History of One Defeat: Reform of the Julian Calendar as Envisioned by Isaac Newton
  Abstract: At the turn of the 18^th century, England was one of many Protestant countries that did not join the calendar reform promulgated by Pope Gregory in 1582. A group of unpublished manuscripts, known after the 1936 Sotheby's auction as Yahuda Ms 24, show that in February-April 1700 Newton developed a proposal for the reform of the Julian and Ecclesiastical calendars. His calendar, if implemented, would have become for England a viable alternative to the Gregorian. Despite having a different algorithm, its solar part agrees with the latter until 2400 AD and is more precise in the long run, within a period of 5,000 years. Its lunar (Ecclesiastical) algorithm is simpler than the Gregorian, but remained incomplete. We explain why blank spaces were left and why data were changed in several of the manuscripts; discuss the time frame and the order in which Newton wrote different drafts of Yahuda MS 24; analyze their relation with two manuscripts from the Cambridge collection and a reply to Leibniz' letter; and suggest a reason for Newton's delay and failure to press for the implementation of his calendar. Newton, as can be discerned from his analysis of Hipparchus of Rhodes's astronomical observations, can be credited, historically, with the first application of a technique known today as regression analysis and also with a remarkable guess about the ancient Greek observations of the equinoxes.

   

• December 1, 2005
  Speaker: Riccardo Pucella (Northeastern University)
  Title: Introduction to Kleene Algebras
  Abstract: Kleene algebras are algebraic structures that arise with surprising frequency in Computer Science---when studying formal languages, finite-state machines, shortest paths in graphs, computational geometry. A Kleene algebra is a set equipped with two binary operations +, . and a unary operation *, related by ring-like properties. In this talk, I describe the main examples of Kleene algebras from Computer Science, and highlight some of the algebraic richness of these structures.

 
• December 7, 2006
  Speaker: Pierre Schapira (Université Pierre et Marie Curie)
  Title: Sheaves and D-modules
  Abstract:Microlocal analysis, which emerged in the 70's, enhances our ability to localize different objects of analysis and geometry by moving the main arena of action from an underlying manifold to its cotangent bundle.
     I shall give an introduction to sheaf theory and D-modules theory from a microlocal point of view. In particular, I will explain the definition of the characteristic variety of a coherent D-module on a complex manifold, that of the micro-support of a sheaf on a real manifold and their relation. I will also briefly discuss the functorial properties of the characteristic variety and of the micro-support, and the link between constructible sheaves and holonomic D-modules.

Created: October 22, 2002. Last modified: December 7, 2006

Comments to: