Department of Mathematics
Northeastern University
Basic Notions Seminar
Meets Thursdays 1:15-2:45 pm in 511 Lake
Hall
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 Sn 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 18th 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 A group of unpublished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: