Grant: Discovery Grants Program - Individual
University of Western Ontario
$9,000.00
Global motivic integration and the cohomology of moduli spaces
FY 2006-07
Summary
Algebraic geometry, at the crudest level, is the study of the geometry of solutions of polynomial equations in many variables. In order to proceed one must enlarge the collection of solution spaces to a larger collection consisting of spaces that are algebraic gluings of such spaces. We will refer to such spaces as varieties. In the 1950's the Grothendieck school taught us that it is also important to remember the defining equations. The geometry of such solution spaces is usually studied by associating to the space an algebraic invariant. In 1995, inspired by ideas from calculus and number theory, M. Kontsevich proved some conjectures pertaining to some invariants associated to a special class of varieities. The theory of motivic integration was born. The theory has been developed over the last ten years most notably by J. Denef and F. Loeser. The aim of this research is to further extend this theory. The second part of this proposal aims to study some invariants of the a special variety, the so called moduli space of semistable vector bundles over an algebraic curve.
Program
Discovery Grants Program - Individual
Recipient
Location
Ontario, Canada
Recipient Type
Academia
Type
Grant
Source
NSERC's Awards Data
As published
Application id
327639-2006
Name nom
Dhillon, Ajneet
Department département
Mathematics
Organization id
36
Institution établissement
University of Western Ontario
Province en
Ontario
Province fr
Ontario
Country en
CANADA
Country fr
CANADA
Fiscal year exercice financier
2006
Competition year année de concours
2006
Award amount
9000
Program id
RGPIN
Program name en
Discovery Grants Program - Individual
Program name fr
Programme de subventions à la découverte - individuelles
Group en
Discovery grants programs
Group fr
Programmes de subventions à la découverte
Committee code
336
Committee name en
Pure & Applied Maths - A
Committee name fr
Maths pures et appliquées - A
Area of application code
1205
Area of application group en
Advancement of knowledge
Area of application group fr
Avancement des connaissances
Area of application en
Mathematical sciences
Area of application fr
Sciences mathématiques
Research subject code
2909
Research subject group en
Pure mathematics
Research subject group fr
Mathématiques pures
Research subject en
Algebraic geometry
Research subject fr
Géométrie algébrique
Partie
1
Nb partie
5
Application title
Global motivic integration and the cohomology of moduli spaces
Keyword
NA
Application summary
Algebraic geometry, at the crudest level, is the study of the geometry of solutions of polynomial equations in many variables. In order to proceed one must enlarge the collection of solution spaces to a larger collection consisting of spaces that are algebraic gluings of such spaces. We will refer to such spaces as varieties. In the 1950's the Grothendieck school taught us that it is also important to remember the defining equations. The geometry of such solution spaces is usually studied by associating to the space an algebraic invariant. In 1995, inspired by ideas from calculus and number theory, M. Kontsevich proved some conjectures pertaining to some invariants associated to a special class of varieities. The theory of motivic integration was born. The theory has been developed over the last ten years most notably by J. Denef and F. Loeser. The aim of this research is to further extend this theory. The second part of this proposal aims to study some invariants of the a special variety, the so called moduli space of semistable vector bundles over an algebraic curve.
