Trustees of Indiana University
Grant: $124,929 - National Science Foundation - Aug. 12, 2009
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Award Description: The PI will use techniques from algebraic geometry, noncommutative algebra, and cat- egory theory to approach concrete algebraic and geometric questions as well as problems in mathematical physics. Proposed new activities. Three problems will be studied. The first problem suggests a general approach to prove uniqueness of an enhancement for a given triangulated category. The second problem introduces the notion of a categorical resolution of singularities and compares it with the traditional resolution of singularities in the geometric case. The third problem suggests the study of the moduli stack of point objects in a triangulated category. Intellectual merit of the proposed activities. The suggested problems constitute an essential step in our understanding of modern commutative and noncommutative geometry. They suggest to apply abstract methods to concrete problems in algebra and geometry. The problems will also shed light on the important homological mirror symmetry conjecture which remains to a large extent a mathematical mystery discovered by physicists. Broader impacts. The PI will continue mentoring graduate students and collaborating with postdocs, especially with regard to the research in this proposal. The PI works in the area of mathematics which is new, rapidly developing with an enormous range of applications in many areas of mathematics and physics. This makes it easy for young mathematicians to find a suitable problem and to establish themselves as researchers. The proposed work will be disseminated through talks at research seminars, international conferences and publications in major scientific journals.
Project Description: The PI will use techniques from algebraic geometry, noncommutative algebra, and category theory to approach concrete algebraic and geometric questions as well as problems in mathematical physics. Three problems will be studied. The first problem suggests a general approach to prove uniqueness of an enhancement for a given triangulated category. The second problem introduces the notion of a categorical resolution of singularities and compares it with the traditional resolution of singularities in the geometric case. The third problem suggests the study of the moduli stack of point objects in a triangulated category. The suggested problems constitute an essential step in our understanding of modern commutative and noncommutative geometry. They suggest to apply abstract methods to concrete problems in algebra and geometry. The problems will also shed light on the important homological mirror symmetry conjecture which remains to a large extent a mathematical mystery discovered by physicists. The PI will continue mentoring graduate students and collaborating with postdocs, especially with regard to the research in this proposal. The PI works in the area of mathematics which is new, rapidly developing with an enormous range of applications in many areas of mathematics and physics. This makes it easy for young mathematicians to find a suitable problem and to establish themselves as researchers. The proposed work will be disseminated through talks at research seminars, international conferences and publications in major scientific journals.
Jobs Summary: Additional Pay: Acad Services (Total jobs reported: 0)
Project Status: Less Than 50% Completed
This award's data was last updated on Aug. 12, 2009. Help expand these official descriptions using the wiki below.
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