Research Interests
Currently I am interested in various aspects of the structure of yang mills moduli spaces and the structure of singularities of Yang-Mills fields. I am also studying various aspects of the interaction of geometry and topology and the spectrum of the Laplace beltrami operator on forms. This includes spectral estimates motivated by questions in number theory and betti number estimates motivated by questions in geometric topology.
Selected Grants
The Geometry and Analysis of Yang-Mills Instantons.
Institutional SupportPrincipal Investigator · Awarded by Simons Foundation · 2023 - 2028Instanton Decay and Nonlinear Harmonic Forms
ResearchPrincipal Investigator · Awarded by Simons Foundation · 2015 - 2022Chern-Simons Invariance Instantons and Mass
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2010 - 2014Positive Mass, Singularities, and Supersymmetry
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2005 - 2010Bound States, Singularities, and Supersymmetry
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2002 - 2006Non-Fredholm Index Theory, Matrix, Models, and Hodge Theory
ResearchPrincipal Investigator · Awarded by National Science Foundation · 1998 - 2003Hodge Structures and L2 Cohomology
ResearchPrincipal Investigator · Awarded by National Science Foundation · 1995 - 1999Hodge Structures and L2 Cohomology
ResearchPrincipal Investigator · Awarded by National Science Foundation · 1995 - 1999Presidential Young Investigator Award: Mathematical Sciences
ResearchPrincipal Investigator · Awarded by National Science Foundation · 1989 - 1994Some New Spectral Invariants and Their Relationship to Automorphic Forms and Geodesics
ResearchPrincipal Investigator · Awarded by National Science Foundation · 1986 - 1988External Relationships
- Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA)
This faculty member (or a member of their immediate family) has reported outside activities with the companies, institutions, or organizations listed above. This information is available to institutional leadership and, when appropriate, management plans are in place to address potential conflicts of interest.