
Peter Kronheimer
· William Caspar Graustein Professor of MathematicsHarvard University · Mathematics
Active 1981–2022
Research topics
- Mathematical physics
- Genetics
- Mathematics
- Combinatorics
- Philosophy
- Bioinformatics
- Pure mathematics
- Biology
- Epistemology
Selected publications
Instantons and some concordance invariants of knots
Journal of the London Mathematical Society · 2021 · 8 citations
1st authorCorresponding- Mathematics
- Pure mathematics
- Combinatorics
Concordance invariants of knots are derived from the instanton homology groups with local coefficients, as introduced in earlier work of the authors. These concordance invariants include a 1-parameter family of homomorphisms (Formula presented.), from the knot concordance group to (Formula presented.). Prima facie, these concordance invariants have the potential to provide independent bounds on the genus and number of double points for immersed surfaces with boundary a given knot.
Recent grants
Gauge Theory and Spatial Graphs
NSF · $267k · 2017–2021
Gauge Theory and Geometry in Dimensions Three and Four
NSF · $550k · 2004–2010
Gauge theory and spatial graphs
NSF · $391k · 2014–2018
Gauge Theory and Geometry in Dimensions Three and Four
NSF · $804k · 2009–2015
Frequent coauthors
- 72 shared
Tomasz Mrowka
- 15 shared
Simon Donaldson
- 5 shared
E. H. Kronheimer
Birkbeck, University of London
- 2 shared
Michael T. Anderson
Stony Brook University
- 2 shared
Ciprian Manolescu
Stanford University
- 2 shared
Peter Ozsváth
Princeton University
- 2 shared
Claude LeBrun
Stony Brook University
- 2 shared
Zoltán Szabó
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