Tools and computations
Conley-Zehnder indices in prequantization bundles (also known as Boothby-Wang bundles)
This pdf-file contains some details on how to compute the Conley-Zehnder/Maslov index of periodic Reeb orbits in a prequantization bundle.
We work out a simple relation between this index and the first Chern class of the symplectic manifold (the quotient by the circle action). This is often helpful in symplectic homology computations.
CZ_index_BW_bundle.pdf
Some explicit computations
This pdf-file contains some explicit computations of symplectic/contact homology of some well-known manifolds.
SHnames.pdf
Notes and slides
Talk/tutorial on TDA: mapper and persistent homology
Slides for two talks on TDA in Busan:
TDA_tutorial2019busan1.pdf
TDA_tutorial2019busan2.pdf
Lecture on singularity theory and exotic spheres
Notes for a lecture given at the 1st International Undergraduate Mathematics Summer School, Peking University 2018:
singularity.pdf
Talk on Sasakian geometry and symplectic topology
Notes for a talk given at the conference ``Differential Geometry, Geometric Analysis and PDEs'', Academica Sinica, Taipei 2018:
sasaki_einstein.pdf
Slides from a talk in Cologne (September 2014)
PDF-file from my talk in Cologne:
surface_cologne.pdf
Slides from a talk at the astronomy colloquium at SNU (May 2021)
PDF-file from my talk:
symplectic_celestial.pdf
Slides from a zoom talk given at Shanghai Jiao Tong University (March 2022)
PDF-file from my talk:
holo_convex2022_3.pdf