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