Welcome to my website!
I am a postdoc at UT Austin.
You can find my CV here.
I like thinking about holomorpic curves. For most of my PhD I've thought about the foundational aspects of this area. Now I'm trying to learn more about the geometric applications.
Pre-preprints:
An invitation to obstruction bundle gluing through Morse trajectories (with Ipsita Datta), in preparation.
Preprints:
Anchored symplectic embeddings (Joint with Michael Hutchings, Agniva Roy and Morgan Weiler). https://arxiv.org/abs/2407.08512
Fixed-point Floer cohomology and closed string mirror symmetry for nodal curves (Joint with Maxim Jeffs, Ziwen Zhao), https://arxiv.org/abs/2307.08180
Embedded contact homology for Legendrians (with Julian Chaidez, Oliver Edtmair, Luya Wang, Ziwen Zhao) https://arxiv.org/abs/2302.07259
Morse-Bott Embedded contact homology
From cascades to J-holomorphic curves and back. https://arxiv.org/abs/2206.04334
Computing Embedded Contact Homology in Morse-Bott Settings https://arxiv.org/abs/2211.13876
Prints:
On symplectic packings in higher dimensions (Joint with Kyler Siegel). https://arxiv.org/abs/2312.13224 To appear in Mathematische Annalen.
Product and co-product of Fixed Point Floer homology of Dehn twists (with Ziwen Zhao) -https://arxiv.org/abs/2205.14516 To appear in Algebraic and Geometric Topology.
Jointly with Vincent Colin, Paolo Ghiggini and Ko Honda, the Appendix of "ECH and Open Book decompositions" https://arxiv.org/abs/1008.2734. To appear in Geometry and Topology.
Phase spaces that cannot be cloned in classical mechanics. https://arxiv.org/abs/2303.00255 J. Math. Phys. 64, 102901 (2023)
Tilings Defined by Root Systems of Kac-Moody Algebras
C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (3) 2017, pp. 103-115
If you have any questions about my work, papers, or would like to collaborate, or just chat about math, please contact me at the following email address: yuan.yao.yy.1995@gmail.com. For teaching related inquiries please send it to: yuan.yao@austin.utexas.edu.
If you wish to talk to me in person, here is a forecast of my future locations (usually more reliable than the average weather forecast).