Kaiying's Website

Mathematics

• Large Rank Simple Bundles of All Homological Dimensions
  Currently under review for Proceedings of the AMS.
• BGG Correspondence and the Construction of Vector Bundles on Projective Spaces
  My senior thesis supervised by Professor Mihnea Popa.
• p-Anisotropy on the Moment Curve for Homology Manifolds and Cycles
  Research supervised by Professor Karim Adiprasito during the Einstein Institute REU in the Hebrew University of Jerusalem.

Physics

• Two-Loop Beta Function for Bosonic Sigma Model in Ricci-Flat Target Space
  Expository write-up for Physics 253b.
• Learning quantum symmetries with interactive quantum-classical variational algorithms
  Research supervised by Professor Susanne F. Yelin.

CS

• Universal Length Generalization with Turing Programs
  Developed an innovative CoT technique that emulates Turing machines, marking the first instance in literature to achieve significant length generalization for multiplication.
• The Computational Complexity of Finding Hamiltonian Cycles in Grid Graphs of Semiregular Tessellations
  Research with Dr. Jayson Lynch, published in Proceedings of the 30th Canadian Conference on Computational Geometry.

Fun

• Transformer to generate metal guitar tracks with conherent riffs.
  
• Deep Q-learning for the Multiplayer Snake Game.