Tianyu Yuan's homepage

Research

Preprints

  1. (with Yuan Gao and Weiwei Wu) Nearby Lagrangians in the cotangent bundle of the Klein bottle, arXiv preprint (2026).

  2. (with Yuan Gao) Log-concavity of flat arrangement polynomials, arXiv preprint (2026).

  3. (with Zhiyun Cheng and Yin Tian) A polynomial invariant of planar curves, arXiv preprint (2026).

  4. (with Yuan Gao) Trapezoidality of flat arrangement polynomials, arXiv preprint (2026).

  5. (with Ko Honda, Roman Krutowski and Yin Tian) Obstructions to smoothing orbicurves and orbifold Hecke algebras, arXiv preprint (2026)

  6. (with Ko Honda and Yin Tian) Higher-dimensional Heegaard Floer homology and spectral networks, arXiv preprint (2026).

  7. (with Yuan Gao, Eilon Reisin-Tzur and Yin Tian) Higher-dimensional Heegaard Floer homology and the polynomial representation of double affine Hecke algebras, arXiv preprint (2025).

  8. (with Ko Honda, Roman Krutowski and Yin Tian) Morse theory of loop spaces and Hecke algebras, arXiv preprint (2025).

  9. (with Roman Krutowski) Heegaard Floer Symplectic homology and Viterbo’s isomorphism theorem in the context of multiple particles, arXiv preprint (2023).

  10. Folded Morse flow trees, arXiv preprint (2023).

Publications

  1. A link invariant from higher-dimensional Heegaard Floer homology, J. Symplectic Geom. (2025)

  2. (with Yin Tian) An example of higher-dimensional Heegaard Floer homology, Algebr. Geom. Topol. (2025)

  3. (with Ko Honda and Yin Tian) Higher-dimensional Heegaard Floer homology and Hecke algebras, J. Eur. Math. Soc. (2024)

  4. T. Yuan and G. Tanaka, Robustness of coupled oscillator networks with heterogeneous natural frequencies, Chaos, 27, 123105 (2017)

  5. T. Yuan, K. Aihara, and G. Tanaka, Robustness and Fragility in Coupled Oscillator Networks under Targeted Attacks, Physical Review E, Vol.95, No.1, pp.012315-1-6 (2017)

  6. T. Yuan, K. Aihara, G. Tanaka, Theory for Dynamical Robustness of Complex Networks against Targeted Attacks, Proc. Int. Symp. Nonlinear Theory and Its Applications (NOLTA, Yugawara, Nov. 27-30, Oral, Nov. 30), pp. 602-605 (2016)