Yanli Song

Research

I am interested in equivariant index theory for manifolds with various group actions, and interactions with non-commutative geometry, symplectic geometry and representation theory.

Projects

BC4lean: Baum–Connes Conjecture

An ongoing open-source project to formalize the coefficient-free, reduced Baum–Connes conjecture for countable discrete groups in Lean. The project includes a mathematical blueprint, dependency graphs, and machine-checked proofs of supporting results.

Project website

Preprints

4

  1. Lefschetz formula for locally symmetric spaces

    arXiv

  2. Heat kernel, large-time behavior, and representation theory

    with S. Shen and X. Tang

    arXiv

  3. Higher Lefschetz formulas on Γ-proper manifolds

    with P. Piazza, H. Posthuma, and X. Tang

    arXiv

  4. Well-tempered symmetric spaces

    with A. Afgoustidis, P. Hochs, and S. Nishikawa

    arXiv

Publications

26

  1. K-theory and the quantization commutes with reduction problem

    with N. Higson

    Chin. Ann. Math. Ser. B 35 (2015), pp. 703-732.

  2. Dirac operators on quasi-Hamiltonian G-spaces

    J. Geom. Phys 106 (2016), pp. 70-86.

    arXiv

  3. An equivariant index for proper actions III: the invariant and discrete series indices

    with P. Hochs

    Differential Geom. Appl 49 (2016), pp. 1-22.

    arXiv

  4. An equivariant index for proper actions I

    with P. Hochs

    J. Funct. Anal 272 (2017), no.2, pp. 661-704.

    arXiv

  5. A K-homological approach to the quantization commutes with reduction problem

    J. Geom. Phys 112 (2017), pp. 29-44.

    arXiv

  6. On the Vergne conjecture

    with P. Hochs

    Archiv der Mathematik 108 (2017), no. 1, 99-112.

    arXiv

  7. An equivariant index for proper actions II: properties and applications

    with P. Hochs

    J. Noncommut. Geom. 108 (2017), no. 1, 99-112.

    arXiv

  8. Equivariant indices of Spin^c-Dirac operators for proper moment maps

    with P. Hochs

    Duke Math. J. 166 (2017), no. 6, 1125-1178.

    arXiv

  9. Quantization of Hamiltonian loop group spaces

    with Y. Loizides

    Math. Ann 374 (2019), no. 1-2, 681-722

    arXiv

  10. A geometric formula for multiplicities of K-types of tempered representations

    with P. Hochs and S. Yu

    Trans. Amer. Math. Soc. 372 (2019), no. 12, 8553-8586

    arXiv

  11. Spinor modules for Hamiltonian loop group spaces

    with Y. Loizides and E. Meinrenken

    J. Symplectic Geom. 18 (2020), no. 3, 889-937

    arXiv

  12. Witten deformation for Hamiltonian loop group spaces

    with Y. Loizides

    J. Funct. Anal. 278 (2020), no. 9

    arXiv

  13. A geometric realisation of tempered representations restricted to maximal compact subgroups

    with P. Hochs and S. Yu

    Math. Ann. 378 (2020), no. 1-2, 97-152

    arXiv

  14. Spinc-Dirac operators and geometric quantization of b-symplectic manifolds

    with M. Braverman and Y. Loizides

    J. Symplectic Geom. 19 (2021), no. 1, 1–36

    arXiv

  15. A KK-theoretic perspective on deformed Dirac operators

    with Y. Loizides and R. Rodsphon

    Adv. Math. 380 (2021)

    arXiv

  16. Log symplectic manifolds and [Q,R]=0

    with Y. Loizides, Y. Lin, and R. Sjamaar

    Int. Math. Res. Not. 2022, no. 18, 14034–14066

    arXiv

  17. An index theorem for higher orbital integrals

    with P. Hochs and X. Tang

    Math. Ann. 382 (2022), no. 1-2, 169–202

    arXiv

  18. Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids

    with Y. Loizides, Y. Lin, and R. Sjamaar

    Pure Appl. Math. Q. 19 (2023), no. 4, 2067–2131

  19. Riemannian foliations and geometric quantization

    with Y. Loizides, Y. Lin, and R. Sjamaar

    J. Geom. Phys. 198 (2024), Paper No. 105133.

    arXiv

  20. Cartan Motion Group and Orbital Integrals

    with X. Tang

    AMS Proceedings Symp. Pure Math. 105

  21. On the Connes-Kasparov Isomorphism, I. The Reduced C*-algebra of a Real Reductive Group and the K-theory of the Tempered Dual

    with P. Clare, N. Higson, and X. Tang

    Japanese Journal of Mathematics. 19 (2024), no. 1, 67–109.

    arXiv

  22. On the Connes-Kasparov Isomorphism, II. The Vogan Classification of Essential Components in the Tempered Dual

    with P. Clare and N. Higson

    Japanese Journal of Mathematics. 19 (2024), no. 1, 111–141.

    arXiv

  23. Higher orbital integrals, rho numbers and index theory

    with P. Piazza, H. Posthuma, and X. Tang

    Math. Ann. 391 (2025), no. 3, 3687–3763.

    arXiv

  24. Higher Orbital Integrals, Cyclic Cocycles and Noncommutative Geometry

    with X. Tang

    Forum of Math, Sigma. 13 (2025), Paper No. e37

    arXiv

  25. Higher orbital integrals on motion groups and Mackey deformation

    with A. Roman and X. Tang

    Journal of Geometry and Physics 228 (2026), Article 105909.

    arXiv

  26. Delocalized eta invariants of the signature operator on G-proper manifolds

    with P. Piazza, H. Posthuma, and X. Tang

    Journal of Functional Analysis (2026), Article 111671.

    arXiv