Yiannis Loizides


I am a Postdoc in mathematics at Pennsylvania State University. My mentor is Nigel Higson. Previously I was a PhD student in Toronto under the supervision of Eckhard Meinrenken. My research interests are in symplectic geometry and index theory.

E-mail: yxl649 `at' psu `dot' edu

Papers and preprints

  • Norm-square localization for Hamiltonian LG-spaces. J. Geom. and Phys. 114 (2017), 420--449.
  • Quantization of Hamiltonian loop group spaces, with Y. Song. Mathematische Annalen 374(1) (2019), 681--722.
  • Spinor modules for Hamiltonian loop group spaces, with E. Meinrenken and Y. Song. J. Sympl. Geom., to appear.
  • Quasi-polynomials and the singular [Q,R]=0 theorem. SIGMA, 15 (2019), 090, 15 pages.
  • Norm-square localization and the quantization of Hamiltonian loop group spaces (title changed), with Y. Song. J. Functional Analysis. , to appear.
  • The decomposition formula for Verlinde sums, with E. Meinrenken, preprint (2018).
  • Geometric K-homology and the Freed-Hopkins-Teleman theorem, preprint (2018).
  • Semi-classical analysis of piecewise quasi-polynomial functions, with P-E. Paradan and M. Vergne, preprint (2019).
  • A KK-theoretic perspective on deformed Dirac operators, with R. Rodsphon and Y. Song, preprint (2019).
  • Geometric quantization of b-symplectic manifolds, with M. Braverman and Y. Song, preprint (2019).
  • Thesis pdf

    Slides

    CMS summer meeting, June 2019, Quasi-polynomials, asymptotics and [Q,R]=0

    Banff workshop on geometric quantization, April 2018, Geometric K-homology and the Freed-Hopkins-Teleman theorem

    CMS winter meeting, Dec 2016, [Q,R]=0 and Verlinde series

    Penn State, Nov 2016, Quantization of Hamiltonian LG-spaces

    Workshop on Geometric Quantization, July 2015, Norm-square localization for Hamiltonian LG-spaces

    Expository notes

    Introductory notes on the Atiyah-Hirzebruch spectral sequence pdf

    Subelliptic estimates and hypoelliptic Laplacian for T*S^1 pdf

    Introduction to gerbes (2015) pdf

    Transversally elliptic operators (2013) pdf

    Moduli spaces of flat connections with boundary conditions (2012) pdf

    Fock-Rosly Poisson structure (2013) pdf

    Singularity theorems in GR (2009) pdf