Yiannis Loizides

I am an assistant professor in the Department of Mathematical Sciences at George Mason University. My research interests are symplectic/Poisson geometry, moduli spaces, loop groups, index theory and noncommutative geometry (in the sense of Alain Connes).

GMU students interested in hearing more about possible research topics are welcome to reach out. The broad subject areas involved are: differential geometry, functional analysis, Lie theory. Some of what I work on is inspired by physics (although background in physics is not necessary).

E-mail: yloizide `at' gmu `dot' edu

Before coming to Mason, I was a postdoc at Cornell (mentored by Reyer Sjamaar) and at Penn State (mentored by Nigel Higson), and a PhD student in Toronto under the supervision of Eckhard Meinrenken. Before that I spent a year in Cambridge for Part III (focus: theoretical physics), and studied mathematics and physics as an undergrad at Waterloo.

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. 18(3), (2020), 889--937.
  • 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, with Y. Song. J. Functional Analysis 278(9), (2020).
  • Semi-classical analysis of piecewise quasi-polynomial functions and applications to geometric quantization, with P-E. Paradan and M. Vergne, Indag. Math. 32(1), (2021), 151--192.
  • Geometric quantization of b-symplectic manifolds, with M. Braverman and Y. Song, J. Sympl. Geom. 19(1), (2021), 1--36.
  • Geometric K-homology and the Freed-Hopkins-Teleman theorem, J. Noncommutative Geometry 16(1), (2022), 77--118.
  • The decomposition formula for Verlinde sums, with E. Meinrenken, Ann. l'Inst. Fourier 72(3), (2022), 1207--1248.
  • A KK-theoretic perspective on deformed Dirac operators, with R. Rodsphon and Y. Song, Advances in Math. 380, (2021).
  • Log symplectic manifolds and [Q,R]=0, with Y. Lin, R. Sjamaar, and Y. Song, Int. Math. Res. Not. 2022(18), (2022), 14034--14066.
  • Connes-Moscovici residue cocycle for some Dirac-type operators, with A.R.H.S. Sadegh and J. Sanchez, Muenster J. Math. 23, (2023), 25--50.
  • Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids, with Y. Lin, R. Sjamaar and Y. Song, Pure and Appl. Math. Quart., 19(4), (2023), 2067--2131.
  • Differential geometry of weightings, with E. Meinrenken, Advances in Math. 424, (2023).
  • Singular Lie filtrations and weightings, with E. Meinrenken, Pure and Appl. Math. Quart., 19(4), (2023), 2133--2168.
  • Riemannian foliations and geometric quantization, with Y. Lin, R. Sjamaar and Y. Song, J. Geom. and Phys., to appear.
  • Index formula for Hamiltonian loop group spaces, preprint (2021).
  • Families of elliptic boundary problems and index theory of the Atiyah-Bott classes, preprint (2023).
  • Verlinde sums and [Q,R]=0, with E. Meinrenken, (2022).
  • A fixed-point formula for Dirac operators on Lie groupoids, with A.R.H.S. Sadegh, S. Liu, and J. Sanchez, preprint (2023).
  • Thesis pdf


    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