I am an assistant professor in the Mathematics Department at George Mason University.
My research interests are symplectic/Poisson geometry, moduli spaces, index theory and noncommutative geometry.
Before coming to Mason, I was a postdoc at Cornell
(mentored by Reyer Sjamaar) and at
Penn State (mentored by Nigel Higson).
Before that I was a PhD student in Toronto under the supervision
of Eckhard Meinrenken.
E-mail: yloizide `at' gmu `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. 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).
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 , (2022).
The decomposition formula for Verlinde sums, with
E. Meinrenken, Ann. l'Inst. Fourier , to appear.
A KK-theoretic perspective on deformed Dirac operators,
with R. Rodsphon and Y. Song, Advances in Math. , to appear.
Log symplectic manifolds and [Q,R]=0,
with Y. Lin, R. Sjamaar, and Y. Song, Int. Math. Res. Not. , to appear.
Connes-Moscovici residue cocycle for some Dirac-type operators, with A.R.H.S. Sadegh and J. Sanchez,
Muenster J. Math , to appear.
Differential geometry of weightings, with E. Meinrenken, preprint (2020).
Hamiltonian loop group spaces and a theorem of Teleman and Woodward, preprint (2021).
Singular Lie filtrations and weightings, with E. Meinrenken, preprint (2022).
Verlinde sums and [Q,R]=0, with E. Meinrenken, (2022).
Riemannian foliations and geometric quantization, with Y. Lin, R. Sjamaar and Y. Song, preprint (2022).
Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids, with Y. Lin, R. Sjamaar and Y. Song, preprint (2022).
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
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