Yiannis Loizides

**
**

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).
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 *, (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).
### 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