Yiannis Loizides

**
**

I am an assistant professor in the Mathematics Department 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). 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.

GMU students interested in hearing more about possible research topics should 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

## 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 Appl. Math. Quart. *, to appear.
Differential geometry of weightings, with E. Meinrenken,
* Advances in Math.* **424**, (2023).
Singular Lie filtrations and weightings, with E. Meinrenken,
*Pure Appl. Math. Quart. *, 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).
Riemannian foliations and geometric quantization, with Y. Lin, R. Sjamaar and Y. Song, preprint (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

## 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