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

## 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