9 citations · 30 across the 21 of their papers we have counts for
22 papers
Weightings and Lie groupoids
Yiannis Loizides
This note originated with a mini-course taught at KU Leuven by the author in June 2026. We review the definition of weightings (or quasi-homogeneous structures), the weighted norma…
Slices for reductive group actions in algebraic and holomorphic symplectic geometry
Peter Crooks, Rebecca Goldin, Yiannis Loizides
Symplectic slice theorems elucidate the local structure of symplectic manifolds carrying Hamiltonian actions of compact Lie groups. We generalize these theorems in two natural sett…
Integral Points and Volume of Integral-Integral Affine Manifolds
Oded Elisha, Yael Karshon, Yiannis Loizides
Using rational Ehrhart theory and Fourier analysis, we give an elementary proof that the volume of a closed manifold equipped with an integral-integral affine structure equals the…
A fixed-point formula for Dirac operators on Lie groupoids
Ahmad Reza Haj Saeedi Sadegh, Shiqi Liu, Yiannis Loizides +1
We study equivariant families of Dirac operators on the source fibers of a Lie groupoid with a closed space of units and equipped with an action of an auxiliary compact Lie group.…
Families of elliptic boundary problems and index theory of the Atiyah-Bott classes
Yiannis Loizides
We study a natural family of non-local elliptic boundary problems on a compact oriented surface parametrized by the moduli space of flat -connections with fr…
Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We extend the Marsden-Weinstein reduction theorem and the Darboux-Moser-Weinstein theorem to symplectic Lie algebroids. We also obtain a coisotropic embedding theorem for symplecti…
Riemannian foliations and geometric quantization
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-…
Singular Lie filtrations and weightings
Yiannis Loizides, Eckhard Meinrenken
We study weightings (a.k.a. quasi-homogeneous structures) arising from manifolds with singular Lie filtrations. This generalizes constructions of Choi-Ponge, Van Erp-Yuncken, and H…
Index formula for Hamiltonian loop group spaces
Yiannis Loizides
We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to…
Connes-Moscovici Residue Cocycle For Some Dirac-Type Operators
Ahmad Reza Haj Saeedi Sadegh, Yiannis Loizides, Jesus Sanchez
The residue cocycle associated to a suitable spectral triple is the key component of the Connes-Moscovici local index theorem in noncommutative geometry. We review the relationship…
Differential Geometry of Weightings
Yiannis Loizides, Eckhard Meinrenken
We describe the notion of a \emph{weighting} along a submanifold , and explore its differential-geometric implications. This includes a detailed discussion of weighted…
Log symplectic manifolds and
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We show, under an orientation hypothesis, that a log symplectic manifold with simple normal crossing singularities has a stable almost complex structure, and hence is Spin. In…
Geometric quantization of b-symplectic manifolds
Maxim Braverman, Yiannis Loizides, Yanli Song
We introduce a method of geometric quantization for compact -symplectic manifolds in terms of the index of an Atiyah-Patodi-Singer (APS) boundary value problem. We show further…
A KK-theoretic perspective on deformed Dirac operators
Yiannis Loizides, Rudy Rodsphon, Yanli Song
We study the index theory of a class of perturbed Dirac operators on non-compact manifolds of the form , where is a Clifford mul…
Quasi-polynomials and the singular theorem
Yiannis Loizides
In this short note we revisit the `shift-desingularization' version of the theorem for possibly singular symplectic quotients. We take as starting point an elegant proof…
Semi-classical analysis of piecewise quasi-polynomial functions and applications to geometric quantization
Yiannis Loizides, Paul-Emile Paradan, Michele Vergne
Motivated by applications to multiplicity formulas in index theory, we study a family of distributions associated to a piecewise quasi-polynomial function . The family…
Norm-square localization and the quantization of Hamiltonian loop group spaces
Yiannis Loizides, Yanli Song
In an earlier article we introduced a new definition for the `quantization' of a Hamiltonian loop group space , involving the equivariant -index of a Dirac-type o…
Geometric K-homology and the Freed-Hopkins-Teleman theorem
Yiannis Loizides
We describe a map from the equivariant twisted K-homology of a compact, connected, simply connected Lie group to the Verlinde ring. Our map is described at the level of `D-cycl…
Quantization of Hamiltonian loop group spaces
Yiannis Loizides, Yanli Song
We prove a Fredholm property for spin-c Dirac operators on non-compact manifolds satisfying a certain condition with respect to the action of a semi-direct product gro…
The decomposition formula for Verlinde Sums
Yiannis Loizides, Eckhard Meinrenken
We prove a decomposition formula for Verlinde sums (rational trigonometric sums), as a discrete counterpart to the Boysal-Vergne decomposition formula for Bernoulli series. Motivat…
Spinor modules for Hamiltonian loop group spaces
Yiannis Loizides, Eckhard Meinrenken, Yanli Song
Let be the loop group of a compact, connected Lie group . We show that the tangent bundle of any proper Hamiltonian -space has a natural completion $\over…
Norm-square localization for Hamiltonian -spaces
Yiannis Loizides
We prove a formula for twisted Duistermaat-Heckman distributions associated to a Hamiltonian -space. The terms of the formula are localized at the critical points of the norm-s…