Poisson, Dirac, and deformation geometry
Poisson and Dirac structures, including deformations between additive and multiplicative Hamiltonian geometry and their behavior under reduction.
Research profile
Mohamed Moussadek Maiza
Doctoral Researcher in Mathematics
Université de Sherbrooke · Québec, Canada
I am a doctoral researcher in mathematics at the Université de Sherbrooke, supervised by Jean-Philippe Burelle and Maxence Mayrand.
My research lies at the intersection of Poisson, Dirac, symplectic, and hyperkähler geometry, deformation theory, and moduli spaces. I study how geometric structures defined by Lie-group-valued moment maps relate to their Lie-algebra-valued counterparts, and how the resulting spaces behave under reduction and gluing.
My work also develops Hamiltonian and quasi-Hamiltonian field theories from quiver moduli, and hyperkähler moduli spaces arising from Nahm--Kirchhoff equations.
Research directions
Geometry across structures and scales
Quiver moduli and field theories
Symplectic moduli spaces defined by Lax--Kirchhoff equations and their cutting, gluing, and two-dimensional TQFT structures.
Hyperkähler geometry and analysis
Nahm--Kirchhoff moduli spaces, hyperkähler quotients, and variational methods in gauge-theoretic moduli problems.
Selected work
Recent research
Nahm--Kirchhoff moduli spaces, hyperkähler quotient and 2D field theories
My recent work develops hyperkähler moduli spaces from Nahm--Kirchhoff equations on quivers and studies their field-theoretic structure. arXiv:2610.03384
My work in Poisson geometry is developed in From multiplicative to additive geometry: Deformation theory and 2D TQFT; my work on Dirac structures is developed in Dirac geometry, deformation theory and shifted symplectic geometry.
Get in touch
Contact
| mohamed.moussadek.maiza@usherbrooke.ca | |
| Address | Department of Mathematics, Université de Sherbrooke 2500 boul. de l'Université, Sherbrooke, QC J1K 2R1, Canada |