Homepage of Hessel Posthuma

Address

Research interests

• Symplectic and Poisson Geometry, in connection with quantization and noncommutative geometry.
• Mathematical approaches to Quantum Field Theory, such as Conformal Field Theory and Topological Quantum Field Theory.
• Frobenius manifolds and integrable systems

Publications and preprints

• Higher genera for proper actions of Lie groups (joint with P. Piazza)  
• Resolutions of proper Riemannian Lie groupoids (joint with K. Wang and X. Tang)  
• The Grauert-Grothendieck complex on differentiable spaces and a sheaf complex of Brylinski (joint with M. Pflaum and X. Tang) To appear in Methods and Applications of Analysis.  
• An index theorem for Lie algebroids (joint with A. Blom)  
• The bi-Hamiltonian cohomology of a scalar Poisson pencil (joint with G. Carlet and S. Shadrin) Bull. London Math. Soc. 48 (2016) pp. 617-627  
• Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed. (joint with G. Carlet and S. Shadrin) To appear in J. Diff. Geom.  
• Bihamiltonian cohomology of KdV brackets. (joint with G. Carlet and S. Shadrin) Comm. Math. Phys. 341 (2016) pp. 805-819.  
• Quantization and reduction of Whitney functions. (joint with M. Pflaum and X. Tang) J. of Sing. 13 (2015) pp. 217-228.  
• The index of geometric operators on Lie groupoids. (joint with M. Pflaum and X. Tang) Indag. Math. 25 (2014) pp. 1135-1153.  
• The transverse index theorem for proper cocompact actions of Lie groupoids. (joint with M. Pflaum and X. Tang) J. Diff. Geom. 99 (2015) pp. 443-472.  
• Quantization of Whitney functions. (joint with M. Pflaum and X. Tang) Trav. Math. 20 (2012) pp. 153-165.  
• Towards Lax formulation of integrable hierarchies of topological type. (joint with G. Carlet, J. van de Leur and S. Shadrin) Comm. Math. Phys. 326 Issue 3, pp 815-849 (2014) 
• The localized longitudinal index theorem for Lie groupoids and the van Est map (joint with M. Pflaum and X. Tang) Adv. Math. 270 (2015) pp. 223-262.  
• On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracket. (joint with A. Buryak and S. Shadrin) J. Geom. Phys. 62 (2012) pp. 1639-1651.  
• Geometry of orbit spaces of proper Lie groupoids. (joint with M. Pflaum and X. Tang) J. Reine u. Angew. Math. 694 (2014) pp. 49-84.  
• A Polynomial bracket for the Dubrovin--Zhang hierarchies. (joint with A. Buryak and S. Shadrin)   J. Diff. Geom. 92 (2012) pp. 153-185.  
• Frobenius manifolds, projective special geometry and Hitchin systems. (joint with L. Hoevenaars and C. Hertling) J. Reine u. Angew. Math. 649 (2010) pp. 117-165.  
• The cyclic theory of Hopf algebroids (joint with N. Kowalzig) J. Noncomm. Geom. 5 (2011) pp. 423-476  
• Dirac induction for loop groups Lett. Math. phys.   95 (2011) p. 89-107.
• On the algebraic index for riemannian etale groupoids (joint with M. Pflaum and X. Tang) Lett. Math. Phys. 90 (2009) p. 287-310.  
• Cyclic cocycles on deformation quantizations and higher index theory. (joint with M. Pflaum and X. Tang) Adv. Math. 223 (2010) p. 1958-2021.  
• The Heisenberg group and conformal field theory. Quart. J. Math. 63 (2012) p. 423-465.  
• Orbifold cup products and ring structures on Hochschild cohomologies. (joint with M. Pflaum, X. Tang and H.-H. Tseng.) Comm. Contemp. Math. 13 (2011) p. 123-182.  
• An algebraic index theorem for orbifolds. (joint with M. Pflaum and X. Tang.) Adv. Math.  210 (2007) p. 83-121.
• Homology of formal deformations of proper etale Lie groupoids. (joint with N. Neumaier, M. Pflaum and X. Tang) J. Reine u. Angew. Math. 593 (2006) p. 117-168.

Here you can find some of these papers.

Teaching

• Topology in Physics
  

Links

Mathematical Research Cluster ``Geometry and Quantum Theory''