Publications in VIVO

Co-author Network

Pflaum, Markus J

Professor

Positions

Professor, Mathematics

Research Areas

Research

keywords

Topology (in particular of stratified spaces), Global Analysis, Noncommutative Geometry, Deformation Quantization (in particular in the singular setting), Topological Data Analysis, Computational Algebraic Geometry, Mathematical Physics, Axiomatic Quantum Field Theory, Chemical Topology

Publications

selected publications

book
- Analytic and geometric study of stratified spaces. Ed. 1768. 2001
- Quantization of Singular Symplectic Quotients 2001
chapter
- Quantization of Whitney functions. 153-165. 2012
- From Weyl quantization to modern algebraic index theory. 84-99. 2008
- Regularized traces and $K$-theory invariants of parametric pseudodifferential operators. 161-177. 2008
- A HOMOLOGICAL APPROACH TO SINGULAR REDUCTION IN DEFORMATION QUANTIZATION. 443-461. 2007
- Smooth structures on stratified spaces. 231-258. 2001
conference proceeding
- Localization in Hochschild homology. Proceedings of Symposia in Pure Mathematics. 2023
- Noncommutative Geometry and Global Analysis. Contemporary Mathematics. 2011
journal article
- A Classifying Space for Phases of Matrix Product States. Communications in Mathematical Physics. 2026
- Charting the space of ground states with tensor networks. SciPost Physics. 2025
- On the weak contractibility of the space of pure states. Journal of Functional Analysis. 2025
- Homotopical foundations of parametrized quantum spin systems. Reviews in Mathematical Physics. 2024
- ALGEBRAIC MACHINE LEARNING WITH AN APPLICATION TO CHEMISTRY. Foundations of Data Science. 62-84. 2024
- Challenges in the Mathematics Description of Energy Landscapes 2024
- Flow of higher Berry curvature and bulk-boundary correspondence in parametrized quantum systems. Physical review B (PRB). 2023
- Differentiable stratified groupoids and a de Rham theorem for inertia spaces. Journal of Geometry and Physics. 2023
- On the Hochschild homology of proper Lie groupoids. Journal of Noncommutative Geometry. 101-162. 2023
- Continuous dependence on the initial data in the Kadison transitivity theorem and GNS construction. Reviews in Mathematical Physics. 2022
- Representations of energy landscapes by sublevelset persistent homology: An example with n-alkanes. Journal of Chemical Physics. 2021
- Deformation Quantization and Homological Reduction of a Lattice Gauge Model. Communications in Mathematical Physics. 1061-1109. 2021
- EQUIVARIANT CONTROL DATA AND NEIGHBORHOOD DEFORMATION RETRACTIONS. Methods and Applications of Analysis. 13-36. 2019
- Invariant Whitney functions. International Journal of Mathematics. 2019
- THE GRAUERT-GROTHENDIECK COMPLEX ON DIFFERENTIABLE SPACES AND A SHEAF COMPLEX OF BRYLINSKI. Methods and Applications of Analysis. 321-332. 2017
- The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2017
- THE TRANSVERSE INDEX THEOREM FOR PROPER COCOMPACT ACTIONS OF LIE GROUPOIDS. Journal of differential geometry. 443-472. 2015
- The localized longitudinal index theorem for Lie groupoids and the van Est map. Advances in Mathematics. 223-262. 2015
- QUANTIZATION OF WHITNEY FUNCTIONS AND REDUCTION. Journal of Singularities. 217-228. 2015
- STRATIFICATIONS OF INERTIA SPACES OF COMPACT LIE GROUP ACTIONS. Journal of Singularities. 107-140. 2015
- The index of geometric operators on Lie groupoids. Indagationes Mathematicae. 1135-1153. 2014
- Geometry of orbit spaces of proper Lie groupoids. Journal für die Reine und Angewandte Mathematik. 49-84. 2014
- Connes-Chern Character for Manifolds with Boundary and Eta Cochains Introduction. Memoirs of the American Mathematical Society. 1-+. 2012
- Connes–Chern character for manifolds with boundary and eta cochains. Memoirs of the American Mathematical Society. 2012
- ORBIFOLD CUP PRODUCTS AND RING STRUCTURES ON HOCHSCHILD COHOMOLOGIES. Communications in Contemporary Mathematics. 123-182. 2011
- Cyclic cocycles on deformation quantizations and higher index theorems. Advances in Mathematics. 1958-2021. 2010
- On the Algebraic Index for Riemannian A parts per thousand tale Groupoids. Mathematical Physics Studies. 287-310. 2009
- On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions. Mathematical Physics Studies. 101-113. 2009
- Relative pairing in cyclic cohomology and divisor flows. Journal of K-theory. 359-407. 2009
- Relative pairing in cyclic cohomology and divisor flows. Journal of K-theory. 359-407. 2009
- Poisson Geometry and Applications. Oberwolfach Reports. 1243-1298. 2008
- On the homology of algebras of Whitney functions over subanalytic sets. Annals of Mathematics. 1-52. 2008
- An algebraic index theorem for orbifolds. Advances in Mathematics. 83-121. 2007
- Homology of formal deformations of proper étale Lie groupoids. Journal für die Reine und Angewandte Mathematik. 2006
- Phase Space Reduction of Star Products on Cotangent Bundles. Annales Henri Poincare. 485-552. 2005
- On the deformation quantization of symplectic orbispaces. Differential Geometry and its Application. 343-368. 2003
- On representations of star product algebras over cotangent spaces on Hermitian line bundles. Journal of Functional Analysis. 1-47. 2003
- A deformation-theoretic approach to normal order quantization. Russian Journal of Mathematical Physics. 82-113. 2000
- Traces on algebras of parameter dependent pseudodifferential operators and the eta–invariant. Transactions of the American Mathematical Society. 4911-4936. 2000
- Deformation quantization on cotangent bundles. Reports on Mathematical Physics. 291-297. 1999
- Holomorphic deformation of Hopf algebras and applications to quantum groups. Journal of Geometry and Physics. 31-44. 1998
- A Deformation-Theoretical Approach to Weyl Quantization on Riemannian Manifolds. Mathematical Physics Studies. 277-294. 1998
- On Continuous Hochschild comology and Cohomology Groups. Mathematical Physics Studies. 43-51. 1998
- The normal symbol on Riemannian manifolds. New York Journal of Mathematics. 97-125 (electronic). 1998
- Quantum groups on fibre bundles. Communications in Mathematical Physics. 279-315. 1994

Background

education and training

Dr. habil., Humboldt Univ of Berlin (Germany) 2001
Ph.D., Univ of Munich (Germany) 1995
B.S., Univ of Munich (Germany) 1992

awards and honors

Collaboration Grants for Mathematicians, conferred by Simons Foundation, 2015

International Activities

geographic focus

http://dbpedia.org/page/Taiwan Geographic Region
Brazil Country
Canada Country
China Country
Croatia Country
France Country
Germany Country
Japan Country
Netherlands Country
Poland Country
Singapore Country
Viet Nam Country

Other Profiles

ORCID iD

http://orcid.org/0000-0002-9446-8039

Google Scholar

https://scholar.google.com/citations?user=u80zHf4AAAAJ&hl=en&oi=ao

ResearchGate

https://www.researchgate.net/profile/Markus_Pflaum