keywords
- Topology, in particular of stratified spaces, Geometric Analysis, Noncommutative Geometry, and Deformation Quantization, in particular in the singular setting, Chemical Topology
- Contact Info
Pflaum, Markus Josef Professor
Positions
- Professor, Mathematics
Research Areas
Research
Publications
selected publications
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book
- Analytic and geometric study of stratified spaces. Ed. 1768. 2001
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Quantization of singular symplectic quotients.
Ed. 198.
2001
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chapter
- Quantization of Whitney functions. 153-165. 2012
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From Weyl quantization to modern algebraic index theory.
84-99.
2008
- Regularized traces and $K$-theory invariants of parametric pseudodifferential operators. 161-177. 2008
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A homological approach to singular reduction in deformation quantization.
443-461.
2007
- Smooth structures on stratified spaces. 231-258. 2001
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conference proceeding
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Noncommutative geometry and global analysis.
xx+315-xx+315.
2011
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Noncommutative geometry and global analysis.
xx+315-xx+315.
2011
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journal article
- THE GRAUERT-GROTHENDIECK COMPLEX ON DIFFERENTIABLE SPACES AND A SHEAF COMPLEX OF BRYLINSKI. Methods and Applications of Analysis. 321-332. 2017
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The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs.
Symmetry, Integrability and Geometry : Methods and Applications.
2017
- THE TRANSVERSE INDEX THEOREM FOR PROPER COCOMPACT ACTIONS OF LIE GROUPOIDS. Journal of Differential Geometry. 443-472. 2015
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The localized longitudinal index theorem for Lie groupoids and the van Est map.
Advances in Mathematics.
223-262.
2015
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QUANTIZATION OF WHITNEY FUNCTIONS AND REDUCTION.
Journal of Singularities.
217-228.
2015
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STRATIFICATIONS OF INERTIA SPACES OF COMPACT LIE GROUP ACTIONS.
Journal of Singularities.
107-140.
2015
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The index of geometric operators on Lie groupoids.
Indagationes Mathematicae.
1135-1153.
2014
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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
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Connes–Chern character for manifolds with boundary and eta cochains.
Memoirs of the American Mathematical Society.
0-0.
2012
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ORBIFOLD CUP PRODUCTS AND RING STRUCTURES ON HOCHSCHILD COHOMOLOGIES.
Communications in Contemporary Mathematics.
123-182.
2011
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Cyclic cocycles on deformation quantizations and higher index theorems.
Advances in Mathematics.
1958-2021.
2010
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On the Algebraic Index for Riemannian A parts per thousand tale Groupoids.
Letters in Mathematical Physics.
287-310.
2009
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On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions.
Letters in Mathematical Physics.
101-113.
2009
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Relative pairing in cyclic cohomology and divisor flows.
Journal of K-Theory.
359-359.
2009
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Relative pairing in cyclic cohomology and divisor flows.
Journal of K-Theory.
359-407.
2009
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On the homology of algebras of Whitney functions over subanalytic sets.
Annals of Mathematics.
1-52.
2008
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An algebraic index theorem for orbifolds.
Advances in Mathematics.
83-121.
2007
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Poisson Geometry and Applications.
Oberwolfach Reports.
1243-1298.
2007
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Homology of formal deformations of proper étale Lie groupoids.
Journal für die reine und angewandte Mathematik.
2006
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Phase Space Reduction of Star Products on Cotangent Bundles.
Helvetica Physica Acta.
485-552.
2005
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On the deformation quantization of symplectic orbispaces.
Differential Geometry and its Applications.
343-368.
2003
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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
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Traces on algebras of parameter dependent pseudodifferential operators and the eta-invariant.
Transactions of the American Mathematical Society.
4911-4936.
2000
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Deformation quantization on cotangent bundles.
Reports on Mathematical Physics.
291-297.
1999
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Holomorphic deformation of Hopf algebras and applications to quantum groups.
Journal of Geometry and Physics.
31-44.
1998
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A deformation-theoretical approach to Weyl quantization on Riemannian manifolds.
Letters in Mathematical Physics.
277-294.
1998
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On continuous Hochschild homology and cohomology groups.
Letters in Mathematical Physics.
43-51.
1998
- The normal symbol on Riemannian manifolds. New York Journal of Mathematics. 97-125 (electronic). 1998
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Quantum groups on fibre bundles.
Communications in Mathematical Physics.
279-315.
1994
editor of
Teaching
courses taught
- MATH 4890 Honors Independent Study (Spring 2019)
- MATH 4900 Independent Study (Spring 2019)
- MATH 6900 Independent Study (Spring 2019)
- MATH 6940 Master's Degree Candidate (Spring 2019)
- MATH 6950 Master's Thesis (Spring 2019)
- MATH 8900 Independent Study (Spring 2019)
- MATH 8990 Doctoral Dissertation (Spring 2019)
- MATH 2002 Number Systems: An Introduction to Higher Mathematics (Fall 2018)
- MATH 4890 Honors Independent Study (Fall 2018)
- MATH 4900 Independent Study (Fall 2018)
- MATH 6280 Advanced Algebraic Topology (Fall 2018)
- MATH 6900 Independent Study (Fall 2018)
- MATH 6940 Master's Degree Candidate (Fall 2018)
- MATH 6950 Master's Thesis (Fall 2018)
- MATH 8900 Independent Study (Fall 2018)
- MATH 8990 Doctoral Dissertation (Fall 2018)
- MATH 4810 Special Topics in Mathematics (Summer 2018)
- MATH 5810 Special Topics in Mathematics (Summer 2018)
- MATH 8990 Doctoral Dissertation (Summer 2018)
- MATH 3001 Analysis 1 (Spring 2018)
- MATH 4890 Honors Independent Study (Spring 2018)
- MATH 4900 Independent Study (Spring 2018)
- MATH 6900 Independent Study (Spring 2018)
- MATH 6940 Master's Degree Candidate (Spring 2018)
- MATH 6950 Master's Thesis (Spring 2018)
- MATH 8900 Independent Study (Spring 2018)
- MATH 8990 Doctoral Dissertation (Spring 2018)
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