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
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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
2007
- Smooth structures on stratified spaces. 231-258. 2001
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conference proceeding
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Noncommutative Geometry and Global Analysis.
Contemporary Mathematics.
2011
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Noncommutative Geometry and Global Analysis.
Contemporary Mathematics.
2011
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journal article
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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
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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.
359-407.
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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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
- 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
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Invariant Whitney functions.
International Journal of Mathematics.
2019
editor of
Teaching
courses taught
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MATH 2002 - Number Systems: An Introduction to Higher Mathematics
Primary Instructor - Fall 2018
Introduces the concepts of mathematical proofs using the construction of the real numbers from set theory. Topics include basic logic and set theory, equivalence relations and functions, Peano's axioms, construction of the integers, the rational numbers and axiomatic treatment of the real numbers. Credit not granted for this course and MATH 2001. -
MATH 2130 - Introduction to Linear Algebra for Non-Mathematics Majors
Primary Instructor - Spring 2019
Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who do not plan to major in Mathematics. Degree credit not granted for this course and MATH 2135 or APPM 3310. Formerly MATH 3130. -
MATH 3001 - Analysis 1
Primary Instructor - Spring 2018
Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral. -
MATH 4810 - Special Topics in Mathematics
Primary Instructor - Summer 2018 / Summer 2019
Covers various topics not normally covered in the curriculum. Offered intermittently depending on student demand and availability of instructors. May be repeated up to 7 total credit hours. Same as MATH 5810. -
MATH 5810 - Special Topics in Mathematics
Primary Instructor - Summer 2018 / Summer 2019
Covers various topics not normally covered in the curriculum. Offered intermittently depending on student demand and availability of instructors. May be repeated up to 7 total credit hours. Same as MATH 4810. -
MATH 6280 - Advanced Algebraic Topology
Primary Instructor - Fall 2018
Covers homotopy theory, spectral sequences, vector bundles, characteristic classes, K-theory and applications to geometry and physics. Department enforced prerequisite: MATH 6220. Instructor consent required for undergraduates.
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