Jonathan Rosenberg - Academia.edu (original) (raw)

Uploads

Papers by Jonathan Rosenberg

Research paper thumbnail of Kinematics

Multivariable Calculus with MATLAB®, 2017

Research paper thumbnail of Excerpt More information

1 Introduction 3 elbridge gerry's salamander The word gerrymander describes a distinctively (... more 1 Introduction 3 elbridge gerry's salamander The word gerrymander describes a distinctively (albeit not uniquely) American practice, that of redrawing district lines to achieve partisan (or other) advantage. The word also has a distinctively American etymology, dating back to Elbridge Gerry's term as governor of Massachusetts (1810–1812), when political observers made sport of a district drawn by his party that looked something like a salamander. At the broadest level, indicated by its title, this book is about gerrymandering. The principles of our analysis could be applied to the original Gerry-mander or to any of its various and long line of descendants (for one such effort, see Engstrom 2001). At a narrower and more specific level, indicated by its subtitle, this book concerns what was arguably the most important change in the practice of American gerrymandering since its invention. 1 Whereas previously the game of drawing salamanders with district lines was limited to le...

Research paper thumbnail of Multivariable Calculus with MATLAB®

Multivariable Calculus with MATLAB®, 2017

Research paper thumbnail of C∗-algebras with approximately inner flip

Pacific Journal of Mathematics, 1978

Research paper thumbnail of Flux quantization for a superconducting ring in the shape of a M\"obius band

We give two derivations of magnetic flux quantization in a superconducting ring in the shape of a... more We give two derivations of magnetic flux quantization in a superconducting ring in the shape of a M\"obius band, one using direct study of the Schr\"odinger equation and the other using the holonomy of flat U(1)-gauge bundles. Both methods show that the magnetic flux must be quantized in integral or half-integral multiples of Phi_0=hc/(2e)\Phi_0=hc/(2e)Phi_0=hc/(2e). Half-integral quantization shows up in "nodal states" whose wavefunction vanishes along the center of the ring, for which there is now some experimental evidence.

Research paper thumbnail of Realization of Square-Integrable Representations of Unimodular Lie Groups on L 2 -Cohomology Spaces

Transactions of the American Mathematical Society, 1980

Research paper thumbnail of Fine structure of the Mackey machine for actions of abelian groups with constant Mackey obstruction

Pacific Journal of Mathematics, 1995

Research paper thumbnail of Lie Group Representations III

Lecture Notes in Mathematics, 1984

Research paper thumbnail of Introduction to Non-Commutative Geometry

Research paper thumbnail of Book Review: The theory of group representations

Bulletin of the American Mathematical Society, 1999

Research paper thumbnail of The behavior of Fourier transforms for nilpotent Lie groups

Transactions of the American Mathematical Society, 1996

We study weak analogues of the Paley-Wiener Theorem for both the scalar-valued and the operator-v... more We study weak analogues of the Paley-Wiener Theorem for both the scalar-valued and the operator-valued Fourier transforms on a nilpotent Lie group G G . Such theorems should assert that the appropriate Fourier transform of a function or distribution of compact support on G G extends to be “holomorphic” on an appropriate complexification of (a part of) G ^ \hat G . We prove the weak scalar-valued Paley-Wiener Theorem for some nilpotent Lie groups but show that it is false in general. We also prove a weak operator-valued Paley-Wiener Theorem for arbitrary nilpotent Lie groups, which in turn establishes the truth of a conjecture of Moss. Finally, we prove a conjecture about Dixmier-Douady invariants of continuous-trace subquotients of C ∗ ( G ) C^{*}(G) when G G is two-step nilpotent.

Research paper thumbnail of Manifolds of Positive Scalar Curvature

Mathematical Sciences Research Institute Publications, 1994

Research paper thumbnail of Some Work of Stefan Banach and the Mathematics It Has Generated

Wiadomości Matematyczne, 2012

Research paper thumbnail of Metrics of positive scalar curvature and connections with surgery

Princeton University Press eBook Package 2014, 2001

Research paper thumbnail of T-duality for circle bundles via noncommutative geometry

Advances in Theoretical and Mathematical Physics, 2014

Research paper thumbnail of String Theory on Elliptic Curve Orientifolds and KR-Theory

Communications in Mathematical Physics, 2014

Research paper thumbnail of T-Duality for Orientifolds and Twisted KR-Theory

Letters in Mathematical Physics, 2014

Research paper thumbnail of An analogue of the Novikov Conjecture in complex algebraic geometry

Transactions of the American Mathematical Society, 2008

Research paper thumbnail of A quick proof of Harish-Chandra’s Plancherel theorem for spherical functions on a semisimple Lie group

Proceedings of the American Mathematical Society, 1977

Some lemmas of S. Helgason and R. Gangolli, originally conceived for proving an analogue of the P... more Some lemmas of S. Helgason and R. Gangolli, originally conceived for proving an analogue of the Paley-Wiener theorem for symmetric spaces, are used to give a quick proof of Harish-Chandra’s inversion formula and Plancherel theorem for bi-invariant functions on a semisimple Lie group. The method is elementary in that it does not require introduction of Harish-Chandra’s “Schwartz space."

Research paper thumbnail of Continuous-trace algebras from the bundle theoretic point of view

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1989

Using various facts about principal bundles over a space, we give a unified treatment of several ... more Using various facts about principal bundles over a space, we give a unified treatment of several theorems about the structure of stable separable continuous-trace algebras, their automorphisms, and their K-theory. We also present a classification of real continuous-trace algebras from the same point of view.

Research paper thumbnail of Kinematics

Multivariable Calculus with MATLAB®, 2017

Research paper thumbnail of Excerpt More information

1 Introduction 3 elbridge gerry's salamander The word gerrymander describes a distinctively (... more 1 Introduction 3 elbridge gerry's salamander The word gerrymander describes a distinctively (albeit not uniquely) American practice, that of redrawing district lines to achieve partisan (or other) advantage. The word also has a distinctively American etymology, dating back to Elbridge Gerry's term as governor of Massachusetts (1810–1812), when political observers made sport of a district drawn by his party that looked something like a salamander. At the broadest level, indicated by its title, this book is about gerrymandering. The principles of our analysis could be applied to the original Gerry-mander or to any of its various and long line of descendants (for one such effort, see Engstrom 2001). At a narrower and more specific level, indicated by its subtitle, this book concerns what was arguably the most important change in the practice of American gerrymandering since its invention. 1 Whereas previously the game of drawing salamanders with district lines was limited to le...

Research paper thumbnail of Multivariable Calculus with MATLAB®

Multivariable Calculus with MATLAB®, 2017

Research paper thumbnail of C∗-algebras with approximately inner flip

Pacific Journal of Mathematics, 1978

Research paper thumbnail of Flux quantization for a superconducting ring in the shape of a M\"obius band

We give two derivations of magnetic flux quantization in a superconducting ring in the shape of a... more We give two derivations of magnetic flux quantization in a superconducting ring in the shape of a M\"obius band, one using direct study of the Schr\"odinger equation and the other using the holonomy of flat U(1)-gauge bundles. Both methods show that the magnetic flux must be quantized in integral or half-integral multiples of Phi_0=hc/(2e)\Phi_0=hc/(2e)Phi_0=hc/(2e). Half-integral quantization shows up in "nodal states" whose wavefunction vanishes along the center of the ring, for which there is now some experimental evidence.

Research paper thumbnail of Realization of Square-Integrable Representations of Unimodular Lie Groups on L 2 -Cohomology Spaces

Transactions of the American Mathematical Society, 1980

Research paper thumbnail of Fine structure of the Mackey machine for actions of abelian groups with constant Mackey obstruction

Pacific Journal of Mathematics, 1995

Research paper thumbnail of Lie Group Representations III

Lecture Notes in Mathematics, 1984

Research paper thumbnail of Introduction to Non-Commutative Geometry

Research paper thumbnail of Book Review: The theory of group representations

Bulletin of the American Mathematical Society, 1999

Research paper thumbnail of The behavior of Fourier transforms for nilpotent Lie groups

Transactions of the American Mathematical Society, 1996

We study weak analogues of the Paley-Wiener Theorem for both the scalar-valued and the operator-v... more We study weak analogues of the Paley-Wiener Theorem for both the scalar-valued and the operator-valued Fourier transforms on a nilpotent Lie group G G . Such theorems should assert that the appropriate Fourier transform of a function or distribution of compact support on G G extends to be “holomorphic” on an appropriate complexification of (a part of) G ^ \hat G . We prove the weak scalar-valued Paley-Wiener Theorem for some nilpotent Lie groups but show that it is false in general. We also prove a weak operator-valued Paley-Wiener Theorem for arbitrary nilpotent Lie groups, which in turn establishes the truth of a conjecture of Moss. Finally, we prove a conjecture about Dixmier-Douady invariants of continuous-trace subquotients of C ∗ ( G ) C^{*}(G) when G G is two-step nilpotent.

Research paper thumbnail of Manifolds of Positive Scalar Curvature

Mathematical Sciences Research Institute Publications, 1994

Research paper thumbnail of Some Work of Stefan Banach and the Mathematics It Has Generated

Wiadomości Matematyczne, 2012

Research paper thumbnail of Metrics of positive scalar curvature and connections with surgery

Princeton University Press eBook Package 2014, 2001

Research paper thumbnail of T-duality for circle bundles via noncommutative geometry

Advances in Theoretical and Mathematical Physics, 2014

Research paper thumbnail of String Theory on Elliptic Curve Orientifolds and KR-Theory

Communications in Mathematical Physics, 2014

Research paper thumbnail of T-Duality for Orientifolds and Twisted KR-Theory

Letters in Mathematical Physics, 2014

Research paper thumbnail of An analogue of the Novikov Conjecture in complex algebraic geometry

Transactions of the American Mathematical Society, 2008

Research paper thumbnail of A quick proof of Harish-Chandra’s Plancherel theorem for spherical functions on a semisimple Lie group

Proceedings of the American Mathematical Society, 1977

Some lemmas of S. Helgason and R. Gangolli, originally conceived for proving an analogue of the P... more Some lemmas of S. Helgason and R. Gangolli, originally conceived for proving an analogue of the Paley-Wiener theorem for symmetric spaces, are used to give a quick proof of Harish-Chandra’s inversion formula and Plancherel theorem for bi-invariant functions on a semisimple Lie group. The method is elementary in that it does not require introduction of Harish-Chandra’s “Schwartz space."

Research paper thumbnail of Continuous-trace algebras from the bundle theoretic point of view

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1989

Using various facts about principal bundles over a space, we give a unified treatment of several ... more Using various facts about principal bundles over a space, we give a unified treatment of several theorems about the structure of stable separable continuous-trace algebras, their automorphisms, and their K-theory. We also present a classification of real continuous-trace algebras from the same point of view.