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Professor Vern Paulsen

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Math 6395, Mathematics of Quantum Information Theory, Spring 2015
TuTh 11:30--1, SW229

Prior Semesters:

Math 3333, Section 20579, Fall 2014
TuTh 1--2:30, SEC 203
Text: Kenneth A. Ross, "Elementary Analysis: The Theory of Calculus"Chapter 1
Syllabus and Grading: 3333 syllabus
Final Exam: December 16, 2--5pm, SEC 203
HW1, Due 9/4: 1.2, 1.3, 1.6, 1.8, 1.9
HW2, Due 9/11: 2.2, 2.3, 2.4
HW3, Due 9/18: 3.6, 3.7, 4.1a,e,g, 4.2a,e,g
HW4, Due 10/2: 7.1, 7.3a--i, 7.5, 8.1a,c, 8.2a,c, 8.5a,b
HW5, Due 10/9: 9.1, 9.3, 9.9, 9.10a, 10.9, 10.10
Practice Test 1: Test 1
Test 1: 10/14
HW6, Due 10/28: 11.3, 11.4, 12.3
HW7, Due 11/4: 14.2, 14.3, 15.4, 15.6
HW8, Due 11/11: 17.5a, 17.9a,b, 17.10c, 17.13a
HW9, Due 11/18: 18.7, 18.8, 18.10, 19.2, 19.3
Test 2: 11/25. Covers: 14, 15, 17, 18, 19
Practice Test 2: Test 2 Sample
Practice Final: Final Sample
No class 12/4. We will meet 12/9 for a review session, usual time, usual place.

Math 4331, Section 22624 and Math 6312, Section 22625, Fall 2014
TuTh 10--11:30, CBB 104
Syllabus and Grading: 4331 syllabus
This is a dual listed undergraduate/graduate course.
Final Exam: December 16, 11am--2pm, CBB 104
Homework assignments and lecture notes will be posted here. There will be no need to purchase a textbook.
4331 Lecture Notes: 4331 Notes Updated 11/6/14
4331 Solutions to HW: Solutions Updated 12/04/14
HW1, Due 9/4: 1.12, 1.13, 1.14, 1.15, 1.16
HW2, Due 9/11: 1.38, 1.39, 1.46, 1.47. Grad also do: 1.37, 1.40
HW3, Due 9/18: 1.69, 1.70, 1.71. Grad also do: 1.58
HW4, Due 10/2: 1.90, 1.91, 1.92, 1.94, 1.106
HW5, Due 10/14: 1.125, 1.126
HW6, Due 10/28: 3.13, 3.15, 3.16. Grad also do: 3.14, 3.17
HW7, Due 11/4: 3.26, 3.36, 3.41. Grad also do: 3.27
HW8, Due 11/13: 4.5, 4.9. Grad also do: 4.6
HW9, Due 11/18: 3.52, 3.54.
HW10, Due 11/25: 5.7, 5.8, 5.17, 5.18
Alternate Midterm/Practice Final: Alternate Test Updated 12/03/14
No Class 12/2/14. On 12/4/14 we will review for the final and go over the Alternate Test


Research interests: Operator Algebras, Operator Theory, Frame Theory, Reproducing Kernel Hilbert Spaces, Quantum Computation and Quantum Information Theory.
I am part of the Analysis Research Group follow the link for our activities.
Curriculum Vita, including a list of all publications CV.pdf file

Recent Publications

Copies of some of my student's theses are available here.

Completely Bounded Maps and Operator Algebras, Cambridge University Press, February 2003. cover.jpeg
Solutions to Exercises Prepared by Mrinal Ragupathi Solutions Manual .

Extensions of the Inequalities of Hardy and Hilbert(with D. Singh)Arxiv Abstract

The Functional Analysis of Quantum Information Theory(edited by Ved Prakash Gupta, Prabha Mandayam, V. S. Sunder)Arxiv Abstract

A Spectral Characterization of AN Operators(with S. Pandey) Arxiv Abstract

Lovász theta type norms and Operator Systems(with C. Ortiz) Arxiv Abstract

Estimating Quantum Chromatic Numbers(with S. Severini, D. Stahlke, I. Todorov and A. Winter)Arxiv Abstract

Quantum chromatic numbers via operator systems(with I. Todorov) Arxiv Abstract Q. J. Math., to appear.

Characterisations of the weak expectation property(with D. Farenick, A.S. Kavruk, and I. Todorov)Arxiv Abstracts New York Journal of Mathematics, to appear.

Complete positivity of the map from a basis to its dual basis(with F. Shultz) Arxiv Abstract Journal of Mathematical Physics 54 072201 (2013); http://dx.doi.org/10.1063/1.4812329

The isomorphism relation for separable C*-algebras(with G.A. Elliott, I. Farah, C. Rosendal, A.S. Toms, and A. Tornquist) Arxiv Abstract Mathematical Research Letters, to appear.

Operator Systems from Discrete Groups(with D. Farenick, A.S. Kavruk and I. Todorov) Arxiv Abstract, Communications in Mathematical Physics, April 2014, DOI 10.1007/s00220-014-2037-6

C*-algebras with the weak expectation property and a multivariable analogue of Ando's theorem on the numerical radius(with D. Farenick and A. Kavruk) Arxiv Abstract, J. Operator Theory 70 (2013), no. 2, 573–590.

Operator system quotients of matrix algebras and their tensor products(with D. Farenick) Arxiv Abstract Mathematica Scandinavica, Vol. 111, 2012, 210-243.

An approximation theorem for nuclear operator systems(with K.H. Han) Arxiv Abstract J. Funct. Anal., Vol. 261, 2011, 999-1009.

Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory(with D. Kribs, N. Johnston and R. Pereira) JKPP_Aug31.pdf , J. Funct. Anal., Vol. 260, Issue 8, 2011, 2407-2423.

Quotients, exactness and nuclearity in the operator system category(with A. Kavruk, I. Todorov and M. Tomforde) Arxiv Abstract Advances in Math., Vol. 235, 1 March 2013, 321-360.

The Feichtinger conjecture and reproducing kernel Hilbert spaces(with S. Lata) Arxiv Abstract, Indiana Univ. Math. J. 60 (2011), no. 4, 1303–1317.

Spanning and independence properties of frame partitions(with B. Bodmann, P. Casazza and D. Speegle) Arxiv Abstract, Proceedings of the AMS, Volume 140, Number 7, July 2012, 2193-2207.

Syndetic Sets and Amenability Arxiv Abstract, Proceedings of the AMS, Volume 140, Number 6, June 2012, 1997-2001.

Syndetic Sets, Paving and the Feichtinger Conjecture Arxiv Abstract, Proceedings of the AMS, Vol. 139, No. 3, March 2011, 1115-1120.

Tensor Products of Operator Systems(with A. Kavruk, I. Todorov and M. Tomforde) Arxiv Abstract, J. Funct. Anal, 261(2011), 267-299.

Operator algebras of functions(with M. Mittal) Arxiv Abstract, J. Funct. Anal., 258(2010), 3195-3225.

Operator System Structures on Ordered Spaces(with I. Todorov and M. Tomforde) Arxiv Abstract, Proc. of the LMS, 102(1)(2011), 25-49.

Stable Isomorphism of Dual Operator Spaces(with G. Eleftherakis and I. Todorov) Arxiv Abstract, J. Funct. Anal., 258(2010), 260-278.

Weak expectations and the injective envelopeAbstract, TAMS, Volume 363, Number 9, September 2011, 4735-4755.

An operator algebraic proof of Agler's factorization theorem(with S. Lata and M. Mittal) Abstract PAMS, Vol. 137, No. 11, Nov. 2009, 3741-3748.

A Constrained Nevanlinna-Pick Interpolation Problem(with K.R. Davidson, M. Raghupathi, and D. Singh) Abstract IUMJ, Vol. 58, No. 2, 2009, 709--732.

Representations of logmodular algebras(with M. Raghupathi) Final version TAMS, Vol. 363, No. 5, May 2011, 267-240.

Equiangular Tight Frames from Complex Seidel Matrices Containing Cube Roots of Unity (with B. Bodmann and M. Tomforde) Abstract LAA, 430(2009), 396--417.

Computing stabilized norms for quantum operations via the theory of completely bounded maps(with N. Johnston and D. Kribs) Abstract , Quantum Inf. Comput., 9(2009), no. 1-2, 16-35.

Vector Spaces with an Order Unit(with M. Tomforde) Abstract , IUMJ, 58(2009), no. 3, 1319-1359.

Injectivity and projectivity in analysis and topology(with D. Hadwin) gequi.pdf Sci. China Math. 54 (2011), no. 11, 2347–2359.

Lectures on the Kadison-Singer Problem Lecture Notes

A dynamical systems approach to the Kadison-Singer problemdynks.pdf, J. Funct. Anal., 255(2008), 120--132.

Some new equivalences of Anderson's paving conjectures(with M. Ragupathi)newpave.pdf, Proc. AMS, Vol. 136, No. 12, Dec. 2008, 4275-4282.

Stably Isomorphic Dual Operator Algebras(with G.K. Eleftherakis) Abstract, Math. Ann., (2008)341:99--112.

Projections and the Kadison-Singer Problem(with P. Casazza, D. Edidin and D. Kalra) Abstract Matrices and Operators, to appear.

State extensions and the Kadison-Singer Problem(with C. Akemann) ARCC-ap.pdf, AIM preprint.

Injective and projective Hilbert C*-modules, and C*-algebras of compact operators(with M. Frank) Abstract

Interpolation and balls in C^k(with J. Solazzo) Abstract JOT, 60:2(2008), 379--398.

Decoherence-insensitive quantum communication by optimal C*-encoding(with B. Bodmann and D. Kribs), Abstract IEEE Transactions on Information Theory, Vol. 53, Number 12, December 2007, 4738--4749.

Smooth frame-path termination for Higher Order Sigma-Delta Quantization(with S. Abdulbaki and B. Bodmann) HOSD-JFAA.pdf JFAA, Vol. 13, Issue 3(2007), 285--307.

Frame Paths and Error Bounds for Sigma-Delta Quantization(with B. Bodmann) sigmadelta.pdf ACHA, to appear.

Equivariant Maps and Bimodule Projections solelprob.pdf JFA 240(2006), 495-507.

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces, Course Notes rkhs.pdf

Loss-Insensitive Vector Encoding with Two-Uniform Frames(with B. Bodmann) FGE_SPIE.pdf, in Wavelets XI, Proceedings of the SPIE, vol. 5914(2005), M. Papadakis, A.F. Laine, M.A. Unser (Eds.), pp. 591403-1-12.

A Simple Proof of Bohr's Inequality(with D. Singh) bohrconf.pdf

An Introduction to the Theory of Topological Groups and Their Representations, Course Notes grouprepn.pdf

Modules Over Subalgebras of the Disk Algebra(with D. Singh) diskalg.pdf IUMJ, Vol. 55, No. 5(2006), 1751-1766.

Schur multipliers and operator-valued Foguel-Hankel operators(with C. Badea), Abstract,, IUMJ, Vol. 50, No. 4(2001), 1509--1522.

Frames, Graphs and Erasures(with B. Bodmann), Abstract, LAA 404(2005), 118-146.

Extensions of Bohr's Inequality(with D. Singh) bohrext.dvi file Bull. LMS 38(2006), 991-999.

Two Reformulations of Kadison's Similarity Problem(with D. Hadwin) kadsim.dvi file JOT, Vol. 55, No. 1, Winter 2006, 3-16.

Quasimultipliers of Operator Spaces(with M. Kaneda), quasi.dvi file JFA, 217(2004), 347-365. Reprints available.

Injective Envelopes of C*-algebras as Operator Modules (with M. Frank), Pac.J. Math., 212(2003), 57-69. Reprints available.

Characterizations of Essential Ideals as Operator Modules (with M. Kaneda), J.O.T., 49(2003), 245-262. Reprints available.

Diffusing with Stefan and Maxwell (with N.R. Amundson and T.-W. Pan), AIChE, April 2003, Vol.49, No. 4, 813-830. Reprints available.

Optimal Frames for Erasures (with R.B. Holmes), Lin. Alg. Appl., 377(2004), 31-51. Reprints available. opframe.pdf

Bohr's Inequality for Uniform Algebras (with D. Singh) PAMS, 132(2004), 3577-3579. Reprints available.

Lie ideals in Operator Algebras(with A. Hopenwasser), J.O.T.,52(2004), 325-340, reprints available, posted on arXiv

On the Ranges of Bimodule Projections(with A. Katavolos), Can. Bull. Math., 48(1), 2005, 97-111, reprints available, Arxiv Abstract


Operator Systems: Quotients, Duals and Tensors with Applications to Connes' Embedding Problem Banff International Research Station, February 27, 2012 Video

The Functional Analysis of Quantum Information Theory, I, Chennai, India, January 2, 2011, Youtube

The Functional Analysis of Quantum Information Theory, II, Chennai, India, January 3, 2011, Youtube

The Functional Analysis of Quantum Information Theory, III, Chennai, India, January 4, 2011, Youtube

The Functional Analysis of Quantum Information Theory, IV, Chennai, India, January 5, 2011, Youtube

The Functional Analysis of Quantum Information Theory, V, Chennai, India, January 6, 2011, Youtube

Last updated: August 14, 2013