Professional Appointments


  • Saint Louis University, St Louis MO, USA
    •      Associate Professor, June 2018-current.
         Assistant Professor, August 2012-June 2018.
  • Duke University, Durham NC, USA
    •      Visiting Associate Professor, August 2018-May 2019.
  • University of Texas, Austin TX, USA
    •      R. H. Bing Instructor, August 2010-August 2012.
  • Texas A&M University, College Station TX, USA
    •      Visiting Assistant Professor, September 2009-August 2010.

Education


  • Texas A&M University, College Station TX, USA
    •      Ph.D., Mathematics, August 2009
         Thesis title: Upper estimates for Banach spaces.
         Advisor: Thomas Schlumprecht
  • Guilford College, Greensboro NC, USA
    •      B.S., Mathematics and Physics, May 2003
         Thesis title: Ellipsoidal and convex tight frames.
         Advisors: Ruddy Gordh and Elwood Parker

Awards


  • National Science Foundation Research Grant, PI, "Frame theory and phase retrieval", DMS-2154931, $332,696, June 2022-May 2025.
  • Simons Foundation Collaboration Grant for Mathematicians, PI, "Frames and bases in theory and application", 706481, $42,000, Sep 2020-May 2022.(concluded early due to receiving NSF grant)
  • Simons Foundation Collaboration Grant for Mathematicians, PI, "Coordinate systems of Banach spaces", 353293, $35,000, Sep 2015-Aug 2020.
  • National Science Foundation Research Grant, PI, "Topics in the geometry of Banach spaces", DMS-1001929, $76,443, June 2010-May 2014.
  • Faculty Travel Grant, $1,200 per year, University of Texas at Austin, 2011-2013.
  • R.H. Bing fellowship, $7,000 per year and $1,000 travel allowance per year, University of Texas at Austin, 2010-2013
  • Mathematical Association of America Project NExT fellow, 2010-2011.
  • L.F. Guseman Prize in Mathematics Award, Texas A&M University, 2009. Given for outstanding research, teaching, and service as a graduate student.
  • AUF Fellowship, Texas A&M University, Sep 2004-Aug 2005 and Sep 2006-Aug 2009.
  • NSF-VIGRE Fellowship, Texas A&M University, Sep 2003-Aug 2004 and Sep 2005-Aug 2006.
  • The Learning Commons Outstanding Tutor Award, Guilford College, 2003. Given to the tutor who has contributed in the most positive, responsible, and creative ways.

Advising


  • Postdoc advisor for Dorsa Ghoreishi, St Louis University, Fall 2020-present
  • Phd advisor for Wedad Alharbi, St Louis University, Spring 2021-present
  • Phd advisor for Salah Alshabhi, St Louis University, Fall 2020-present
  • Masters thesis advisor for Joseph Eisner, St Louis University, Fall 2016-Spring 2017. Thesis title: Continuous Schauder frames and reflexivity in Banach spaces. Entered Phd program at University of Virginia after graduating.
  • Undergraduate thesis advisor for Eileen Martin, University of Texas, Fall 2010-Spring 2012. Thesis title: Global coordinate systems: Continuously moving finite-dimensional unit norm tight frames on smooth manifolds. Received Goldwater fellowship for her research. Entered Phd program at Stanford University after graduating.

Service


Papers


  1. W. Alharbi, D. Freeman, D. Ghoreishi, C. Lois, and S. Sebastian Stable phase retrieval and perturbations of frames, submitted, 13 pages.
  2. P. Balazs, D. Freeman, R. Popescu, and M. Speckbacher, Quantitative bounds for unconditional pairs of frames, submitted, 19 pages.
  3. D. Freeman, T. Oikhberg, B. Pineau, and M.A. Taylor, Stable phase retrieval in function spaces, submitted, 57 pages.
  4. W. Alharbi, S. Alshabhi, D. Freeman, and D. Ghoreishi, Locality and stability for phase retrieval, submitted, 14 pages.
  5. K. Beanland and D. Freeman, Shrinking Schauder frames and their associated spaces, submitted, 18 pages.
  6. R. Calderbank, I. Daubechies, D. Freeman, and N. Freeman, Stable phase retrieval for infinite dimensional subspaces of L2(ℝ), submitted, 27 pages.
  7. D. Freeman and D. Ghoreishi, Discretizing Lp norms and frame theory, J. Math. Anal. and Applications, (2022) 17 pages. doi.org/10.1016/j.jmaa.2022.126846
  8. D. Freeman, Th. Schlumprecht, and A. Zsák, Banach spaces for which the space of operators has 2𝔠 closed ideals, Forum of Mathematics, Sigma, 9, E27, (2021) 20 pages. doi:10.1017/fms.2021.23
  9. D. Freeman, Th. Schlumprecht, and A. Zsák, Addendum Closed ideals of operators between the classical sequence spaces. Bull. Lond. Math. Soc, 53, no. 2, (2021), 593-–595.
  10. D. Freeman, A.M. Powell, and M. Taylor, A Schauder basis for L2 consisting of non-negative functions, Mathematische Annalen, (2021) 28 pages, https://doi.org/10.1007/s00208-021-02143-4
  11. J. Eisner and D. Freeman, Continuous Schauder frames for Banach spaces, J. Fourier Anal. and Apps., 26 , no. 4, (2020), 30 pages, https://doi.org/10.1007/s00041-020-09776-0
  12. J.A. Chavez-Dominguez, D. Freeman, and K. Kornelson Frame potential for finite-dimensional Banach spaces. , Linear Algebra and Applications, 578 (2019), 1--26.
  13. D. Freeman and D. Speegle, The discretization problem for continuous frames, Advances in Math., 345 (2019), 784--813.
  14. D. Freeman, E. Odell, B. Sari, and B. Zheng, On spreading sequences and asymptotic structures, (with , Trans. AMS, 370, no. 10, (2018) 6933--6953.
  15. D. Freeman, Th. Schlumprecht, and A. Zsak, Closed ideals of operators between the classical sequence spaces, Bulletin of the London Math. Soc., 49 , no. 5 (2017), 859--876.
  16. K. Beanland, D. Freeman, R. Causey, and B. Wallis Classes of operators determined by ordinal indices, J. Functional Analysis, 271, no. 1, (2016) 1691--1746.
  17. P. G. Casazza, D. Freeman, and R. Lynch, Weaving Schauder frames, J. Approximation Theory, 211 (2016) 42--60.
  18. F. Baudier, D. Freeman, Th. Schlumprecht, and A. Zsak, The metric geometry of the Hamming Cube and applications, Geometry and Topology, 20 (2016), 1427--1444.
  19. K. Beanland, D. Freeman, and P. Motakis The stabilized set of p's in Krivine's Theorem can be disconnected, Advances in Math., 281 (2015), 553--577.
  20. K. Beanland, D. Freeman, and R. Liu, Upper and lower estimates for Schauder frames and atomic decompositions, Fund. Math. 231 (2015), 161--188.
  21. D. Freeman, R. Hotovy, and E. Martin, Moving finite unit norm tight frames for Sn, Illinois J. Math., 58 (2014), no. 2, 311--322
  22. D. Freeman, E. Odell, Th. Schlumprecht, and A. Zsak, Unconditional structures of translates for Lp(Rd). Israel J. Math., 203 (2014), no. 1, 189--209.
  23. P.N. Dowling, D. Freeman, C.J. Lennard, E. Odell, B. Randrianantoanina, and B. Turett A weak Grothendiek compactness principle for Banach spaces with a symmetric basis. Positivity, 18 (2014), no. 1, 147--159.
  24. K. Beanland and D. Freeman, Uniformly factoring weakly compact operators. J. Functional Anal, 266, (2014), no. 5, 2921--2943.
  25. D. Freeman, E. Odell, B. Sari, and Th. Schlumprecht, Equilateral sets in uniformly smooth Banach spaces. Mathematika, 60 (2014), no. 01, 219--231.
  26. D. Freeman, D. Poore, A. R. Wei, and M. Wyse, Moving Parseval frames for vector bundles. Houston J. of Math., 40, (2014), no. 3, 817--832.
  27. P.N. Dowling, D. Freeman, C.J. Lennard, E. Odell, B. Randrianantoanina, and B. Turett, A weak Grothendiek compactness principle. J. Functional Analysis 263 (2012), no. 5, 1378--1381.
  28. S.A. Argyros, D. Freeman, R. Haydon, E. Odell, Th. Raikoftsalis, Th. Schlumprecht, and D.Z. Zisimopoulou, Embedding Banach spaces into spaces with very few operators. J. Functional Anal. 262 (2012), no. 3, 825--849.
  29. K. Beanland and D. Freeman, Ordinal ranks on weakly compact and Rosenthal operators. Extracta Mathematicae, 26 (2) (2011), 173--194.
  30. S. Dilworth, D. Freeman, E. Odell, and Th. Schlumprecht, Greedy bases for Besov spaces. Constructive Approx., 34 (2011), no. 2, 281--296.
  31. D. Freeman E. Odell, and Th. Schlumprecht, The universality of l_1 as a dual space. Math. Annalen. 351 (2011), no. 1, 149--186.
  32. D. Freeman, E. Odell, Th. Schlumprecht, and A. Zsak. Banach spaces of bounded Szlenk index II , Fund. Math. 205 (2009) 161--177.
  33. D. Freeman, Weakly null sequences with upper estimates. Studia Math. 184 (2008), no. 1, 79--102.
  34. K. Dykema, D. Freeman, K. Kornelson, D. Larson, M. Ordower, and E. Weber, Ellipsoidal tight frames and projection decompositions of operators. Illinois J. Math. 48 (2004), no. 2, 477--489.

Invited Talks


  • Colloquium, University of Central Florida, Title: Stable phase retrieval, November 2022.
  • Plenary talk, Strobl22: Applied Harmonic Analysis and Friends, Strobl Austria, Title: Stable phase retrieval for finite and infinite dimensional subspaces, June 2022.
  • Computational Analysis Seminar, Vanderbilt University, Title: Stable phase retrieval for infinite dimensional subspaces, February 2022.
  • International Workshop on Operator Theory and its Applications, Special Session on operator ideals and operators on Banach spaces, Lancaster UK, Title: Banach spaces for which the space of operators has 2𝔠 closed ideals, August 2021.
  • Thematic Programme in Applied Functional Analysis and High-Dimensional Approximation, Erwin Schrodinger Institute, Vienna Austria, April-May 2021. (Cancelled due to COVID-19.)
  • Codes and Expansions Seminar, Zoom, Title: Discretizing Lp norms, March 2021.
  • Plenary talk, Strobl20: Applied Harmonic Analysis and Friends, Strobl Austria, June 2020. (Cancelled due to COVID-19.)
  • Banach spaces webinar, Zoom, Title: A Schauder basis for L2 consisting of non-negative functions, May 2020.
  • Analysis seminar, Georgia Tech, Title: Stable phase retrieval for subspaces of L2(R), March 2020.
  • Colloquium, Saint Louis University, Title: Stable phase retrieval for infinite dimensional subspaces of L2(R), February 2020.
  • Joint Mathematics Meeting, Special Session on Frames, Designs, and Optimal Spherical Configurations, Denver CO, Title: Stable phase retrieval from magnitude of point evaluation for infinite dimensional subspaces of L2(R), January 2020.
  • Colloquium, Acoustic Research Institute, Vienna Austria, Title: The discritization problem for continuous frames, June 2019.
  • Measure theory seminar, Kent State University, Title: Possible and impossible positive coordinate systems for L_p(R), April 2019.
  • Colloquium, Kent State University, Title: The discritization problem for continuous frames, April 2019.
  • Spring western sectional meeting of the AMS, Special Session on Banach Space Theory and Metric Embeddings, University of Connecticut Hartford, Title: Finite unit norm tight frames and the frame potential in Banach spaces, April 2019.
  • Joint Mathematics Meeting, Special session on AMS Special Session on Mappings on Metric and Banach Spaces with Applications to Fixed Point Theory, Baltimore MD, Title: Continuous Schauder frames for Banach spaces, January 2019.
  • Kosorok lab seminar, Department of Bio-statistics, University of North Carolina, Title: A friendly introduction to Hilbert spaces,January 2019.
  • Recent Advances in Functional Analysis, Kent State University, Title: Finite unit norm tight frames and the frame potential in Banach spaces, October 2018.
  • 7th International Conference on Computational Harmonic Analysis, Vanderbilt University, Title: The discretization problem for continuous frames, May 2018.
  • International Conference on Mathematics and Statistics, University of Memphis Title: Continuous Schauder frames for Banach spaces, May 2018.
  • Spring western sectional meeting of the AMS, Special session on wavelets, frames, and related expansions, Portland State University, Title: Finite unit norm tight frames and the frame potential in Banach spaces, April 2018.
  • Fall central sectional meeting of the AMS}, Special session on Banach Space and Applications, University of North Texas, Title: The discretization problem for continuous frames and coherent states, September 2017.
  • Spring Eastern sectional meeting of the AMS, Special session on Banach Space Theory and Metric Embeddings, Hunter College, Title: The discretization problem for continuous frames, May 2017.
  • INFAS, Creighton University, Title: The discretization problem for continuous frames, April 2017.
  • Spring Southeastern sectional meeting of the AMS, Special session on Frame theory, College Of Charleston, Title: The discretization problem for continuous frames and coherent states, March 2017.
  • Joint Mathematics Meeting, Special session on Bases in Function Spaces: Sampling, Interpolation, Expansions and Approximations, Atlanta GA, Title: The discretization problem for continuous frames and coherent states, January 2017.
  • Workshop in Analysis and Probability,Texas A&M University, Title: The Discretization Problem for continuous frames, July 2016.
  • International Wokshop on Operator Theory and Applications, Washington University in St Louis, Title: The Discretization Problem for continuous frames, July 2016.
  • Karcher Colloquium, University of Oklahoma, Title: Coordinate systems formed by translations of a single function in Lp(R), April 2016.
  • Frames seminar, University of Oklahoma, Title: Discrete and Continuous frames, April 2016.
  • Guilford physics reunion, Guilford College, Title: The discretization problem in math and physics, April 2016.
  • Fall Central sectional meeting of the AMS, Special session on Banach Spaces and Applications, University of Memphis Title: Weaving bases and frames for Banach spaces, October 2015.
  • Workshop in Analysis and Probability,Texas A&M University, Title: Weaving bases and frames for Banach spaces, July 2015.
  • Spring Central sectional meeting of AMS}, Special session on Frames, Wavelets, and their Applications, Michigan State, Title: An unconditional FDD of translations of a single function for Lp for p>2, March 2015.
  • Undergraduate Analysis Seminar, Washington and Lee University, Title: The Hairy Ball Theorem, October 2014.
  • Analysis Seminar, National Technical University of Athens, Title: Coordinate systems of translations of a single function in L_p(R), June 2014.
  • 7th Conference on Function Spaces, Southern Illinois University Edwardsville, Title: Unconditional coordinate systems formed by translations of a single function in L_p(R), May 2014.
  • 5th International Conference on Computational Harmonic Analysis, Vanderbilt University, Title: Coordinate systems of translates of a single function in L_p(R), May 2014.
  • Colloquium, University of Miami Ohio, Title: Redundant frames on Manifolds, November 2013.
  • Fall Central sectional meeting of AMS, Special session on Wavelets, Frames, and Related Expansions, Washington University in St Louis, Title: Dilations of Schauder frames for Banach spaces, October 2013.
  • Workshop in Analysis and Probability, The Mathematical Legacy of Ted Odell, Texas A&M University, Title: Greedy bases for Besov spaces, August 2013.
  • Banach Spaces: Geometry and Analysis, Memorial Conference for Joram Lindenstrauss, Hebrew University, Title: Equilateral sets in uniformly smooth Banach spaces, May 2013.
  • Spring Southeastern sectional meeting of AMS, University of Mississippi, Title: Equilateral sets in uniformly smooth Banach spaces, invited talk, Special session on Banach Spaces and Operators on Them, March 2013.
  • Larsonfest: Operator Algebras, Frames, and Undergraduate Research, Texas A&M University, Title: Frames of integer translates for L_p(R) with p>2, July 2012.
  • ICOMAS conference, session on Banach Space Theory and Applications in memory of Nigel Kalton, University of Memphis, Title: A frame of integer translates of a single function for L_p(R) with p > 2, May 2012.
  • Workshop on Banach space theory, Banff International Research Station, Title: Embedding into BD spaces and spaces with very few operators, March 2012.
  • Millican-Colloquium, University of North Texas, Title: Embedding Banach spaces and factoring operators, October 2011.
  • Workshop in Analysis and Probability, Texas A&M University, Title: Shrinking and boundedly complete Schauder frames for Banach spaces, July 2011.
  • Summer meeting of the CMS, session on "Banach Spaces and Operators Between Them", University of Alberta, Schauder frames for Banach spaces, June 2011.
  • Joint Linear Analysis/Banach space Seminar, Texas A&M University, Title: Weak Grothendieck compactness principles, May 2011.
  • Southeastern section meeting of the AMS, Special Session on Geometry of Banach Spaces, University of Richmond, Title: Redundant frames for vector bundles, November 2010.
  • Analysis Seminar, Virginia Commonwealth University, Title: Redundant frames on manifolds, September 2010.
  • VOTCAM, Virginia Commonwealth University, Title: Greedy bases for Besov spaces, September 2010.
  • Linear Analysis Seminar, Texas A&M University, Title: Embedding into L_infty Banach spaces, April 2010.
  • Workshop on Optimal Frames and Operator Algebras, San Francisco State University, Title: Embedding Banach spaces, January 2010.
  • SUMIRFAS, Texas A&M University, Title: The universality of l_1 as a dual space, August 2009.
  • Workshop on analysis and probability, Texas A&M University, Title: A greedy basis for (sum l_p^n)_q, July 2009.
  • Analysis seminar, University of Texas, Title: The universality of l_1 as a dual space, October 2008.
  • IMST conference, session on Banach Space Theory and Applications, University of Memphis Title: Weakly null sequences with upper estimates, May 2008.