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research interests

frame theory, operator theory, matrix theory, projective geometry and the mathematical theory of perspective drawing


curriculum vitae
CV (updated 2/2013)

publications
A. Crannell, M. Frantz, F. Futamura, The Cross ratio as a parameter for Dürer's solid (Party game for a 500th anniversary) J. Math. Arts, accepted and online (2014).

A. Crannell, M. Frantz, F. Futamura
Dürer: Disguise, Distance, Disagreements, and Diagonals! Math Horizons, 22 no. 2, (2014) 10-11.

R. Denman, F. Futamura, K.C. Richards, On sharp frame diagonalization, Linear Algebra Appl., 438 no. 5, (2013) 2210-2224.

F. Futamura, Frame diagonalization of matrices, L
inear Algebra Appl., 436 no. 9, (2012) 3201-3214.

F. Futamura,  Localizable operators and the construction of localized frames, Proc. Amer. Math. Soc., 137 (2009) 4187-4197.

F. Futamura, Symmetrically localized frames and the removal of subsets of positive density, J. Math. Anal. Appl., 326 no. 2, (2007) 122-1235.

F. Futamura, Banach framed, decay in the context of localization, Sampl. Theory Signal Image Process., 6 no. 2, (2007) 151-166.

grants
2012: NSF-DUE TUES Type I grant, awarded $69,432 for the project, "Perspective Geometry: Projective Geometry Applied to Perspective Art".

presentations

conference and seminar talks
:
Jan 2013: Sharp Diagonalization of Matrices, Joint Mathematics Meetings, San Diego, CA

Apr 2012: Drawing Chords:  Harmonic Sets in Math, Music & Art, Joint Math Colloquium, Franklin & Marshall College

Jan 2011: Exploring Diagonalizable and Localizable Operators, Analysis Seminar, University of Houston

Apr 2010: Frame Multipliers and Commutative Banach Algebras, Meeting of the AMS, St. Paul, MN

Oct 2009: Approximate Joint Diagonalization of Matrices, Meeting of the AMS, Boca Raton, FL

Aug 2007: Localized Frames and Localizable Operators, SPIE Optics and Photonics Conference, Wavelets XII, San Diego, CA

Jan 2007: Selected poster presentation: Localized Operators and the Construction of Localized Frames, AWM Workshop for Women Graduate Students and Recent PhDs, Joint Mathematics Meetings, New Orleans, LA.

Oct 2006: Localized Operators and the Construction of Localized Frames, Analysis Seminar, Texas A&M University

Oct 2006: Localized Operators and the Construction of Localized Frames, Computational Mathematics Seminar, Sam Houston University

Oct 2006: Localized Operators and the Construction of Localized Frames, Wavelets Seminar, University of Houston

Sept 2006: Localized Operators and the Construction of Localized Frames, Computational Analysis Seminar, Vanderbilt University

Aug 2006: Localized Operators and the Construction of Localized Frames, International Conference of Harmonic Analysis and Applications, San Luis, Argentina

May 2006: Symmetrically Localized Frames, Current Trends in Harmonic Analysis and Its Applications: Wavelets and Frames, University of Colorado at Boulder

May 2005: On Localized Frames, International Conference on Modern Methods of Time-Frequency Analysis, Strobl, Austria

March 2005: On Localized Frames, Computational Analysis Seminar, Vanderbilt University

Mar 2005: On Localized Frames, Southeastern Sectional Meeting, Western Kentucky University

May 2002: On the Use of Polygonal Diagrams to Depict Finite Affine Planes, Annual Meeting of KYMAA

undergraduate seminar talks
Feb 2012: Mathematics of Wonderland, SU MAA Chapter meeting, Southwestern University

Feb 2011: Drawing Humpty Dumpty in Perspective, an excursion through math, art, literature, philosophy and music, SU MAA Chapter meeting, Southwestern University

Oct 2006: Intersections and Parallels, the Perspective of an Artist Turned Mathematician
Pi Mu Epsilon, Sam Houston University

Oct 2005: Mathematical Influences in Art, from Picasso to Escher to Man Ray
Undergraduate Seminar in Mathematics, Vanderbilt University

May 2005: Whistling Girls and Crowing Hens:Women in Mathematics from Ancient to Modern Times (joint talk with Dr. Jo Ann Staples)
Undergraduate Seminar in Mathematics, Vanderbilt University

Mar 2005: The Poincare Conjecture
Vanderbilt Math Club, Vanderbilt University

Nov 2004: Phi
Undergraduate Seminar in Mathematics, Vanderbilt University