David Matthew Freeman , PhD

I am a teacher and researcher in the field of Mathematics. I have taught a variety of courses, ranging from remedial Algebra to Calculus. My research is primarily focused on the geometry of metric spaces in relation to bi-Lipschitz and quasisymmetric mappings. I have also dabbled in the space between math and the visual arts. 

PhD in Mathematics: University of Cincinnati Cincinnati, OH, 2009 (Geometric Function Theory)

Bachelor of Science: Indiana University Bloomington, IN, 2004 (Mathematics)

Bachelor of Arts: Indiana University Bloomington, IN, 2004 (Studio Art)

Peer Reviewed Publications

Invertible Carnot Groups. Analysis and Geometry in Metric Spaces 2 (2014), 248-257.
 

Transitive bi-Lipschitz group actions and bi-Lipschitz parameterizations. Indiana Univ. Math. J. 62 (2013), no. 1, 311-331.

Inversion Invariant Bilipschitz Homogeneity. Michigan Math. J. 61 (2012), no. 2, 415-430.

Unbounded bilipschitz homogeneous Jordan curves. Ann. Acad. Sci. Fenn. Math. 36 (2011), no. 1, 81-99.

Bilipschitz homogeneous Jordan curves, Mobius maps, and dimension. Illinois J. Math. 54 (2010), no. 2, 753-770.

Bilipschitz homogeneity and inner diameter distance. J. Anal. Math. 111 (2010), 1-46. 

Epicycloid curves and continued fractions, Journal of Mathematics and the Arts, 11 (2018), no. 2, 100-113.

Generalized Palindromic Continued Fractions, The Rocky Mountain Journal of Mathematics, 48 (2018), no. 1, 219-236.

Toward a quasi-Möbius characterization of invertible homogeneous metric spaces, Revista Matemática Iberoamericana, 37 (2021), no. 2, 671-722.

Invited Presentations

David Freeman (09-2018. ) Quasi-Mobius Homogeneous Metric Spaces .Geometry of Metric Groups Seminar, University of Jyväskylä.

David Freeman (09-2017. ) Generalized Palindromic Continued Fractions .Special Session on Numbers, Functions, Transcendence, and Geometry - Sectional Meeting of the American Mathematical Society, University of North Texas.

David Freeman (05-2015. ) Inversion Invariant Homogeneous Metric Spaces .Modern Aspects of Complex Geometry: A Conference in Honor of Taft Professor David Minda, University of Cincinnati.

David Freeman (03-2014. ) Invertible Carnot Groups .Special Session on Complex Analysis, Probability, and Metric Geometry - Sectional Meeting of the American Mathematical Society, University of Tennessee.

David Freeman (02-2013. ) Bi-Lipschitz and Quasihomogeneous Parametrizations .Ohio River Analysis Meeting, University of Cincinnati.

David Freeman (11-2013. ) Invertible Carnot Groups .Mathematics Department Colloquium, University of Dayton.

David Freeman (01-2013. ) Inversion Invariant Homogeneous Metric Spaces .Department of Mathematics and Statistics Analysis Seminar, Bowling Green State University.