Terrence Blackman

Terrence Blackman

  • My Work

    • Mathematics

      I am a number theorist. I work on aspects of the Jacquet-Langlands correspondence in the Langlands program. To be specific: I study the discrete spectrum and the eigenfunctions of the Laplacian for a special class of ``arithmetic'' surfaces, namely those with constant negative curvature, finite area and a finite number of ``punctures'' or ``cusps''. These are of fundamental interest in mathematics and physics. Such surfaces are called hyperbolic and when we ``puncture'' them we have essentially removed a point from the surface and pulled it away to infinity. The ``arithmeticity'' of the surface relates to its association with subgroups of the modular group. The eigenfunctions are called Maass waveforms and they remain a mystery some now sixty years after their discovery. No explicit construction exists for any of these functions on the full modular group. Their existence and information about their eigenvalues come mostly from the Selberg trace formula and from conjectures supported by exhaustive numerical computations. Maass wave forms, non-Euclidean sine waves, arise naturally in such seemingly diverse fields as number theory, dynamical systems, statistical mechanics, quantum chaos in theoretical physics and cosmology. I investigate spectral correspondences predicted by the Jacquet Langlands Correspondence between the spectra of some finite area arithmetic surfaces without ``punctures'' and a related class of finite area surfaces with ``punctures".

      Mathematics Education

      I also work on promoting diversity in mathematics. My emerging research agenda is grounded in the pedagogical, content, soccio-economic, cultural and structural issues which inform the low rates of mathematics achievement by students of color. I want to increase the participation of underrepresented minorities in mathematics from grade school to graduate school. I focus on:
      (i) Strategies which enhance the mathematical preparedness of underrepresented students for college level mathematics and those which support access to meaningful mathematics while in college;
      (ii) Understanding and implementing strategies which foster retention and persistence in mathematics for all students but particularly those from underrepresented communities;
      (iii)Developing and understanding meaningful and innovative uses of emerging instructional technologies in support of mathematics instruction.
      (iv) Community/Social infrastructure that supports mathematics achievement in underrepresented communities, in particular, the challenges and opportunities for the development of institutional partnerships aimed at connecting mathematics to the community specifically the creating and sustaining of links between Middle Schools, High Schools, Two and four year College and Research Institutions in a particular geographic region.
      (v) Strategies to support the participation of members of underrepresented communities in research mathematics.
      (vi) The use of number theory in the teaching and learning of mathematics and in mathematics education research.
      (vii) Here are three resources that inform my thinking on mathematics and mathematics education: (a) The Mathematical Sciences in 2025(http://www.nap.edu/catalog.php?record_id=15269); (b) Fueling Innovation and Discovery: The Mathematical Sciences in 21st Century(http://www.nap.edu/catalog.php?record_id=13373); and (c) Expanding Underrepresented Minority Participation: America's Science and Technology Talent at the Crossroads (2011)(http://nap.edu/catalog.php?record_id=12984).

       

This portfolio last updated: Mar 30, 2015 11:50:43 AM