Research Interests

A complete list of my publications is available below.


  1. Using Topological Data Analysis to Infer the Quality in Point Cloud-based 3D Printed Objects. Joint work with Paul Rosen, Junyi Tu, Tanvirul Arafin and Les Piegl. Submitted 2018. [PDF].


  1. Driving Interactive Graph Exploration Using 0-Dimensional
    Persistent Homology Features (Joint work with A. Suh, Bei Wang, Carlos Scheidegger, and Paul Rosen). Submitted 2017. [PDF].
  2. Distributed Mapper (Joint work with Basem Assiri and Paul Rosen).  Submitted 2017.[PDF].
  3. The Shape of an Image: A Study of Mapper on Images(Joint work with Alejandro Robles and Paul Rosen). Accepted to VISAPP 2018. [PDF].
  4. Unknotted Strand Routings of Triangulated Meshes, (Joint Work with Mohammed Abdulmelik ) International Conference on DNA-Based Computers, 2017. PDF.
  5. Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology.  (Join with with Paul RosenBei Wang and Carlos Scheidegger), Submitted. 2017.
  6. A Bi-Level Methodology for Identification of Types of Secondary Tasks from Observed Driving Behavior Data: Application of Ensemble Tree Machine Learning Algorithms on SHRP2 NDS Data, (Joint work with Osama Osman and Sogand Karbalaieali), 97th annual meeting of the transportation research board. under review, 2017.
  7. Graph Based Analysis for Gene Segment Organization In a Scrambled Genome, (Joint work with Natasha Jonoska,
    Denys Kukushkin, and Masahico Saito) submitted, 2017.
  8. On Rational Knots and Links in the Solid Torus, (Joint work with Khaled Bataineh, Mohamed Elhamdadi), submitted, 2017.
  9. Twist Regions and Coefficients Stability of the Colored Jones Polynomial (Joint work with Mohamed Elhamdadi and Masahico Saito), Accepted to Transactions of the AMS 2017. Arxiv version.
  10. The colored Kauffman skein relation and the head and tail of the colored Jones polynomial, Journal of Knot Theory and Its Ramifications 2017. Arxiv version.
  11. Generating sets of Reidemeister moves of oriented singular links and quandles, (Joint work with Khaled Bataineh, Mohamed Elhamdadi, William Youmans), submitted, 2017.
  12. Foundations of the Colored Jones Polynomial of singular knots, (Joint work with Mohamed Elhamdadi), Accepted to Bulletin of the Korean Mathematical Society, 2017. Arxiv version.
  13. Singular Knots and Involutive Quandles, (Joint work with Indu RU Churchill, Mohamed ElhamdadiSam Nelson) Accepted to Journal of Knot Theory and its Ramifications, 2017.


  1. Segmenting a Surface Mesh into Pants Using Morse Theory, (Joint work with Tamal Dey and Xin Li), 2016. Submitted.
  2. The colored Jones polynomial of singular knots (Joint work with Mohamed Elhamdadi), New York J. Math 2016. Arxiv version.
  3. Pretzel Knots and q-Series (Joint work with Mohamed Elhamdadi), Osaka Journal of Mathematics, 2016. PDF.


  1. The tail of a quantum spin network, The Ramanujan Journal, 2015.
  2. The Bubble skein element and applications, Journal of Knot Theory and Its Ramifications, 2015.


  1. Jones polynomial for links in the handlebody(Joint work with Khaled Bataineh), Rocky Mountain Journal of Mathematics, Vol. 43, No. 2, 2013.