I am interested in applications of algebra to problems outside mathematics. At Berkeley I am working with Eva Nogales (Molecular & Cell Biology) and Bernd Sturmfels (Mathematics) to develop new algorithms for 2D->3D reconstruction in cryo-electron microscopy.
Martin and I organize the interdisciplinary Applied Algebra Seminar. If you're interested in giving a talk, please email us!
I completed my PhD in May 2015 with Shamgar Gurevich.
Gender discrimination remains a significant problem in science in general, and in mathematics in particular (page 11). Women in math face hostile work and educational environments and are forced to fight outdated gender stereotypes at all stages of their education and careers. Please consider supporting organizations working to combat inequality in science, such as the Association for Women in Mathematics.
- Applications of algebra to structural biology
- Real algebraic geometry
- Implementing algorithms based on these ideas
I am interested in applications of algebra to problems outside mathematics. My thesis uses tools from real algebraic geometry and group theory to study the geometry and symmetry of datasets produced in cryo-electron microscopy (cryo-EM). Cryo-EM is a technique used in structural biology to produce 3D models of proteins from very noisy 2D projections.
My thesis consisted of two projects:
- Chapter 2, "Semi-algebraic geometry of common lines", descrbes the geometry of "common lines" datasets. Common lines datasets are computed from images produced in cryo-electron microscopy (cryo-EM), and can be used to build 3D models of biological molecules from 2D projections.
- Chapter 3, "A remark on detecting 3D molecular symmetries from 2D cryo-EM images", describes an algorithm for computing the 3D symmetries of a biological molecule from 2D cryo-EM images.
- David Dynerman, Shamgar Gurevich, and Yoel Shkolnisky. A remark on detecting molecular symmetry from cryo-EM images. In preparation. 2014.
- David Dynerman. Semi-algebraic Geometry of Common Lines. Research in the Mathematical Sciences, December 2014.
- David Dynerman, Erick Butzlaff, and Julie C. Mitchell. CUSA and CUDE: GPU-Accelerated Methods for Estimating Solvent Accessible Surface Area and Desolvation. Journal of Computational Biology. 2009.
- FlowSym: A flowchart algorithm for detecting molecular symmetry from cryo-EM images. In preparation.
- CUDESA: GPU accelerated code for calculating solvent accessible surface area and desolvation for protein-protein interfaces. Download. 2008.