Google

Software Engineer

Roman worked at Google as a Software Engineer

Microsoft

SDE Intern

A project in software defined networking

Texas A&M University

Graduate Instructor/Teaching Assistant

Recitations, Labs and grading for various courses (from Calculus to Differential Geometry) Calculus instructor.

Texas A&M University

Organized an activity for visitors out of 3D printed mathematical toys and puzzles. Helped create a positive image for the department, impact the community via positive outreach, and promote mathematics and education.

Cadence Design Systems

Intern-Software Engineering

OPC/modeling team

Cadence Design Systems

Software Development Engineer

Computational Lithography team. This Wikipedia article is a good intro to what we do:

https://en.wikipedia.org/wiki/Optical_proximity_correction

Projects completed:
-Fast, accurate mask corner rounding model which approximates the Gaussian-convolution corner rounding model for the case of large geometry (relative to CR radius), and approximates the MPC-corrected mask for small geometry (SRAF's, which would disappear after convolution).
-Single-martrix-multiplication method to scale Zernike coefficients when NA changes, and Zernike basis change trasnformation
-Improved resist diffusion model
-Forwards- and backwards-compatible ORM/serializatoin framework for internal use
-Networked caching layer with switchable backends
-Fast contour biasing algorithm that works on 2D intensity data
-Gaussian Curvature computation module
-Illumination source boundary improvement
-Process window computation speedup
-Internal Wiki

On a Basis for the Framed Link Vector Space Spanned by Chord Diagrams

Journal of Knot Theory and Ramifications

A Vassiliev knot invariant is determined by its values on chord diagrams. These values cannot be arbitrary, as they have to satisfy certain relations; a valid assignment is called a weight system. However, one can pick a basis for the algebra of chord diagrams so that a weight system would be determined by assigning values to the basis. The project computes a basis for the space of chord diagrams of colored framed links with up to 6 chords and components. The work follows one of Dror Bar-Natan who did a similar study for knots.