About

My research is interdisciplinary. I use tools from discrete calculus, functional analysis, measure theory, differential and computational geometry, and algebraic topology in developing methods for solving PDEs or constructing theoretical frameworks or computational interfaces for various computer science and engineering problems. The areas of my interest are computational fluid dynamics, multi-physics and multi-scale modeling, solid modeling, electromagnetism and interoperability.

I obtained my Ph.D. and M.Sc. in Mathematics from the University of Pittsburgh under the supervision of Prof. Michael Neilan. My expertise lies in Numerical Analysis and Scientific Computing. I have taken my comprehensive exams in Finite Element Analysis, Partial Differential Equations and Differential Geometry. My M.Sc. thesis concerned the construction of a finite element method for the Stokes problem on rectangular meshes, and my Ph.D. dissertation concerned the construction of finite element methods for the Stokes and Navier-Stokes problems on cubical (with an extension to n-dimensions) and quadrilateral meshes. I have also completed M.Sc. in Electronics & Communication Engineering with a focus on the electromagnetic theory at Istanbul Technical University under the supervision of Prof. Ibrahim Akduman.

My postdoctoral research at the International Computer Science Institute at the UC Berkeley, concerned building a theoretical and an algorithmic framework for the interoperability between CAD systems based on the interchangeability of their models. I worked under the supervision of Prof. Vadim Shapiro. I also provided mathematical reviews for some of the existing geometry validation tools and techniques in industry and military standards.

During my first postdoctoral research at the University of Oxford I worked on developing NURBS-Enhanced finite elements and building an interface to integrate several geometry and analysis tools. I worked under the supervision of Prof. Nik Petrinic. I also worked on the adaptive multi-scale modeling of stress wave propagation in solids and BGG complexes with colleagues from Engineering or Maths departments. In my second postdoctoral research, I have worked with Prof. Patrick Farrell on transient multicomponent fluid flow modeling.

In my current role at the University of Warwick, I provide consultancy to companies on their challenges and contribute to brainstorming sessions that lead to grant proposals. I develop innovative solutions to problems posed by academics from a wide range of disciplines as well as by industry partners. My work is highly interdisciplinary, and depending on the project, I may work as a mathematician, computer scientist, or engineer. I dedicate my remaining time beyond project work to independent or collaborative research. One of the projects I worked on at CAMaCS was an Innovate UK initiative focused on the applications of AI algorithms to image categorization and retrieval. Another project I worked on involved visualizing sensor data collected from a railway system over different time intervals using Topological Data Analysis (TDA) to connect physical events to the topological signatures of the data.