Research Projects

Structure Learning for Bayesian Networks

A Machine Learning research paper which explored and compared different methods and algorithms to learn the structure of Bayesian Networks. It consists of the following sections,

• Discussion of the 3 broad categories of algorithms: constraint-based, score-based, and hybrid, including their mathematical significance and examples/simulations.
• An evaluation of the optimality of the algorithms in terms of space and time complexity
• Applying each algorithm to a music recommender system to observe and compare results on real-world data.

The Impact of Political Symbols on Electoral Success in Turkey

I collaborated with a professor and fellow students to contribute towards a research paper on political propaganda in Turkey, contributing to the technical development of large-scale image collection, preprocessing, and computer vision analysis.

• I helped build a Google Maps API–based pipeline to collect and geocode approximately 750,000 panoramas from Istanbul for political propaganda analysis.
• I assisted in the preprocessing and annotation of nearly 7000 images while exploring equirectangular undistortion, different sampling techniques, and duplicate filtering.
• I trained YOLOv8 models in Roboflow to detect party and national flags, and evaluated depth estimation models for symbol surface area analysis.
• I created district-level geospatial visualizations in Python, mapping propaganda density across Istanbul.

Geometric Transformations of the Complex Plane

A mathematical paper exploring increasingly expressive classes of geometric mappings on the complex plane, organized by the geometric quantities they preserve. Beginning with conformal maps (which preserve the angle between any 2 curves), the paper progresses through stereographic projection, primitive isometries, and linear transformations, culminating in the rich theory of Möbius transformations. It shows how complex analysis and geometry are deeply intertwined, and how the former can be immensely helpful in understanding geometric transformations - be it in 3D graphics, physics, or pure mathematics. A more rigorous and detailed summary of the paper's findings is as follows:

• Establishes the equivalence between conformal maps and analytic functions with non-vanishing derivative, using the complex exponential as a worked example and stereographic projection to motivate the extended complex plane.
• Formalizes the primitive isometries of the complex plane — translations, rotations, and reflections — alongside dilations and inversions, proving precisely which preserve distances, angles, or both.
• Shows that linear transformations z ↦ az + b form a group under composition and decompose into rotations, dilations, and translations, mapping geometrically similar figures to one another.
• Proves that Möbius transformations form a group that is the homomorphic image of GL₂(ℂ), decompose into all four primitive maps, and are uniquely determined by their action on any three distinct points of C∞.

Metric Spaces: The Mathematics of Distance and Similarity

An intuitive exposition of metric spaces designed for a general audience, introducing the formal definition of a distance function and its core properties. Explores real-world and computer science applications (such as recommendation systems, search heuristics, and edit distance) to illustrate how these abstract mathematical structures are all around us.