Project 1:Worked on one-sided and two-sided assignment problems under the supervision of Buğra Çaşkurlu and Özgün Ekici. Explored the literature, analyzed the papers, learned the algorithms and their properties, and implemented 10 of them in C++. Then, coded the simulation to empirically compare the performances of two algorithms for the one-sided assignment problem, gathered data, and analyzed it. The paper will be ready to be sent to a journal soon.Project 2:Our aim is to extend the literature on distortion in social choice problems. Have been meeting with my professors, reading influential papers, analyzing the proofs, and improving proof-writing skills in theoretical computer science. The project is on hold.Project 3:Building on the previous 2 papers on Hedonic Expertise Games and Hedonic Games with Common Ranking Property by Prof. Caskurlu et al. Currently generalizing the past results and completing the analysis of the existence, complexity, and approximation of various stability concepts in Hedonic Games with Common Ranking Property. Have been finding innovative ways to model real-life scenarios with different types of hedonic games and analyzing these interesting applications mathematically.

Met with professors, attended seminars on current research and career experience in academia and industry.

Coded a simulation and developed efficient algorithms to compute various probabilities relating to the Poisson distribution.Conducted numerical experiments bounding the critical drift for the frog model, then proved them rigorously.Paper “Improved critical drift estimates for the frog model on trees” submitted to Electronic Communications in Probability.

Tutored students taking MA274: Mathematical Reasoning and MA253: Linear Algebra in weekly tutoring sessions. Graded weekly homework and provided constructive feedback and hints. Reported outcomes to and consulted with the professors on work progress. Made sure every student got the help they needed by individually helping them and referring them to the professors.

After being selected as a Presidential Scholar, I started working on knot theory under the supervision of Taylor Scott. I self-studied the famous textbook "The Knot Book" by Colin Adams, and followed countless online lectures to get used to the field. I've used Snappy and Orb, two packages for studying topology and geometry of 3-manifolds, and I'm now analyzing the source codes of both packages to add more functionality, especially in the study of theta curves. Our research now focuses on the classification and the properties of theta curves.

Worked on the additivity of Gabai width, a knot invariant. Invented and analyzed different ways of switching between tree representations and path representations of knots by a sequence of “pathizing” moves on compression bodies. Studied the literature on Gabai width with an emphasis on Prof. Taylor and his colleagues’ papers. Proved lemmas and constructed counterexamples. Presented our findings at CUSRR at Colby and at JMM 2023 in Boston.

Guided 10s of aspiring olympiad students. Spearheaded a curriculum and corresponding problem sets for 40 topics. Prepared and organızed weekly lectures and additional problem-solving sessions for the use of non-members. Engaged with other successful programmers including IOI medalists to organize workshops.

Ranked 2nd place at the Turkish Regionals in our first year, 2019. Managed and guided a group of 5 programmers, wrote and oversaw 100s of lines of code.Organized RC Maker Faire, one of the biggest maker faires in Turkey, for 400+ students and 30+ high schools. Connected to sponsors and professors for funding and workshops on topics like AI, autonomous vehicles, and IoT.Worked on personal projects like guitar playing robotic arms.

Was invited to a total of 4 training camps. Took lectures from professors and mentors with IOI medals. Learned many different algorithms and data structures, solved problems, and competed in daily contests.

In an elite group of ~10 students that contains IOI medalists, learned advanced algorithms and data structures, and practiced them by solving competitive programming problems. Participated as the only high school student.

A program intended to teach advanced algorithms and data structures for undergraduate students from the most selective universities in Turkey. Participated as the only high school student. Attended lectures and solved problem sets on algorithms and data structures every week.

Attended different programs in consecutive 4 summers. The programs are as follows:Nevzat Kaptan: An introduction to higher maths with Number Theory, Set Theory, and Combinatorics classes.Real Analysis: Foundations of Analysis, Calculus, Sequences, and Series, Inequalities.Abstract Algebra: Groups, Rings, Fields.Undergraduate Program: Got in as an exception. Took classes ranging from Linear Algebra to Game Theory.

Implemented the Hermite Normal Form for p-adic numbers on SageMath using Python, and explored computational number theory, linear algebra, and abstract algebra under Nadim Rustom.

Participated in the FIRST Robotics Competition 2017 and ranked among the best 8 teams in Turkish Nationals. Worked in the programming subgroup focusing on the correct and efficient movement of the robot.

Got introduced to STEM by conducting experiments and working on projects, along with taking English classes.