# Biography

I am a lecturer in mathematics at University of Twente in the Netherlands. My research lies in the areas of probability theory, enumerative combinatorics, representation theory on symmetric groups, and analytic number theory. In probability theory and enumerative combinatorics my reseach has evolved around problems related to pattern avoiding permutations, card shuffling problems as well as random labellings on graphs. In analytic number theory my work involves representations of integers by quadratic forms, Theta function identities, determining the number of solutions of quadratic equations, and reciprocity laws for the Legendre symbol.

### Interests

• Probability Theory
• Markov Chain Theory
• Combinatorics
• Representation Theory of Symmetric Groups
• Analytic Number Theory

### Education

• PhD in Mathematics

University of Southern California

• MS in Mathematics

Bogazici University

• BS in Mathematics

Bogazici University

# Recent Publications

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(2019). Positive Integers Represented by Regular Primitive Positive-Definite Integral Ternary Quadratic Forms. In INTEGERS.

(2018). Positive-definite ternary quadratic forms which are (4,1)-universal and (4,3)-universal. In INTEGERS.

(2018). $(k,l)$-universality of ternary quadratic forms $ax^2 + by^2+ cz^2$. In INTEGERS.

(2016). Large deviations for permutations avoiding monotone patterns. In The Electronic Journal of Combinatorics.

(2015). Structure of random 312-avoiding permutations. In Random Structures & Algorithms.

(2015). Some new evaluations of the Legendre symbol $\left( \frac{a+b\sqrt{q}}{p}\right)$. In Acta Arithmetica.

(2014). On the number of representations of a positive integer as a sum of two binary quadratic forms. In International Journal of Number Theory.

(2013). What Does It Take to Teach Non-Majors Effectively?. In MAA FOCUS.

(2012). Some product-to-sum identities. In Journal of Combinatorics and Number Theory.

# Projects

#### Pattern-avoiding Permutations

An example of a project page.

# Teaching

I am currently teaching

• Calculus 1 for Applied Mathematics and Physics Majors
• Lectures
• Tutorials
• Team-Based Learning
• Discrete Mathematics for Computer Science Majors
• Lectures
• Tutorials

and have previously taught

• Abstract Algebra I & II
• Differential Equations
• Statistics I & II
• Matrix Algebra
• Discrete Mathematics
• Applied Multivariate and Vector Calculus
• Calculus I & II
• Precalculus I & II