Teaching and Outreach

My teaching spans different aspects of computational and discrete mathematics and theoretical computer science.

Current (2024)

Summer Semester

  • Exercise course on “Topics in Algebraic Combinatorics” (Section of Mathematics, University of Geneva)
  • Lab section of “Numerical Analysis” (Section of Mathematics, University of Geneva)

Winter semester

  • Graduate Seminar mini-course on “Using Computer Algebra” (Section of Mathematics, University of Geneva)

Past

Undergraduate courses

  • 2016 - 2022 Discrete Mathematics (obligatory in Computer Engineering department, Gebze Technical University)
  • 2019 - 2022 Probability and Statistics (obligatory in Computer Engineering department, Gebze Technical University)
  • 2017 - 2022 Theory of Computation (elective in Computer Engineering department, Gebze Technical University)
  • 2016 - 2022 Introduction to Symbolic Computation (elective in Computer Engineering department, Gebze Technical University)
  • 2016 Signals and Systems (obligatory in Computer Engineering department, Gebze Technical University)

Graduate (master’s and PhD) courses

  • 2017 - 2020 Algorithm Design and Analysis (obligatory in Computer Engineering department, Gebze Technical University)
  • 2016 - 2022 Symbolic Computation (elective in Computer Engineering department, Gebze Technical University)
  • 2019 - 2022 Special Topics in Algorithms (elective in Computer Engineering department, Gebze Technical University)

Master’s Theses supervision

  • Nurdan Ünlü (2019, co-advisor), Mathematics Department of Mimar Sinan Fine Arts University.

    ”Chow-Betti numbers and toric h-numbers of dual hypersimplices and Ehrhart polynomials of Minkowski sums with segments”

  • Büşra Sert (2019, co-advisor), Mathematics Department of Mimar Sinan Fine Arts University

    ”A study on the chamber complex”

  • Umutcan Önal (2020), Computer Engineering Department of Gebze Technical University

    ”Volume prediction for high dimensional polytopes with deep learning”

  • Hüseyin Sabri Aliefendioğlu (2023), Computer Engineering Department of Gebze Technical University

    ”Implementation and comparison of methods for real root isolation of univariate polynomials”

Outreach

Invited talks and lectures

Mar 14, 2024 International Conference on Modular Forms and q-Series (Koln, Germany)
Using Polyhedral Omega to study some integer partition problems
Mar 17, 2018 Ankara-Istanbul Algebraic Geometry & Number Theory Meetings (Ankara and Istanbul, Turkey)
Lecture topic ”(Sparse) Elimination Theory”
Jul 28, 2016 RIMS Workshop on ”Algebraic Statistics and Symbolic Computation” (Kyoto, Japan)
Lecture topic ”Polyhedra, Symbolic Computation and Applications”
May 12, 2016 Int. Conference on ”Algebra, Geometry and Topology of Singularities” (Istanbul, Turkey)
Efficient Computation of Dual Space and Directional Multiplicity of an Isolated Singularity

Seminars

Disseminating both new results and new perspectives on known topics is best done through seminars. Here is a selection of seminar talks:

Jan 29, 2024 Greek Algebra & Number Theory Seminar (online)
Linear Diophantine Systems, Integer Partitions, Polyhedra and Applications
May 23, 2023 Lyon 1 - Combinatorics and Number Theory Seminar (Lyon, France)
Polyhedral Omega (+ applications)
Nov 30, 2022 TU Berlin DMG Seminar (Berlin, Germany)
Polyhedral Omega (+ applications)
Oct 12, 2022 Sabancı Algebra Seminar (Ankara, Turkey)
From Sylvester to van der Waerden and beyond
Apr 05, 2022 Institute of Applied Mathmatics (METU) General Seminar (Ankara, Turkey)
Using Polyhedral Geometry for Integer Linear Programming
Dec 11, 2019 Bilkent Algebra Seminar (Ankara, Turkey)
Solving linear Diophantine systems via Polyhedral Omega and applications in optimization
May 10, 2017 Sabanci Engineering and Natural Sciences Colloquium (Istanbul, Turkey)
To err is human and computers can do without it
Mar 10, 2017 Gebze Technical University General Math Seminar (Istanbul, Turkey)
Polyhedral Omega: Solving Linear Diophantine Systems
Nov 24, 2016 Bilkent University Algebra Seminar (Ankara, Turkey)
Polyhedral Omega: Solving Linear Diophantine Systems
Oct 03, 2016 TU Wien - Formal Methods in Systems Engineering Seminar (Vienna, Austria)
Polyhedral Omega: Solving Linear Diophantine Systems
Dec 03, 2015 Yildiz Technical University Math Seminar (Istanbul, Turkey)
Polyhedral Omega: A linear Diophantine system solver
Nov 11, 2015 Galatasaray University Math Seminar (Istanbul, Turkey)
Polyhedral Omega: A linear Diophantine system solver
Oct 25, 2015 Mimar Sinan University of Fine Arts Math Seminar (Istanbul, Turkey)
Polyhedral Omega: A linear Diophantine system solver
Apr 30, 2015 Koç University Math Seminar (Istanbul, Turkey)
A century of Partition Analysis
Apr 29, 2015 Bosphorus University Math Seminar (Istanbul, Turkey)
Polyhedral Omega: A linear Diophantine system solver
Nov 07, 2014 U. of Minnesota Combinatorics Seminar (Twin Cities, USA)
The geometry of partition analysis
Aug 13, 2013 PennState Partitions Seminar (PennState, USA)
The geometry of partition analysis
Oct 29, 2012 ERGA Seminar, University of Athens (Athens, Greece)
Polyhedral geometry for linear diophantine systems
Apr 17, 2012 UC Davis Algebra and Discrete Math Seminar (Davis, USA)
Partition Analysis and its Polyhedral Geometry
Jun 01, 2011 RISC Algorithmic Combinatorics Seminar (Hagenberg, Austria)
Polyhedral geometry - an introduction
Nov 25, 2009 RISC Algorithmic Combinatorics Seminar (Hagenberg, Austria)
Multivariate real root isolation - theory and practice

IMU project “Training Mathematicians in Computation”

The project’s goal was to organize a series of “Experimental Mathematics Meetings” in different cities in Turkey, training mathematicians in computational methods.

Nesin Math Village (Nesin Matematik Köyü)

The Nesin Math Village is a village near Selcuk (Izmir, Turkey), where people of all ages and backgrounds can enjoy mathematics.

Every summer there is a summer school for undergraduate and graduate (mostly math) students with a very large variety of course topics. Since 2010 I have been teaching courses (1 or 2 weeks of lectures) related to computational aspects of mathematics whenever possible:

Polynomial System Solving (2010), Solving Linear Diophantine Systems (2011), Geometry and Number Theory (2012), Geometry that counts (2015), Algorithmic Algebraic Geometry (2015), Symbolic Computation (2016), Combinatorial Counting (2017), Introduction to Polyhedral Geometry (2018), Polyhedral Combinatorics (2019), Symbolic Computation (2022).