Advanced reading course on cluster algebras and related topics. (Closely related to the Cluster Algebras + More 2025-2026 reading seminar.)
Bachelor students
I mentored students in the following projects.
Some names suppressed for privacy purposes.
Click an item to view more details.
Sam Farasyn and Mara Levrau
KU Leuven - Fall 2025
The students studied root systems of quiver respresentations, using a D6 quiver as an guiding example.
They then showed that one may explicitly compute a root system for the Lie algebra so12 using representations of their D5 quiver.
Along the way they computed all the indecomposable objects and irreducible morphisms in the category of representations of their quiver.
Ali Banga and Can Kadıoğlu
KU Leuven - Fall 2025
The students studied the connection between triangulations of the puncutred n-gon and the representation theory of Dn quivers.
As a guiding example, the students used a D5 quiver.
The students also formulated a way to compute the dimension of the Hom space between finite-dimensional (not necessarily indecomposable) representaitons of their quiver.
Along the way, they computed all the indceomposable representations and irreducible morphisms in the category of their representations.
Simeon Duwel and Nistor Mujdei
KU Leuven - Fall 2025
The students studied the homological algebra of Dynkin quivers using an E6 quiver as a guiding example.
They computed all the indecomposable representations and irreducible morphisms in their category of representations.
Moreover, they proved that the indecomposable objects in the bounded derived category of their representations are precisely the shifts of the original representaitons.
Spring 2020 at Brandeis University
Texts:
An Introduction to Category Theory by Harold Simmons
The Structure and Stability of Persistence Modules by Frédéric Chazal, Vin de Silva, Marc Glisse, and Steve Oudot
Spring 2018 at Brandeis University
Texts:
An Introduction to Category Theory by Harold Simmons
Elementary Categories, Elementary Toposes by Colin McLarty
Spring 2017 at Brandeis University
Texts:
An Introduction to Category Theory by Harold Simmons
Categories for the Working Mathematician by Saunders Mac Lane
Seminars
These are the seminars I have organized.
Currently just one but more in the future!
The goal of this seminar is to understand cluster algebras and how they relate to the following topcis:
surface triangulations,
quiver representations,
matroids,
and Grassmannians.
Courses
These are the courses I have been involved with, grouped by my role in the couse.
Below, "recitation" means directed sessions where the students are guided through exercises and solutions relavent to the recent lectures.
Focus on understanding applications of mathematical concepts and techniques; includes numbers, variables and units, algebraic functions, transcendental functions, calculus, complex numbers, first-order differential equations, and linear algebra
Co-planned course and co-wrote final exam in the scope of the university course description. There was no homework.
Co-graded final assessment.
Summer 2019 at Brandeis University (MATH 15a)
Matrices, determinants, linear equations, vector spaces, eigenvalues, quadratic forms, linear programming. Emphasis on techniques and applications.
Planned course, wrote exams, and coded online homework in the scope of the university course description.
Graded all assessments.
Summer 2018 at Brandeis University
Lecture Notes
Exercises
A refresh on point-set topology, an introduction to the notion of homotopy, and a brief introduction to the category of (based) topological spaces.
Taught in a 1-week prep camp for incoming graduate students.
Designed and conducted course (no assessment)
Spring 2018, Fall 2017, Spring 2017, and Fall 2016 at Brandeis University (MATH 10b)
Introduction to integral calculus of one variable with emphasis on techniques and applications.
Conducted course, wrote quizzes, assisted in writing of exams.
Graded quizzes and exams.
Spring 2014 at Purdue University Northwest (HONR 390)
An introduction to linguistics through the construction of one's own language.
Special topics course for honors students
Designed, conducted, and graded entire course.
As a course assistant
Spring 2025 and Spring 2026 at KU Leuven
Supervise 6 exercise sessions in the term
Fall 2018 at Brandeis University (LING 160b)
An introduction to fundamental mathematical concepts needed for advanced work in linguistics and computational linguistics.
Hold office hours.
Grade homework and exams.
Spring 2018, Fall 2017, Fall 2016, Spring 2016, and Fall 2015 at Brandeis University (MATH 15a)
Matrices, determinants, linear equations, vector spaces, eigenvalues, quadratic forms, linear programming. Emphasis on techniques and applications.
Conducted recitation and held office hours.
Graded exams.
Spring 2010 at Purdue University Northwest (MATH 315)
This course is a bridge from the mainly computational mathematics courses to the upper-level abstract courses. It focuses on the development of students' abilities to construct proofs, examples and counter examples.
Conducted recitation.
Summer 2010 and Spring 2010 at Purdue University Northwest (MATH 164)
Completion of introductory study of topics in plane analytic geometry and the calculus of one variable, infinite series.
Conducted recitation.
Graded homework.
Fall 2010 and Fall 2009 at Purdue University Northwest (MATH 163)
Topics from plane analytic geometry. Introduction to differentiation and integration. Applications.
Conducted recitation.
Graded homework.
As a course grader
Spring 2020 at Brandeis University (Math 151b)
Continuation of MATH 151a (Topology I). Manifolds and orientation, cup and cap products, Poincaré duality. Other topics as time permits.
Graded homework.
Fall 2019 at Brandeis University (MATH 40a)
Introduces the problems and issues of applied mathematics, with emphasis on how mathematical ideas can have a major impact on diverse fields of human inquiry.
Graded homework.
Spring 2019 at Brandeis University (MATH 121a)
Introduces a set of mathematical tools of great applicability to the natural sciences. It will prepare students to use these tools in concrete applications. Topics include complex numbers, power series, calculus of variations, and Laplace transform.
Graded homework and exams.
Fall 2018 at Brandeis University (MATH 23b)
Emphasizes the analysis and writing of proofs. Various techniques of proof are introduced and illustrated with topics chosen from set theory, calculus, algebra, and geometry.
Graded homework.
Fall 2014 at Brandeis University (MATH 8a)
Discrete probability spaces, random variables, expectation, variance, approximation by the normal curve, sample mean and variance, and confidence intervals.