Embedded Files
PCMI Lecture Notes
PCMI Lecture Notes
Graduate Students
Graduate Students
Current students:
Current students:
Filip Kucerak (coadvised with Dan Kral).
Varun Sivashankar (coadvised with Noga Alon).
Visiting students:
Visiting students:
Alp Müyesser (VSRC, funded by a Cecil King Grant, Spring 2024).
Micha Christoph (visiting graduate student, Spring 2024).
Current Teaching
Current Teaching
Semester: Fall
Semester: Fall
Academic year: 2024/2025
Academic year: 2024/2025
More abstract than calculus, this course aims to develop basic algebraic tools for work with problems involving many variables. Starting from systems of linear equations and vectors in 2-space and 3-space, this course develops ideas about length, angles and resolving a general vector into useful components, identifying features of linear systems or processes in order to choose a basis that is well-adapted to studying a particular phenomenon and move between different points of view to reveal the essential underlying structure. Companion course to 201 (Multivariable Calculus). Discusses matrices and linear transformations, linear independence and dimension, bases and coordinates, determinants, orthogonal projection, least squares, eigenvalues and their applications to quadratic forms and dynamical systems.
Past Teaching
Past Teaching
Princeton:
Princeton:
Spring 2024 - lecturer Linear Algebra with Applications
Fall 2023 - lecturer Combinatorial Mathematics.
Spring 2022 - lecturer Linear Algebra with Applications.
Fall 2021 - lecturer Combinatorial Mathematics.
Structural Graph Theory Bootcamp, Warszaw:
Structural Graph Theory Bootcamp, Warszaw:
Fall 2023 - lecturer (invited mini-course) Recent progress towards the Erdős-Hajnal Conjecture
ETH:
ETH:
Spring 2021 - course organiser Graph Theory
Fall 2020 - course organiser Probabilistic Methods in Combinatorics
Spring 2020 - teaching assistant, course organiser Graph Theory
Fall 2019 - teaching assistant, course organiser Algebraic Methods in Combinatorics
Spring 2019 - teaching assistant, course organiser Graph Theory
Spring 2018 - teaching assistant Graph Theory
Mentoring
Mentoring
At Princeton I had a pleasure of supervising:
At Princeton I had a pleasure of supervising:
Pablo Blanco-Hinojosa, for a Summer Research Project, resulting in the following publication:
Towards the Erdős-Hajnal Conjecture for P_5-free graphs, published in RMSB.Icey Siyi Ai, for a Summer Research Project titled: Edge Reconstruction Number for Regular Graphs, published in Princeton Undergraduate Research Journal. Icey was awarded a Peter A. Greenberg prize in part based on this work.
Robert Rubin, for a Junior Paper, resulting in the publication: Ramsey numbers of nK_4, in preparation. Robert was awarded a PACM independent project award for his work on this project.
Judah Koslowe for his Senior Thesis titled: Uniformly biased tournaments.
George Bentley for his Junior Paper titled: On unavoidable r-uniform hypergraph.
At ETH I had a pleasure of (co)supervising:
At ETH I had a pleasure of (co)supervising:
Domagoj Bradač, for his Master Thesis, resulting in the following publication:
Covering Random Graphs with Monochromatic Trees, published in RS&A.Vedran Mihal, for his Master Thesis: Generalised Ramsey Theories
Michelle Sweering, for her Master Thesis: Covering Problems in Hypergraphs
Erik Jahn, for his Bachelor Thesis, resulting in the following publication:
2-factors with k cycles in Hamiltonian graphs, published in JCTB.Michelle Sweering, for her Semester project: Combinatorial Perspective on the Log-rank Conjecture
Sven Heberle, for his Master Thesis resulting: in the following publication:
Monochromatic trees in random tournaments, published in CPC.
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