Email: arianagchin@math.ucla.edu
Office: Mathematical Sciences (MS) 2361
Attached is my CV.
Papers
“Classification of Zamolodchikov periodic cluster algebras” [pdf] [arXiv:2510.18031].
2025
“F-Polynomial Ratios in the r-Kronecker” [pdf] [slides].
Joint work with Noah Caplinger, Nyah Davis, and Swapnil Garg. 2021
“Lattice Models and Puzzles for Dual Weak Symmetric Grothendieck Polynomials” [pdf] [slides].
Joint work with Elisabeth Bullock, Noah Caplinger, Nyah Davis, and Gahl Shemy. 2021
“The Polynomial Learning With Errors Problem and the Smearing Condition” [paper] [arXiv:2008.04459]
Joint work with Liljana Babinkostova, Aaron Kirtland, Esther Plotnick, and Vladyslav Nazarchuk. 2019
“The Ring Learning With Errors Problem: Spectral Distortion” [pdf] [arXiv:2007.13189]
Joint work with Liljana Babinkostova, Aaron Kirtland, Esther Plotnick, and Vladyslav Nazarchuk. 2019
Teaching
Math 184 – Enumerative Combinatorics
Spring 2024
Math 170E – Introduction to Probability and Statistics
Fall 2022, Winter 2023, Fall 2023 (Lectures 1 and 3), Spring 2025
Math 131A – Introduction to Real Analysis
Spring 2024, Fall 2024, Winter 2025 (Lectures 3 and 4), Fall 2025
Discussion worksheets: Week 1, Week 2, Week 3, Weeks 4-5, Week 6, Week 7, Weeks 8-9, Week 10
Math 61 – Introduction to Discrete Structures
Winter 2024 (Lectures 1 and 2), Spring 2025, Summer 2025
Discussion worksheets: Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10
Math 33A – Linear Algebra
Spring 2023
Math 32A – Multivariable Calculus
Fall 2024
Talks
Tiling Aperiodically with the Hat (June 2023) [slides]
A presentation of the viral paper introducing the first aperiodic monotile, a single shape that can tile the plane aperiodically. In this talk, we walk through the proof argument for aperiodicity, and examine the continuum of tiles presented in the paper. We also note the more recent discovery of Spectres, a family of strictly chiral aperiodic monotiles.
2-Calabi-Yau Triangulated Categories (June 2024) [notes]
An introduction to categorification of cluster algebras. This talk begins with an overview of cluster algebras, then discusses the motivation and applications of categorification. Finally, we give the complete construction of the cluster category for simply-laced Dynkin diagrams, as well as its cluster structure (what mutation looks like in cluster-tilting sets).
Auslander-Reiten Quivers as a Cluster Algebra of Type A (October 2024) [notes]
An exploration of Auslander-Reiten quivers in the context of Type A cluster algebras. This talk begins with an overview of Type A cluster algebras and then moves on to the construction of the cluster category for Type A. Finally, we present a way to view Auslander-Reiten quivers of Type A as a cluster algebra directly in terms of the triangulations of a regular n-gon.
Catalan Numbers (November 2025) [notes]
An overview of the history of the Catalan numbers, and a presentation of nine different combinatorial interpretations of the Catalan numbers: triangulations, binary trees, bracketings/parenthesizations, plane trees, ballot sequences, Dyck paths, noncrossing chords on a circle, 312-avoiding permutations, and 321-avoiding permutations. The notes from this talk draw heavily from Igor Pak’s history of the Catalan numbers, and Richard Stanley’s talk.
More About Me
I play violin! I also jointly organize the Women in Mathematics group at UCLA.