I am a first year math PhD student at Duke University. Prior, I was an undergraduate at the University of Maryland, where my advisor was Boyu Zhang. I am interested in a variety of topics, including differential geometry, algebraic geometry, knot theory, and applications of mathematics to biology and epistemology.
My email address is ezra.aylaian + @ + duke + . + edu.
Research Papers
- Tile Numbers of Knot Corner Mosaics. November 2023. arXiv:
2311.12258 [math.GT].
Research Talks
- Tile Numbers of Knot Corner Mosaics (Triangle Area Graduate Mathematics Conference, NC State), November 2, 2024
- Tile Numbers of Knot Corner Mosaics (Poster) (Nebraska Conference for Undergraduate Women in Mathematics, UN Lincoln), January 27, 2024
- Hierarchical Temporal Memory for Air and Missile Defense Applications (Military Operations Research Society Emerging Techniques Forum, JHUAPL), December 5, 2023 (Slides)
- Knot Corner Mosaics and Tile Numbers (Towson Undergraduate Mathematics Research Conference, Towson), April 22, 2023
- Three Theorems About Knot Corner Mosaics and Their Tile Numbers (Student Geometry and Topology Seminar, UMD), February 17, 2023
- Investigations of Hierarchical Temporal Memory (Nebraska Conference for Undergraduate Women in Mathematics, UN Lincoln), January 22, 2023
- Generalized Riemann Sums (Garden State Undergraduate Mathematics Conference, Virtual), April 2, 2022
- Generalized Riemann Sums (The Math Club, UMD), March 2022
Expository Talks
- The Isomorphism Between de Rham Cohomology and Cech Cohomology (Math 730, UMD), November 28, 2023
- Introduction to Knot Theory (Girls Talk Math, UMD), June 22, 2023
- Existence and Uniqueness of Stiefel-Whitney Classes (Student Geometry and Topology Seminar, UMD), May 12, 2023
- Sphere Eversion and the Whitney-Graustein Theorem (Math 848L, UMD), May 9, 2023
- The Tale of a Tricky Triangle: An Introduction to Moduli Spaces (The Math Club, UMD), April 17, 2023
- Integration on Manifolds and the de Rham Cohomology (Directed Reading Program Talks, UMD), December 8, 2022
- The History of Geometry: The Changing Nature of Math's Second Oldest Field (The Math Club, UMD), October 17, 2022
- The Poincaré and Super-Poincaré Algebras (Research Interaction Team on Geometry and Physics, UMD), October 13, 2022
- A Chic Card Trick (The Math Club, UMD), October 3, 2022
- The Model Geometries (Geometry and Topology Undergraduate Summer Workshop, Notre Dame), August 4, 2022
- Theory of Nonlinear Equations (The Math Club, UMD), December 2020
Teaching
- In Fall 2024, I mentored two undergraduate students through Duke Math's Directed Reading Program as they learned about metric spaces. At the end of the semester, they gave a presentation expositing a metric space proof due to Laidacker and Poole of the existence of a minimal convex worm blanket.
- In Fall 2022, I taught MATH 299R with Sam Lidz, which explored the way the philosophy of math interacts with math. We studied platonism, formalism, intuitionism, constructivism, finitism, and structuralism, the arguments for and against each, and the mathematical systems arising from them. A news article was written about MATH 299R and another student-run math course.
Service
- Duke University Libraries' Graduate and Professional Student Advisory Board, Fall 2024 - Spring 2025
- Triangle Competition in Mathematical Modeling Judge, Fall 2024
- UMD Math Department Climate Committee Undergraduate Representative, Fall 2023 - Spring 2024
- Treasurer of The Math Club at UMD, Fall 2022 - Spring 2023
Honors
Links