I am a fourth year math major at the University of Maryland where I study geometry and topology. I work at the Johns Hopkins University Applied Physics Laboratory. My primary interests are differential geometry, algebraic topology, gauge theory, and low-dimensional geometric topology. My advisor is Boyu Zhang.
My email address is daylaian + @ + umd + DOT + edu.
Research Papers
- Tile Numbers of Knot Corner Mosaics. November 2023. arXiv:
2311.12258 [math.GT].
Research Talks
- 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
Honors
- Milton Abramowitz Award issued by UMD Math Department in May 2023
- Departmental honors program, expected to graduate with High Honors
Teaching
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
- Undergraduate Student Representative on the UMD Math Department Climate Committee, Fall 2023 - Spring 2024
- Treasurer of The Math Club, Fall 2022 - Spring 2023
Links