18.704
In 18.704, students take turns presenting the subject matter week by week. The Spring ’22 topic is harmonic analysis on finite groups and its applications. In the first half of the course, we introduce the discrete Fourier transform and apply it to graph theory, probability, coding theory, and physics. In the second half, we discuss its nonabelian generalization, focusing on matrix groups over finite fields.
pdf Syllabus
pdf Tentative schedule
Time & Place: MWF, 1–2 PM, Room 2-151
Textbook: Terras, Fourier Analysis on Finite Groups and Applications
Notes
pdf My notes for the first week
pdf Susan Ruff’s slides about known vs. new information in scientific writing
pdf Xiangkai’s notes on Laplacians and their spectra
Final Papers
Krit Boonsiriseth | Radar Cross-Ambiguity and the Heisenberg Group | |
Merrick Cai | The Volume of \(\mathrm{SL}(2, \mathbb{Z})\backslash \mathrm{SL}(2, \mathbb{R})/\mathrm{SO}(2, \mathbb{R})\) | |
Chang-Han Chen | Conjugacy Classes of \(\mathrm{GL}(2, \mathbb{F}_q)\) | |
Matthew Cho | The Wavelet Transform | |
Matthew Cox | The Poincaré Upper Half-Plane | |
Rupert Li | Mackey–Wigner’s Little Group Method with an Application to \(\mathrm{Aff}(q)\) | |
Atharv Oak | \(k\)-Bessel Functions as Eigenfunctions of the Laplacian | |
Jeffery Opoku-Mensah | Constructing the Discrete Series Representation of \(\mathrm{GL}(2, \mathbb{F}_q)\) | |
Tristan Shin | Quadratic Reciprocity and Gauss Sums | |
Carlos Solano | Exceptional Isomorphisms of \(\mathrm{SL}\), \(\mathrm{PSL}\) in Rank \(2\) | |
Xiangkai Sun | Criteria for Finite Symmetric Spaces | |
Derrick Xiong | On the Finite Upper Half Plane | |
Jessica Yuan-Chen Yeh | Conjugacy Classes and Irreducible Representations of \(\mathrm{Heis}(q)\) |