Spring 2026 Analysis Seminar

. Organizers: Lars Niedorf and Andreas Seeger

Emails:

• Lars Niedorf: niedorf at math dot wisc dot edu
• Andreas Seeger: seeger at math dot wisc dot edu

Time and Room: Wednesdays, 3:30--4:30 p.m., Room TBA

In some cases the seminar may be scheduled at different time to accommodate speakers.

If you would like to subscribe to the Analysis seminar list, send a blank email to analysis+subscribe (at) g-groups (dot) wisc (dot) edu

Links to previous seminars

Date	Speaker	Institution	Title	Host(s)	Notes (e.g. unusual room/day/time)
January 28	Shamgar Gurevich	UW Madison	How you think on a function defined on 0,1,…,N-1?
February 4
February 11
February 18
February 25
March 4
March 11	reserved (CL)			Niclas
March 18
March 25	---				No seminar, Spring break
April 1
April 8
April 15
April 22
April 29

Abstracts

Shamgar Gurevich

Title: How you think on a function defined on 0,1,…,N-1?

Abstract: Between thousand to million times per day, your cellphone calculates the Fourier Transform (FT) of certain functions defined on 0,1,…,N-1, with N large (order of magnitude of thousands and more). The calculation is done using the Fast Fourier Transform (FFT) - discovered by Cooley--Tukey in 1965 and by Gauss in 1805. In the lecture I want to advertise a beautiful way—due to Auslander-Tolimieri—to obtain the FFT as a natural consequence of an answer to the following:

Question: How to think on the space of functions on the set 0,1,…,N-1? Engineers tell us that there are two answers for this question:

(A) as functions on that set, where 0,1,…,N-1 regarded as times; and,

(B) as functions on that set, where 0,1,…,N-1 regarded frequencies;

and then the FT is an operator translating between the two spaces. In the lecture, I will explain that there is another answer, i.e., a not so well-known third space (C), of arithmetic nature, that also gives an answer to the above question, and then the FFT appears simply as the composition of two operators: the one translating between spaces (A) and (C), and the one that translates (C) to (B).

Remark: The lecture is prepared to be understood to anyone who is familiar with basic linear algebra. In particular, advanced undergraduate students, from computer science, engineering, mathematics, physics, etc, are more than welcome to attend.