Math 665: Total Positivity

Professor: David E Speyer

Fall 2020

Course meets: Tuesday and Thursday, 11:30-1:00
Zoom number: 923 0365 1115 Password will be sent by e-mail; contact Professor Speyer if you wish to attend and didn't recieve an e-mail.
Office hours: Tuesday 1:30-3:00 PM and Friday 8:30-10:00 AM. Tuesday Zoom link: 925 1371 1581, Friday Zoom link: 946 4875 5047 . Password will be sent by e-mail.
Intended Level: Graduate students past the alpha algebra (593/594) courses. Students should be completely comfortable with abstract linear algebra and with combinatorial arguments.

Expected Work

Students are expected to attend the class Zoom meetings and actively participate in discussion. I am hoping to have some opportunity for collaborative work on most days, and in the final month of the term I want us to read and discuss papers. Your presence is important and valuable!

I will assign problem sets due on Fridays. I suspect these will be shorter than my usual problem sets: In the past, I have tried to assign a consistent amount of work on each problem set. This year, I am going to put problems on the problem set when I expect them to be useful or interesting for our discussion and stop when I run out of ideas for that, taking the old size of my problem sets as an upper bound. So I think these will be shorter, but I don't know.

Students will also be expected to take turns recording notes on what took place in class each day. I will assign two note takers to each date, as I think that the interactive form of class will make note taking more difficult. Notes are due 24 hours after class, and I encourage note takers to be faster.

Finally, in roughly November and December, I want to give the class over to discussion of papers on total positivity. Each student is required to select one paper to present and lead discussion of.

Homework Policy

You are welcome to consult each other provided (1) you list all people and sources who aided you, or whom you aided and (2) you write-up the solutions independently, in your own language. If you seek help from mathematicians/math students outside the course, you should be seeking general advice, not specific solutions, and must disclose this help. I am, of course, glad to provide help!

I don't intend for you to need to consult books and papers outside your notes. If you do consult such, you should be looking for better/other understanding of the definitions and concepts, not solutions to the problems.

You MAY NOT post homework problems to internet fora seeking solutions. Although I participate in some such fora, I feel that they have a major tendency to be too explicit in their help; you can read further thoughts of mine here. You may post questions asking for clarifications and alternate perspectives on concepts and results we have covered.

Problem Sets

Problem sets are due Fridays at 11:59 PM through Gradescope.

Summary of class, and worksheets

Disclaimer: I didn't produce complete worksheets for this class, as I might for a more polished IBL class. I am posting what I have prepared anyway in the hope that it is useful.

Course Notes

This course will feature day to day notes on what happened in class. Here they are!

All students will be required to take turns scribing notes for this file. When it is your turn to scribe, download the template file and write in a summary of what happened in class that day. Then e-mail it to me. The deadline for editing the update is 24 hours after the lecture. I will, in turn, proofread and edit your entries in the next 24 hours and post them back to this webpage, so that the class always has a good record of what we have covered. You are welcome to download and read the source of the notes but please do your writing in the template file; my experience is that it is easier for me to resolve merge conflicts when I copy your text into the master file than if you edit the master file directly.

If you do not know LaTeX, you should learn! I can suggest sources; I also find TeX.stackexchange incredibly useful for specific questions.

If you have forgetten when you are scheduled to scribe, you can check here.

Proposed papers for presentations

All students will be assigned to choose a paper to lead class discussion of. I'll put up more information about the structure of these presentations as the year goes on, but I am imagining something like 35 minutes of presentation, scheduled during class time, in the last two or three weeks of class.

Here are some suggested topics/papers; I am also very glad for you to suggest your own topics.