## Math 499 - Spring 2017

Topic
Diophantine m-tuples and elliptic curves
Instructors
Jen BergAnastassia Etropolski
Time
Friday, 12:00 - 12:50
Room
HBH 423
Office Hours
By appointment

### Calendar

Date Posted Assignment
1/20/17 You have a reading assignment for next week. Read the article "Diophantine Triples" up to (but not including) the section called Recurrence Relations. While you're reading, keep in mind the suggestions from the article "How to read mathematics". Verify calculations, mark anything you don't understand, and keep track of any questions that arise while you're reading. Be ready to discuss with your peers and with us next week.
1/30/17 Your assignment for Friday is to attempt these exercises. We will discuss the solutions on Friday and start talking about elliptic curves. As will be the norm, you do not need to write anything up.
2/7/17 Your assignment for Friday, February 17th is to read Section 1.4 (pg 23-27) of Silverman & Tate and do exercises 1.1, 1.19, and 1.20. While you don't need anything outside of 1.4 to do the exercises, we encourage you to read, or at least skim, the rest of the chapter as well as the introduction to the book. You should read Section 1.4 carefully and mark anything you find interesting or don't understand. This Thursday/Friday is Spring Recess, so we will not be meeting this week. If you're hungry for more, try out 1.10, 1.11, 1.17, and 1.18.
2/17/17 Next week we will be looking at Section 2 of this paper. (You may also want to consult this screenshot of a better defined version of the map defined in Section 2, with elliptic curve defined by y^2 = (x - alpha)(x-beta)(x-gamma).) The section references a "2-descent proposition", which you can find here.
2/25/17 Here is much clearer proof of Proposition 1 in the paper, as well as some magma code for how to find Diophantine quadruples. Read through this carefully and play around with the magma code and come ready to discuss some new material next week!
3/2/17 Tomorrow we will discuss Section 2 of this paper, specifically the part starting at the middle of page 641 with the definition of E_m. If you have some time, take a look at it before our meeting tomorrow. We will be sticking with this paper through spring break.
4/18/17 Please skim/read the paper we've been reading carefully for the past couple of weeks and come up with a few questions and ideas for where to go next with the topic.
Remaining Weeks: Student Presentations