Students should be familiar with first courses in algebraic number theory and in analytic number theory.
Preparatory Reading for certain mini-courses. Each of the following are about 30 pages long:
- Louis-Pierre Arguin “Extrema of Log-Correlated Processes” : Extrema of Log-Correlated Random Variables: Principles & Examples
- Tim Browning (IST Austria): “Beginners guide to the circle method” by Andrew Granville https://dms.umontreal.ca/~andrew/CircleMethodNotes.pdf
- Alexandra Florea : “Traces of high powers of the Frobenius class in the hyperelliptic ensemble” by Zeev Rudnick, Acta Arithmetic, 143.1 (2010), 81-99, obtain from this LINK
- Adam Harper “Moments of random multiplicative functions, III: A short review” https://arxiv.org/abs/
2410.11523, & the introduction of “On the limiting distribution of sums of random multiplicative functions” https://arxiv.org/abs/2508. 12956 - Maksym Radziwill : Lecture 1; Lecture 2; Lecture 3
- Alex Smith: “The Selmer group, the Shafarevich-Tate group, and the weak Mordell Weil theorem” by Bjorn Poonen https://math.mit.edu/~poonen/
f01/weakmw.pdf - Ashvin Swaminathan : “Counting Cubic Num
ber Fields” by Niven Achenjang https://www.mit. edu/~NivenT/assets/pdf/ Counting_Cubic_Number_Fields. pdf. - Melanie Wood : “Probability theory for random groups arising in number theory” https://ems.press/books/
standalone/278/5565
