Random $p$-adic Matrices

12 January – 3 April 2026

We are reading texts on the theory of random $p$-adic matrices and Cohen–Lenstra heuristics. Our sources are

• Topics in random matrix theory by Terence Tao
• An Introduction to Random Matrices by Greg W. Anderson, Alice Guionnet, and Ofer Zeitouni
• Probability theory for random groups arising in number theory by Melanie Matchett Wood
• Heuristics on class groups of number fields by Henri Cohen and Hendrik W. Lenstra Jr.
• Universality of cokernels of random matrix products by Hoi H. Nguyen and Roger Van Peski
• Random integral matrices and the Cohen–Lenstra heuristics by Melanie Matchett Wood

We meet on Fridays at 10:00am. Contact Joshua Maglione if you are interested in joining.

Date	Reading
23 Jan	Section 1.1 (Tao)
30 Jan	Section 1.1 (Tao)
06 Feb	Section 1.1 (Tao)
13 Feb	Section 2.1 (Anderson et al.)
20 Feb	Section 2.1 (Anderson et al.)
27 Feb	TBD
06 Mar	TBD
13 Mar	TBD
20 Mar	TBD
27 Mar	TBD