Distribution of the cokernels of random integral matrices2022.02.14
- 2021-11-10 (16:00 ~ 18:00)
November10 (Wednesday) 2021, 16:00 – 18:00, Building108, Room N319
▶Speaker : Jungin Lee (KIAS)
▶Title : Distribution of the cokernels of random integral matrices
▶Abstract : In this talk, we consider the following questions:
1. For a random matrix A∈Mat_n(Z_p) and given finite abelian p-groups G_1 and G_2, what is the probability that coker(A)≅G_1 and coker(A+I_n)≅G_2 as n->∞?
2. Similarly, for a given finite Z_p[t]/(t^2+1)-module G, what is the probability that coker(A^2+I_n)≅G as n->∞?
The above questions generalize the result of Friedman and Washington on the distribution of the cokernels of random p-adic integral matrices.
First we explain the relation between the Cohen-Lenstra heuristics and the work of Friedman and Washington.
After that, we explain four possible ways to generalize the work of Friedman and Washington, which include the answers to the above questions.
UNIST Number Theory group website