Calendar

May
9
Mon
Colloquium: Evdoridou
May 9 @ 2:30 pm – 3:30 pm
May
10
Tue
Colloquium: Simón
May 10 @ 2:30 pm – 3:30 pm
May
12
Thu
Ha’s MA presentation
May 12 @ 3:00 pm – 4:00 pm

Hien Ha  Thursday May 12,  3pm  Keller 302
Tile: p-adic numbers
Abstract: The field of real numbers is completed from the field of rational numbers with respect to the distance metric. The heart of the completion process is the limit of Cauchy sequences. Recall that a metric space (X, d) is complete if every Cauchy sequence in X converges to a point in X. We know that Q is not complete with respect to the distance metric. For example, the Cauchy sequence of rational numbers 3 , 31/10 , 314 /100 , 3141/ 1000 …. is converging to π which is not in Q . Filling all convergent points of Cauchy sequences we get R. The field of p-adic numbers Qp is also completed from Q with respect to a different metric called the p-adic metric which is induced from the p-adic norm. We also make use of the convergence of the Cauchy sequences for this process. In this project we will see how Qp is completed from Q with respect to the p-adic norm. We also describe two trees associated with Qp: the trees of balls in the field Qp and the trees of lattices in the vector space Qp × Qp.

May
25
Wed
David Webb PhD defense
May 25 @ 3:00 pm – 4:00 pm
Jul
12
Tue
Logic seminar: Bjørn Kjos-Hanssen
Jul 12 @ 11:00 am – 12:00 pm
Aug
5
Fri
Kenny Corea’s Phd defense: Groupoids and Property (T)
Aug 5 @ 2:00 pm – 3:00 pm
Aug
22
Mon
Fall 2022 instruction begins
Aug 22 all-day