Seminar series
Date
Mon, 02 Mar 2026
16:00
16:00
Location
C5
Speaker
Noah Kravitz
Organisation
(Mathematical Institute University of Oxford)
Any two 1 by 1 real matrices commute. This is in general not the case for 2 by 2 real matrices. However, if A, B, C, and D are any 2 by 2 real matrices, then ABCD - ABDC - ACBD + ACDB + ADBC - ADCB - BACD + BADC + BCAD - BCDA - BDAC + BDCA + CABD - CADB - CBAD + CBDA + CDAB - CDBA - DABC + DACB + DBAC - DBCA - DCAB + DCBA = 0. This identity is the first instance of a general result of Amitsur and Levitski; I will explain a simple graph-theoretic proof due to Swan.