Vítězslav Kala: Consecutive real quadratic and cubic fields with large class number

I will discuss several recent results on the existence of sequences of consecutive real quadratic, or real cubic, number fields with large discriminants. (Joint works with M. Cech, G. Cherubini, A. Fazzari, A. Granville, S. H. Man, O. Prakash, S. Roy, P. Yatsyna.)