Nilpotent Frobenius actions and computing Frobenius closures of parameter ideal

Computing Frobenius closures of ideals is a classically difficult problem. Starting in 2006 with work of Katzman-Sharp the problem is made tractable for Cohen-Macaulay rings.  Since roughly 2019, starting from work of Quy and Maddox, there has been an explosion of activity in computing Frobenius closure of parameter ideals. This has come by studying F-nilpotent singularities. In this talk, we will review the recent aspects of this research, applications of F-nilpotence to computing Frobenius test exponents, and the significant recent advances in F-nilpotent singularities that arose from this.

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