讲座内容：

This talk reports new results on the automorphism groups of infinitary power semigroups of numerical semigroups, that is, cofinite subsemigroups of the non-negative integers under addition, extending prior research limited to finitary (finite-subset-only) power structures.

Let $S$ be an additively written semigroup. Denote by $\mathcal P(S)$ the semigroup consisting of all non-empty subsets of $S$ endowed with the naturally induced operation of setwise addition. We call $\mathcal P(S)$ the large power semigroup of $S$. When $S$ is a monoid with neutral element $0_S$, the family $\mathcal P_0(S)$ of all subsets of $S$ containing $0_S$ is a submonoid of $\mathcal P(S)$, whose identity element is the singleton $\{0_S\}$; we call $\mathcal P_0(S)$ the reduced large power monoid of $S$.

We prove that the automorphism groups of the reduced large power monoid of a numerical monoid and the large power semigroup of a numerical semigroup are both trivial. A key technical tool is the $T$-conjugacy quotient, which links the automorphism group of $\mathcal P(S)$ when $S$ is numerical to the automorphism group of $\mathcal P_0(\mathbb N)$, where $\mathbb N$ is the monoid of non-negative integers under addition.