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Thu, Aug 27, 2026 Number Theory Seminar 3:00 PM MSCS 509 Growth rate functions for partially commutative semigroups Wade Hindes, Texas State University Host: Paul Fili Abstract ⌄ PDF Abstract: We establish asymptotics for the degree and height growth rate functions of partially commutative semigroups of endomorphisms on varieties, i.e., semigroups where the only relations between generators, if any, are commuting ones. To do this, we prove a general result connecting the growth rates of two abstract functions, one multiplicative and one simply non-negative, subject to a Tate telescoping hypothesis and a sufficiently nice normal form on the underlying semigroup. Finally, we construct several new families of endomorphisms on which our asymptotics apply. To do this, we generalize the standard ping-pong lemma for elements to a ping-pong lemma for sub-semigroups.

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