## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Friday, August 13, 2021 — 9:00 AM EDT

**Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo**

"F-automatic sets"

Given a set of natural numbers A, is the set of base p representations of elements of A a regular language over {0,...,p-1}? In other words, given a string of digits base p, can we check whether it represents an element of A using a bounded amount of memory? The sets for which the answer is "yes" are called the *p-automatic sets*, and are an important object in the study of formal languages. In this talk, we will see that this notion can be generalized to subsets A of certain abelian groups Γ, with an injective endomorphism F : Γ -> Γ taking the role of p; we call these *F-automatic sets*. We will consider the question of which abelian groups we can do this in: we will characterize these groups in terms of the existence of certain functions on Γ called *length functions*, and in the finitely generated case in terms of the eigenvalues of F. We will also give a general notion of sparsity for F-automatic sets, called F-sparsity, and characterize F-sparsity in terms of length functions. Finally, we will examine how F-automaticity and F-sparsity interact with model theoretic tameness properties, namely stability and NIP.

Please contact Nancy Maloney (nfmalone@uwaterloo.ca) if you are interested in virtually attending Christopher's talk.

Event tags

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

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