### Speaker

#### Pedro Teixeira

Knox College

Mathematics

(309) 341-7749

pteixeir@knox.edu

Fractal Patchwork Quilts

In this talk I describe some aspects of the theory of "fractal patchwork quilts" that Monsky and I have developed in connection to our work on Hilbert-Kunz functions. We look at examples of such fractals, investigate their self-similarity properties, and see how they arise from considerations about algebraic objects such as polynomials and syzygies. This theory has allowed us to obtain some interesting results on Hilbert-Kunz functions, and in its elegance and strangeness has an independent interest.

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