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Friday, Feb. 14, 2025, 4–5 p.m.
Puttipong Pongtanapaisan — Arizona State University Title: Organizing the Space of Colorings of Knotted Objects Abstract: Deciding whether one shape can be smoothly deformed into another is often challenging. A powerful approach to this problem involves coloring a diagram of a knotted shape according to algebraic rules that remain consistent under smooth deformations. In this talk, we introduce an invariant called the coloring quiver, which not only counts valid colorings but also tracks how different colorings relate to one another. This additional structure captures subtleties that the mere count of colorings (the coloring number) can miss. In particular, we present examples of knotted shapes with the same number of valid colorings that are nevertheless distinguished by their coloring quivers, illustrating that this new invariant is strictly stronger than the traditional coloring number.
Accessibility Information: Persons with disabilities who need accommodations or have questions about physical access may call the program sponsoring the event or call Accessibility Resource Center at 530-898-5959.
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