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Title: Graphs and the Cut & Project Method Speaker: Greg McColm Time: 2:00pm‐3:00pm Place: Zoom Meeting
One popular model for molecules and materials is the geometric graph, i.e. a graph embedded in Euclidean space, and one popular model for quasicrystalline materials is the cut & project tiling. We resurrect a proposal (from two decades ago) to generalize the cut & project method to graphs, and we encounter a longstanding open problem in tiling theory.
Title: Cataloging and Information Retrieval Systems Speaker: Michael Hendry Time: 2:00pm‐3:00pm Place: Zoom Meeting
Cataloging systems map entries to their associated objects or categories for easier retrieval or classification. For example, MathSciNet and the Library of Congress both assist users in finding documents relevant to a topic. Additionally, many websites with user-generated content also use cataloguing systems for categorizing entries. This talk will discuss the specifics of an algorithm that uses computer-defined keywords to classify documents into a list of inputted topics.
Title: Dissection in Category Theory Speaker: Greg McColm Time: 2:00pm‐3:00pm Place: Zoom Meeting
We look at the problem of using categories to classify complex combinatorial objects with local symmetries (a local symmetry is a symmetry of a subobject that does not extend to the entire object). Local symmetries show up in geometric art and crystallographic structures, two areas with vast catalogues that require organizing.
This talk is intended to be accessible to a broad (mathematical) audience and does not presume any prior experience in category theory.
No seminar this week.
Title: Satisfactory colorings of the positive integers Speaker: Lon Mitchell Time: 2:00pm‐3:00pm Place: Zoom Meeting
An \(n\)-satisfactory coloring of the postive integers is a coloring with with \(n\) colors so that, for any integer \(z\), no two elements of \(\{z, 2z, 3z, \dots, nz\}\) are assigned the same color. The question of for which \(n\) such colorings exist is about 10-years old. We will survey the known results and discuss a number of open questions.
Title: What is a hyperbolic group?, Part II Speaker: Milé Krajčevski Time: 2:00pm‐3:00pm Place: Zoom Meeting
Title: What is a hyperbolic group? Speaker: Milé Krajčevski Time: 2:00pm‐3:00pm Place: Zoom Meeting
This will be an elementary talk about a (relatively new) notion in Combinatorial Group Theory, that opened the whole new area of research in Geometric Group Theory. Other than providing necessary definitions and examples we'll mention some of the highlights in this area of research. The talk is meant to be accessible to undergraduate and graduate students.