# Research

## Discrete Mathematics

### Monday, November 30, 2020

Title: Graphs and the Cut & Project Method
Speaker: Greg McColm
Time: 2:00pm‐3:00pm
Place: Zoom Meeting

#### Abstract

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.

### Monday, November 23, 2020

Title: Cataloging and Information Retrieval Systems
Speaker: Michael Hendry
Time: 2:00pm‐3:00pm
Place: Zoom Meeting

#### Abstract

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.

### Monday, November 16, 2020

Title: Dissection in Category Theory
Speaker: Greg McColm
Time: 2:00pm‐3:00pm
Place: Zoom Meeting

#### Abstract

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.

### Monday, November 9, 2020

No seminar this week.

### Monday, November 2, 2020

No seminar this week.

### Monday, October 26, 2020

No seminar this week.

### Monday, October 19, 2020

No seminar this week.

### Monday, October 12, 2020

Title: Satisfactory colorings of the positive integers
Speaker: Lon Mitchell
Time: 2:00pm‐3:00pm
Place: Zoom Meeting

#### Abstract

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.

### Monday, October 5, 2020

No seminar this week.

### Monday, September 28, 2020

No seminar this week.

### Monday, September 21, 2020

Title: What is a hyperbolic group?, Part II
Speaker: Milé Krajčevski
Time: 2:00pm‐3:00pm
Place: Zoom Meeting

### Monday, September 14, 2020

Title: What is a hyperbolic group?
Speaker: Milé Krajčevski
Time: 2:00pm‐3:00pm
Place: Zoom Meeting

#### Abstract

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.