# Research

## Discrete Mathematics (Leader: Prof. Greg McColm <mccolm (at) usf.edu>document.write('<a href="mai' + 'lto:' + 'mccolm' + '&#64;' + 'usf.edu' + '">Prof. Greg McColm</a>');)

### Monday, November 14, 2022

No seminar this week.

### Monday, November 7, 2022

No seminar this week.

### Monday, October 31, 2022

No seminar this week.

### Monday, October 17, 2022

No seminar this week.

### Monday, October 10, 2022

Title: Structure(s), structure in classes of structures, arbitrary truth and three related, widely discussed mathematical statements of our era: Cantor's Theorem, the Axiom of Choice and the Continuum Hypothesis
Speaker: Yiannis Vourtsanis
Time: 2:00pm–3:00pm
Place: CMC 108 or on Zoom

#### Abstract

Aspects of structure(s), structure (in particular, operational) in classes of structures and arbitrary truth (Mathematical Logic) will be discussed, both with respect to a brief historical introduction, as well as, with respect to earlier work of mine.

Subsequently, certain relations or applications to CT (Cantor's Theorem), AC (Axiom of Choice) and CH (Continuum Hypothesis) will also be presented.

### Monday, October 3, 2022

No seminar this week.

### Monday, September 26, 2022

No seminar this week.

### Monday, September 19, 2022

Title: Abstract Geometric Crystallography, Part II
Speaker: Greg McColm
Time: 2:00pm–3:00pm
Place: CMC 108 or on Zoom

### Monday, September 12, 2022

Title: Abstract Geometric Crystallography
Speaker: Greg McColm
Time: 2:00pm–3:00pm
Place: CMC 108 or on Zoom

Abstract

Geometric crystallography is concerned with periodic'' and subperiodic'' structures in Euclidean space, where a periodic structure is an infinite structure in Euclidean space whose symmetry group has a subgroup (of finite index) of translations spanning that space; subperiodic structures are defined similarly. (In materials science, these structures represent crystals; in this talk, we focus on graphs.) We generalize this approach and consider graphs embedded in more general spaces. We are interested in cataloguing all possible periodic graphs, and we propose a method based on a parametrization of periodic graphs by tuples of vectors.