# HELLO! IāM JOSHUA MILLER

Lecturer

Georgia State University

25 Park Place

Office: 1427

Email: jmiller208@gsu.edu

Summer 2023 Office Hours:

Current Courses: College Algebra, Linear Algebra

Curriculum Vitae: Updated 02/2023

## ACADEMICS

August 2016- July 2021

### PH. D MATHEMATICS, KANSAS STATE UNIVERSITY

Dissertation: Generalized Pak-Stanley labeling for Multigraphical Hyperplane Arrangements in n=3

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August 2016 - December 2019

### M.S. MATHEMATICS, KANSAS STATE UNIVERSITY

Research included work in multigraphical hyperplane arrangements and their Pak-Stanley labelings, and continued work on Whitney duals for graded posets.

August 2014- May 2016

### M.S. MATHEMATICS, SAM HOUSTON STATE UNIVERSITY

Research included finding ways to explicitly calculate the invariant factors of the sandpile group for the class of graphs known as thick cycle graphs.

August 2012- May 2014

### B.S. MATHEMATICS, SAM HOUSTON STATE UNIVERSITY

Research included creating models for ventricular septal defects in newborns.

## RESEARCH

Areas of Interest

### GRAPH THEORY & COMBINATORICS

Current areas of focus include multigraphical hyperplane arrangements and their relation with Pak-Stanley labelings, the Whitney duals of graded posets, and applications of the Tutte polynomial or polynomials of a similar nature.

### ALGEBRA

Current areas of interests are sandpile for different families of graphs, as well as chromatic symmetric function, and relations between the Laplacian matrix of a graph G and graphical properties.

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### NUMBER THEORY

Current areas of interest are geared towards combinatorial number theory problems like Singmaster's conjecture and Frobenius numbers for n larger than three.