Hunter Rehm
Graduate Student and Teaching Assistant
University of Vermont (UVM)
Deparment of Mathematics and Statistics
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About
Doctoral candidate in pure mathematics focusing on graph theory with experience in probabilistic network analysis and computer programming at NASA GRC. My graduate Advisor is Puck Rombach and my undergraduate advisor was Nathan Warnberg.
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Name, Email, Office
Hunter Rehm
hunter.rehm@uvm.edu
Innovation Hall E324
CV/Resume
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Education
University of Wisconsin-La Crosse, B.S.
Major: Mathematics
Minor: Computer Science
GPA: 3.55
University of Vermont, Ph.D.
Field of Study: Mathematics
Funding: NASA Vermont Space Grant Consortium Graduate Research Fellowship
GPA: 3.95 -
Publications
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Submitted Manuscripts
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The effect of the Katz parameter on node ranking, with a medical application
by Hunter Rehm, Mona Matar, Puck Rombach, and Lauren McIntyre (Preprint)
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Presentations
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Anti-van der Waerden numbers on Graphs Products (April 2019)
Discrete Math Days of the NorthEast, Amherst, MA
Poster Presentation -
Anti-van der Waerden numbers on Graphs Products (March 2019)
50th Southeastern International Conference on Combinatorics, Graph Theory & Computing
Oral Presentation, 15 minutes -
Rainbows in Graphs (January 2018)
Joint Mathematics Meeting (JMM) 2018, San Diego, CA
Oral Presentation, 10 minutes -
Rainbows in Graphs (November 2017)
Seven Rivers Symposium 2018
Oral Presentation, 20 minutes -
Rainbows in Graphs (October 2017)
UWL Math and Stats Club
Oral Presentation, 1 hour -
Anti-van der Waerden numbers on Graphs (June 2017)
Deans Distinguished Fellowship Meeting
Oral Presentation, 20 minutes -
Anti-van der Waerden numbers on an m x n Grid Graphs (April 2017)
Research at the Rotunda Event in Madison, Wisconsin
Poster Presentation -
Anti-van der Waerden numbers on an m x n Grid Graphs (April 2017)
National Conferences on Undergraduate Research 2017, Memphis, TN
Oral Presentation, 15 minutes -
A Bayesian Approach to Predicting the Outcome of Endovenous Laser Ablation (January 2017)
Joint Mathematics Meeting (JMM) 2017, Atlanta, GA
Oral Presentation, 10 minutes -
A Bayesian Approach to Predicting the Outcome of Endovenous Laser Ablation (October 2016)
The UWL Mathematics Colloquium
Oral Presentation, 30 minutes
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Anti-van der Waerden numbers of graph products
by Hunter Rehm, Alex Shulte, and Nathan Warnberg
In this paper, anti-van der Waerden numbers on Cartesian products of graphs are investigated and a conjecture made by Schulte, et al. is answered. In particular, the anti-van der Waerden number of the Cartesian product of two graphs has an upper bound of four. This result is then used to determine the anti-van der Waerden number for any Cartesian product of two paths. -
Rainbow numbers of [n] for Σxi = xk
by K. Fallon, C. Giles, H. Rehm, S. Wagner, and N. Warnberg
Consider the set {1, 2,..., n} = [n] and an equation eq. The rainbow number of [n] for eq, denoted rb([n], eq), is the smallest number of colors such that for every exact rb([n], eq)-coloring of [n], there exists a solution to eq with every member of the solution set assigned a distinct color. This paper focuses on linear equations and, in particular, establishes the rainbow number for the equations Σxi = xk for k ≥ 3.
Submitted Manuscripts
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The effect of the Katz parameter on node ranking
by H. Rehm, M. Matar, P. Rombach, and L. McIntyre
Katz centrality takes a (weighted) count of all walks starting at each node, with an additional damping factor of α that tunes the influence of walks as lengths increase. We introduce a tool to compare different centrality measures in terms of their node rankings, which takes into account that a relative ranking of two nodes by a centrality measure is unreliable if their scores are within a margin of error of one another. We employ this tool to understand the effect of the α-parameter on the lengths of walks that significantly affect the ranking of nodes.
Videos
The following videos are posted on my YouTube channel. The software used to make the videos was created by Grant Sanderson, more popularly known as 3Blue1Brown.
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An Introduction to Ramsey Theory
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What is a Graph?
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Adjacency Matrix
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Incidence Matrix
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Coin Flipping Paradox
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Breadth first search algorithm
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Centrality Measures
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2018 Fall Semester UVM: College Algebra
Sets, relations, functions with particular attention to properties of algebraic, exponential, logarithmic functions, their graphs and applications in preparation for MATH 019. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered MATH 019 or above. Pre/co-requisites: Two years of secondary school algebra; one year of secondary school geometry. -
2019 Spring Semester UVM: College Algebra
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2019 Fall Semester UVM: Fundamentals of Calculus
Introduction to limits and differential calculus with a wide variety of applications. Students interested in intensive use of mathematics should take MATH 021. Credit not given for more than one of the courses MATH 019, MATH 021 unless followed by MATH 022. See MATH 023. Prerequisite: MATH 009 or MATH 010, or sufficiently strong background in secondary school algebra and geometry. -
2020 Spring Semester UVM: Fundamentals of Calculus
Introduction to limits and differential calculus with a wide variety of applications. Students interested in intensive use of mathematics should take MATH 021. Credit not given for more than one of the courses MATH 019, MATH 021 unless followed by MATH 022. See MATH 023. Prerequisite: MATH 009 or MATH 010, or sufficiently strong background in secondary school algebra and geometry.