GREGORY J. CLARK
About Me
I am an Academic Fellow in Marketing and Reputation, Saïd Business School, University of Oxford, United Kingdom (2019-2022).
I am working with Felipe Thomaz, Associate Professor of Marketing at Oxford Saïd.
My research is in Discrete Mathematics, but more specifically, Spectral Hypergraph Theory. The goal of Spectral Hypergraph Theory is to relate the structure of a hypergraph to its spectrum; that is to say, how one can relate the structure of a multi-dimensional network to a (relatively) short list of numbers. I am excited for the opportunity to apply this work to problems concerning reputation and the future of marketing.
My mathematical research interests also include Computational Algebra, k-planar Crossing Numbers, Additive Combinatorics, and Graph Coloring. My interdisciplinary research interests include Analyzing Networks, Trend Detection, and Modeling Reputation.
I received a PhD in Mathematics from the University of South Carolina in May 2019 and hold a Bachelor's degree in Mathematics from Westminster College, New Wilmington, PA. My PhD dissertation is titled 'On The Characteristic Polynomial of a Hypergraph'.
Education
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Ph.D. Mathematics, University of South Carolina, Columbia, SC. Dissertation Title: On the Characteristic Polynomial of a Hypergraph. Advisors: Professor Joshua N. Cooper. (May 2019)
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B.S. Mathematics, Westminster College, New Wilmington, PA. (May 2014)
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Budapest Semesters in Mathematics, BSM, Budapest, Hungary (Spring 2013)
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French Language and Culture Summer Immersion Program, Paris, France, Institut Catholique de Paris, Central College (Summer 2012)
Publications
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G. J. Clark, J. Cooper, A Harary-Sachs Theorem for Hypergraphs. (Submitted)
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G. J. Clark, F. Thomaz, A. Wiedemann, Designed to go dark: an examination of incentives for digital black markets to self-terminate. (Submitted)
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G. J. Clark, J. Cooper, Adjacency Spectral Theory for Uniform Hypergraphs, IMAGE (Bull Lin. All. Soc.), 62 (2019), pp.7-10 (Submitted)
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G. J. Clark, J. Cooper, Leading Coefficients and the Multiplicity of Known Roots. https://arxiv.org/abs/1806.05222 (Submitted)
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J. Asplund, E. Czabarka, G. J. Clark, et al., Using Block Designs in Crossing Number Bounds. To appear in Journal of Combinatorial Designs. (To appear)
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G. J. Clark. J. Cooper, On the Adjacency Spectra of Hypertrees, The Electronic Journal of Combinatorics, 25 (2018), no.2, pp. 2-48.
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G. J. Clark, G. Spencer, New Bounds on the Biplanar Crossing Number of Low-dimensional Hypercubes. Bulletin of the Institute of Combinatorics and its Applications (BICA) 83(2018), 52-60.
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A. Bright, G. J. Clark, C. Dunn, K. Evitts, M. Hitchman, B. Keating, B. Whetter, Tiling Annular Regions with Skew and T-tetrominoes, Involve, a Journal of Mathematics 10-3 (2017), 505–521. DOI 10.2140/involve.2017.10.505.
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G. J. Clark, Optimal Numbers and Solutions in the Euclidean Algorithm, The Pentagon, A Mathematics Magazine for Students, 73-01 (2013), 23-35.
Teaching
Department of Mathematics, University of South Carolina, Columbia, SC (July 2014 - May 2019)
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Math 115: Precalculus (Fall 2015)
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Math 122: Business Calculus (Fall 2018, Spring 2018, Fall 2017)
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Math 170: Finite Mathematics (Spring 2016, Fall 2015, Summer 2015)
Invited Addresses
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2018 Annual Reputation Symposium (Fall 2018)
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Distinguishing Between Reputation and Influence of Users in a Complex System
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Oxford University, Oxford, United Kingdom
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NSF-CBMS Workshop on Additive Combinatorics (Summer 2018)
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University of South Carolina, Columbia, SC
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Research Highlights Seminar (Spring 2018)
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Designed to Fail: Determining Illicit Market Life Spans with Stochastic Calculus.
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Practice for Coordinators of Large Undergraduate Courses on Campus (Fall 2017)
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A Mentorship Mode for Graduate School Instructors in Large Undergraduate Courses.
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University of South Carolina Center for Teaching Excellence, Columbia, SC
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Mathematical Research Communities (Summer 2017)
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Beyond Planarity: Crossing Numbers of Graphs
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Snowbird Resort, Snowbird, UT
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Joint Mathematics Meeting (Spring 2017)
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Graduate Student Instructor Mentorship Model: A professional development that trains experienced graduate students to pedagogically mentor novice mathematics graduate student instructors.
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Hyatt Regency Atlanta and Marriott Atlanta Marquis, Atlanta, GA
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AMS Sectional Meeting (Fall 2016)
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The Splitting Number of an Integer Tile
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North Carolina State University, Raleigh, NC
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Carolina Math Seminar (Fall 2016)
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The Splitting Number of Integer Tile
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Columbia College, Columbia, SC
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Mentorship
Teaching Mentorship
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Graduate Student Mentor, Department of Mathematics, University of South Carolina (Fall 2016-Spring 2018)
Research Mentorship
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A Summary of Splitting Numbers for Integer Tiles, C. Simmons, C. Stewart, J. Folks, S. Lee, S. Miyasaki, University of South Carolina (Summer 2016). Click here for a description of this project and a sample of student work.
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Generalized Dinitz Conjecture, E. Miller, University of South Carolina (Fall 2015, Spring 2016). Click here for a description of this project and a sample of student work.
Grants and Honors
Grants
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SPARC Grant Recipient, University of South Carolina (Summer 2017)
Honors
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Preparing Future Faculty With Distinction In Teaching, under review.
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'Preparing Future Faculty' Certificate - Successful PFF candidates have completed activities designed to prepare participants in the critical areas of faculty competence: teaching, research and service. This accomplishment is an indicator of the participant’s initiative and a measure of experience toward becoming future faculty. University of South Carolina (Spring 2018)
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Outstanding Teaching Award, University of South Carolina (Spring 2018)
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Discrete Mathematics Seminar Organizer, University of South Carolina (Fall 2016-Spring 2017)
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Discover Poster Session Judge, University of South Carolina (Spring 2016, Spring 2017)
