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Boatwright Memorial Library

Spring 2024 Math & Stats Colloquium

These presentations come from the Math and Stats Colloquium. For more information on the Colloquium Series check out https://math.richmond.edu/academics/colloquium/index.html

Under each presentation:

You will find related resources curated by the science librarian. These resources might be broad overviews of topics or they might be specific. They are meant to serve as a starting point. 

Want to just see all the resources at once? Check out the Zotero Folder for Math Colloquium Presentations. 

*Zotero Folder reflects updates quickest*

Math Colloquium Archives

Over the following tabs, you will find the Math Colloquium listings from previous semesters. 

Check out the Zotero Folder for Math Colloquium Presentations. 

Student Summer Research Presentations ▼

I was unfortunately unable to attend these presentations. Here is the line up though:

  • Non-abelian Partial Difference Sets
    Student Researchers: Aiden Hills, Ziqi Meng, Yoonha Nam
    Mentor: Dr. James Davis
  • Modeling the Opioid Epidemic: Medicated vs. Non-medicated Treatment
    Students: Muskan Agarwal, Maniha Agram, Gabe Greenberg
    Mentor: Dr. Joanna Wares
  • Parallel Algorithms for High-Dimensional Clustering
    Student: Andrew Brady
    Special Program: Research Experience for Undergraduates in Combinatorics, Algorithms, and AI for Real Problems (REU-CAAR)
    Mentor: Dr. Laxman Dhulipala", University of Maryland, College Park

Knotted Graphs and Graphs of Knots: How Combinatorics and Knot Theory Inform Each Other
- Allison Moore ▼

A knot is an embedding of a circle in a three-dimensional space, up to a type of deformation called ‘ambient isotopy.’ Informally, we can think of a knot as being a closed, flexible loop made out of stretchy rubber cord. Knot theory is a part of geometry and topology, but it enjoys connections to many other branches of math including algebra, analysis, and combinatorics; knot theory even provides a framework for mathematical modeling in molecular biology!

In this talk, we’ll investigate how concepts from graph theory help us to better understand the complexity of knots and to devise tools to calculate their properties. I’ll emphasize several research projects that were joint work with the following VCU students: Matthew Elpers, Christopher Flippen, Rayan Ibrahim, Essak Seddiq, and Anna Shaw.

[1] Allison H. Moore: Publications, https://people.vcu.edu/˜moorea14/research.html.

[2] Colin Adams, Erica Flapan, Allison Henrich, Louis H. Kauffman, Lewis D. Ludwig, and Sam Nelson (eds.), Encyclopedia of knot theory, CRC press, Boca Raton (Fla.), 2021.

[3] Colin Conrad Adams, The Knot book: An elementary introduction to the mathematical theory of knots, W. H. Freeman, New York, 1994.

[4] J. W. Alexander, A Lemma on Systems of Knotted Curves, Proceedings of the National Academy of Sciences 9 (1923), no. 3, 93–95.

[5] _____, Topological invariants of knots and links, Transactions of the American Mathematical Society 30 (1928), no. 2, 275–306.

[6] J. W. Alexander and G. B. Briggs, On Types of Knotted Curves, The Annals of Mathematics 28 (1926), no. 1/4, 562.

[7] R Bott and J P Mayberry, Matrices and trees, Economic Activity Analysis, 1954, pp. 391– 400.

[8] Mihai Ciucu, Weigen Yan, and Fuji Zhang, The number of spanning trees of plane graphs with reflective symmetry, Journal of Combinatorial Theory, Series A 112 (2005), no. 1, 105–116.

[9] Matthew Elpers, Rayan Ibrahim, and Allison H. Moore, Determinants of Simple Theta Curves and Symmetric Graphs, 2022.

[10] Christopher Flippen, Allison H. Moore, and Essak Seddiq, Quotients of the Gordian and H(2)-Gordian graphs, April 2021.

[11] M Gromov, Hyperbolic Groups, Essays in Group Theory (S.M. Gersten, ed.), Mathematical Sciences Research Institute Publications, Springer-Verlag, New York, 1987.

[12] Stanislav Jabuka, Beibei Liu, and Allison H. Moore, Knot graphs and Gromov hyperbolicity, Mathematische Zeitschrift 301 (2022), no. 1, 811–834.

[13] Vaughan Jones, A polynomial invariant for knots via von Neumann algebras, Bulletin of the American Mathematical Society 12 (1985), no. 1, 103–111.

Converting Local Consumption Responses to an Aggregate Fiscal Multiplier
- M. Saif Mehkari ▼

Economists use mathematics in many different ways. In this colloquium I will discuss one of my recently accepted papers on calculating the aggregate fiscal multiplier. Using data, we estimate that a $1 increase in county-level government spending increases local non-durable consumer spending by $0.29. The starting point for the talk will be the intuition (economic, mathematical, and practical) for our interest in the multiplier. We then translate this to an aggregate multiplier using a Heterogeneous Agent New Keynesian model. We further use this calibrated mathematical model to understand the mechanisms that link a local multiplier to an aggregate multiplier. Through the discussion of this paper and its results I will explain the process economists use to perform such calculations and highlight how mathematics acts as a foundation for economic analysis. The paper uses techniques and ideas from statistics, calculus, differential equations, and numerical analysis.