Dr. Carmen Caprau

Carmen CaprauDr. Carmen Caprau has supervised 15 undergraduate research students during the last years, half of whom were women. The projects involved topics in knot theory and its connections to graph theory and abstract algebra. She has been a faculty mentor in Fresno State’s 2013 Summer REU and the Faculty-Undergraduate Research Student Teams Program during the pilot year 2014-2015. Dr. Caprau’s research students have given numerous talks and poster presentations at various conferences, including the Joint Mathematics Meetings, Sectional Meetings of the Mathematical Association of America, the Nebraska Conference for Undergraduate Women in Mathematics, Underrepresented Students in Topology and Algebra Symposium, and the Pacific Coast Undergraduate Conference. Some of her students have received awards for best presentation in their category. Her undergraduate students’ research endeavors also resulted in co-authored research papers, listed below (undergraduate students are in bold):

  1. C. Caprau, la Pena and S. McGahan, “Virtual singular braids and links”, Manuscripta Mathematica (Sept. 2016), Vol. 151, No. 1, 147-175; DOI 10.1007/s00229-016-0835-1.

  2. E. Aceves and J. Elder, “On invariants for spatial graphs”, Rose-Hulman Undergraduate Mathematics Journal, Vol. 16, No. 2 (Fall 2015), 17 pages.

  3. C. Caprau and J. Tipton, “The Kauffman polynomial and trivalent graphs”, Kyungpook Math. Journal, Vol. 55, No. 4 (2015), 779-806.

  4. C. Caprau, A. Chichester and P. Chu, “Three approaches to a bracket polynomial for singular links”, 18 pages; it will appear in Involve-A Journal of Mathematics.

  5. C. Caprau, T. Okano and D. Orton, “Singular links and Yang-Baxter state models”, 21 pages, it will appear in Rocky Mountain Journal of Mathematics.

  6. C. Caprau and J. Smith, “The singular Temperley-Lieb category”, ISRN Geometry, Vol. 2014, Article ID 321509, 9 pages, 2014. DOI: 10.1155/2014/321509.

  7. C. Caprau, D. Heywood, and D. Ibarra, “On a state model for the SO(2n) Kauffman polynomial”, Involve-A Journal of Mathematics, Vol. 7, No.4 (2014), 547-563. DOI:10.2140/involve.2014.7.547. 

Dr. Comlan de Souza

Comlan de Souza