Mathematics Faculty & Staff

1988  Ph.D., Mathematics, Florida State University

1986  Masters, Mathematics, Florida State University

1983  Vordiplom, Mathematics, Johann Wolfgang Goethe Universität, Germany

Geometric topology and knot theory. In particular, applications of knot theory to molecular biology (DNA recombination experiments) and chemistry. This branch of knot theory is called physical knot theory.

• Ernst, C. & Gover, S. Families of curly knots. Journal of Knot Theory and Its Ramifications Vol. 31, No. 14 (2022) 2250101 (16 pages) DOI: 10.1142/S0218216522501012
• Ernst, C. & Gover, S. Almost all 2-bridge knots are curly. Journal of Knot Theory and Its Ramifications Vol. 31, No. 13 (2022) 2250101 (24 pages) DOI: 10.1142/S0218216522500845
• Diao Y., Ernst C., Hetyei G., and Liu P. (2021), A diagrammatic approach for determining the braid index of alternating links, to appear in J. of Knot Theory and Its Ramifications Vol. 30, No. 5 (2021) 2150035
• Ernst, C., Rawdon, E., Ziegler (2021) Knotting spectrum of polygonal knots in extreme confinement. J. Phys. A: Math. Theor. J. Phys. A: Math. Theor. 54 235202 (24pp) https://doi.org/10.1088/1751-8121/abf8e8 
• Diao Y., Ernst C., and Hetyei G. (2020), Invariants of rational links represented by reduced alternating diagrams, to appear, SIAM J. Discrete Math. Vol. 34, No. 3, pp. 1944–1968
• Diao, Y., Ernst, C. Por A., Ziegler, U. (2019), The Ropelengths of Knots Are Almost Linear in Terms of Their Crossing Numbers, Vol. 28, No. 14, 1850075 doi.org/10.1142/S0218216519500858
• Bettersworth Z. and Ernst C. (2019), On the Incoherent Nullification of Knots and Links, J. of Knot Theory and Its Ramifications, Vol. 28, No. 05, doi.org/10.1142/S0218216519500330
• Ernst, C. and Pham, V. (2018), Loop Numbers of Knots J. of Knot Theory and Its Ramifications, Vol. 27, No. 14, 1850075 , doi.org/10.1142/S021821651850075X
• Diao, Y., Ernst C, Rawdon, E. J. and Ziegler U. (2018), The Knot Spectrum of Random Knot Spaces, New Directions in Geometric and Applied Knot Theory/Ed. Blatt, Reiter, Schikorra, DeGruyter, pp.205- 237, DOI: 10.1515/9783110571493-010
• Diao, Y., Ernst C, Rawdon, E. J. and Ziegler U. (2018), Average crossing number and writhe of knotted random polygons in confinement Reactive and Functional Polymers 131(10) doi.org/10.1016/j.reactfunctpolym.2018.07.028
• Diao, Y., Ernst C., Ziegler U., and Rawdon, E. J. (2018), Total curvature and total torsion of knotted random polygons in confinement. J. Phys. A: Math. Theor, 51(15) DOI: 10.1088/1751-8121/aab1ed
• Diao, Y., Ernst, C. D., Rawdon, E., Ziegler, U. (2017). Relative Frequencies of Alternating and Nonalternating Prime Knots and Composite Knots in Random Knot Spaces. Experimental Mathematics, 1- 18, DOI: 10.1080/10586458.2017.1320239