Student and Faculty Research and Publications 2021

Not even a global pandemic can stop the progress of mathematics. Students and faculty were active in their field last year, researching and publishing on topics such as Coarse Ricci curvature, functional connectivity in the brain and Gross-Pitaevskii equations.

Student-Faculty Research

Eric Brussel worked with undergraduates Ian Gallagher, Andy Haase and Bailey Wickham in the 2020 Frost Summer Research Program. They presented a poster on these results titled “Spheres of Planes in Generalized Quaternions” at the Mathematical Association of America Golden Section Meeting in February. 

Vincent Bonini worked with students Caroline Semmens, Tyler Tran and Shiaohan Liu during the Frost Summer Research Program. The students studied Coarse Ricci Curvature of Paley graphs and used their algebraic structure to establish an explicit formula for the Coarse Ricci curvature of Paley Graphs. They hope to publish this work in a college journal when time permits.

Goro Kato continued to run two Alexander von Humboldt Institute Seminars: “Non-linear PDEs” with Jerry Lin from George Mason University, Caixing Gu and math student Joel Pion; and “Sheaves and Categories” with Neil Theise from New York University, Menas Kafatos from Chapman University, Jerry Lin from George Mason University, Caixing Gu and math students Joel Pion and Grace Hochrein.

Stathis Charalampidis worked with undergraduates Marisa Lee, Rachel Loh and Harry Yan during the Frost Summer Research Program on a project titled “Energy localization in granular crystals for energy harvesting.” Charalampidis also worked with math major Wesley Khademi on an independent study on physically-informed neural networks.

Elena Dimintrova worked with students Fred Streetman, Jackie Driscoll, Matthew Mazzagatte and Vanessa Newsome-Slade during the Frost Summer Research Program on a project titled “Inferring functional connectivity in the brain.” Dimintrova also worked with graduate students Cameron Fredrickson, Nick Rondoni and Codi Barnett on a National Science Foundation-funded summer research project on the selection methods for algebraic design of experiments.

Faculty Publications

• Bonini V, Carroll C, Dinh U, Dye S, Frederick J, and Pearse E. (2020) Condensed Ricci Curvature of Complete and Strongly Regular Graphs. Involve 13:559-576. https://doi.org/10.2140/involve.2020.13.559 
• Boullé N, Charalampidis EG, Farrell PE and Kevrekidis PG. (2020) Deflation-based Identification of Nonlinear Excitations of the 3D Gross-Pitaevskii equation. Phys. Rev. A, 102:053307 
• Charalampidis EG, Boullé N, Kevrekidis PG and Farrell PE. (2020) Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation. Commun. Nonlinear Sci. Numer. Simulat, 87:105255
• Charalampidis EG, Dawson J, Cooper F, Khare A and Saxena A. (2020) Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential. J. Phys. A: Math. and Theor., 53:455702
• von der Heydt AS, Ashwin P, Camp CD, Crucifix M, Dijkstra HA, Ditlevsen P , and Lenton TM. (2021) Quantification and interpretation of the climate variability record, Global and Planetary Change 197: 103399, https://doi.org/10.1016/j.gloplacha.2020.103399
• Kato G and Nishimura K. (2020) Toward a descent theoretic formulation for organization and emergence -An initial object sheaf hypothesis and its consequence. 10.13140/RG.2.2.30759.37282
• Koshy-Chenthittayil S, Dimitrova E. (2020). From Chaos to Permanence Using Control Theory (Research). In: Acu B., Danielli D., Lewicka M., Pati A., Saraswathy RV, Teboh-Ewungkem M. (eds) Advances in Mathematical Sciences. Association for Women in Mathematics Series, vol 21. Springer, Cham.
• Murrugrarra D and Dimitrova E. (2021) Quantifying the total effect of edge interventions in discrete multistate networks. Automatica, 125:109453
• Paquin D, Kato D, and Kim P. (2020) A mathematical model for the effects of grandmothering on human longevity. Mathematical Biosciences and Engineering 17:3175-3189. doi: 10.3934/mbe.2020180
• Phillipson K, Dimitrova E, Honecker M, Hu J, Liang Q. (2020). Gröbner Bases of Convex Neural Code Ideals (Research). In: Acu B., Danielli D., Lewicka M., Pati A., Saraswathy RV, Teboh-Ewungkem M. (eds) Advances in Mathematical Sciences. Association for Women in Mathematics Series, vol 21. Springer, Cham.
• Sullivan J, Charalampidis EG, Cuevas-Maraver J, Kevrekidis PG and Karachalios NI. (2020) Kuznetsov-Ma breather-like solutions in the Salerno model. Eur. Phys. J. Plus, 135:607