All in a Day's Work - Research and Publications

Scholarly activity in the Mathematics Department kept going strong whether remote or in-person. Students and faculty achieved a great deal during the past year.

Frost Summer Undergraduate Research Program

Ryan Tully-Doyle conducted research with Jackie Driscoll and Justin Hexem on the iteration of complex functions on matrices. 

Linda Patton worked with Mav Lara and Brooke Randell on "Characterizing the Numerical Range of Block Toeplitz Operators." They described the numerical ranges of some block Toeplitz operators with symbols of the form F(z)=A+Bz, where A and B are two by two matrices. This required analyzing the convex hull of an infinite collection of ellipses. Their poster was accepted to present at the Joint Mathematics Meeting, which was postponed but will be held virtually in April. 

Linda Patton also worked with Kelsey Lowrey, Tim Royston, and Karl Zieber studying "Flat Portions on Numerical Ranges of Nilpotent Matrices." They worked to generalize a conjecture about the maximum number of such flat portions to bigger matrices.  

Joyce Lin worked with Aidan Chandrasekaran and Srirag Vuppala on simulating a mean-field equation for the electrical activity in cardiac tissue, as well as with Brady Berg and Joseph Mcguire (jointly supervised with Elena Dimitrova) on creating an agent-based model for cardiac tissue. 

Stathis Charalampidis worked with Cal Poly ugraduates: Andy Chiv, Riley Prendergast, and Alexis Saucerman on the project titled "Computation of matter waves in atomic physics." 

Elena Dimitrova worked on Topological Data Analysis for Comparison of Simulated and Experimental Images with students Laura Bialozynski, Jaxon Green, Vanessa Newsome-Slade, and Stephen Wessel; in collaboration with Paul Anderson from CS.

Workshops

Professors Elsa Medina and Amélie Schinck-Mikel offered the annual Cal Poly Math Academy in summer 2021. Because of the pandemic, the academy met virtually. Backpacks were sent to each participant's house filled with math manipulatives and fun goodies, providing a hands-on experience even in the remote environment. Every summer the academy employs two Cal Poly undergraduate students who are studying to become secondary mathematics teachers to assist in creating activities and running the sessions. 

Medina and Schinck-Mikel plan to bring the Math Academy back in-person for summer 2022. The academy is offered in partnership with the Migrant Education Program for the region.

Publications

E.G. Charalampidis, F. Cooper, J. Dawson, A. Khare and A. Saxena. “Behavior of solitary waves of coupled nonlinear Schrodinger equations subjected to complex external periodic potentials with odd-PT symmetry.” J. Phys. A: Math. and Theor. 54, 145701 (2021) 

E.G. Charalampidis, F. Cooper, A. Khare, J. Dawson and A. Saxena. “Stability of trapped solutions of a nonlinear Schrodinger equation with a nonlocal nonlinear self-interaction potential.” J. Phys. A: Math. and Theor. 55, 015703 (2021) 

E.G. Charalampidis and V.M. Hur. “Numerical bifurcation and stability for the capillary-gravity Whitham equation.” Wave Motion. 106, 102793 (2021)   

C. Chong, Y. Wang, D. Marechal, E.G. Charalampidis, M. Moleron, A.J. Martinez, M.A. Porter, P.G. Kevrekidis and C. Daraio. “Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices.” New J. Phys. 23, 043008 (2021) 

M. Cox, W. Grewe, G. Hochrien, L. Patton, and I. Spitkovsky. “Nonparallel flat portions on the boundaries of numerical ranges of 4-by-4 nilpotent matrices.”  Electronic Journal of Linear Algebra. 37 (2021), 504-523 

E. Dimitrova, J. Hu, Q. Liang, B. Stigler, A. Zhang. “Algebraic Model Selection and Experimental Design in Biological Data Science.” Advances in Applied Mathematics. 133, 102282 (2022) 

T.A. Grundmeier, D. Retsek, A. Berg, S. Mann, A. Hamlin-Prieto. “Assumption and Defintion Use in an Inquiry-Based Introduction to Proof Course.” PRIMUS. 32(1) (2022) 1-13. 

G. Kato and K. Nishimura. “Time and Mnemonic Morphism.” Constructive Destruction to Destructive Construction, edited by K. Nishimura, M. Murase, and K. Yoshimura. Springer, October, 2021. 

D. R. King, M. Entz 2nd, G. A. Blair, I. Crandell, A. L. Hanlon, J. Lin, G. S. Hoeker, and S. Poelzing. “The conduction velocity-potassium relationship in the heart is modulated by sodium and calcium.” Pflugers Arch. Mar; 473(3) (2021): 557-571. doi: 10.1007/s00424- 021-02537-y. Epub 2021 Mar 4. PMID: 33660028; PMCID: PMC7940307. 

S. Koshy-Chenthittayil, E. Dimitrova, E. W. Jenkins, and B. C. Dean. “A Computational Framework for Finding Parameter Sets Associated with Chaotic Dynamics.” In Silico Biology. 14 (1-2) (2021) 41-51 

D. Murrugarra and E. Dimitrova. “Quantifying the total effect of edge interventions in discrete multistate networks.” Automatica. 125, 109453 (2021) 

F. Ruz, B. Chance, E. Medina, and J. Contreras. “Content Knowledge and Attitudes Towards Stochastics and Its Teaching in Pre-service Chilean Mathematics Teachers.” Statistics Education Research Journal. 20(1) (2021) 

A.S. Von der Heydt, P. Ashwin, C.D. Camp, M. Crucifix, H.A. Dijkstra, P. Ditlevsen, and T.M. Lenton. “Quantification and interpretation of the climate variability record.” Global and Planetary Change 197, 103399 (2021) 

W. Wang, L.-C. Zhao, E.G. Charalampidis and P.G. Kevrekidis. “Dark-dark soliton breathing patterns in multi-component Bose-Einstein condensates.” J. Phys. B: At. Mol. Opt. Phys. 54, 055301 (2021) 

H. Yasuda, E.G. Charalampidis, P.K. Purohit, P.G. Kevrekidis and J.R. Raney. “Wave manipulation using a bistable chain with reversible impurities.” Phys. Rev. E 104, 054209 (2021) 

T.D. Todorov, “Infinite-Dimensional Linear Algebra and Solvability of Partial Differential Equations,” Journal of Logic & Analysis (ISSN:1759-9008), 13:5 (2021), p.1-34, (http://arxiv.org/abs/2106.04039), DOI: https://doi.org/10.4115/jla.2021.13.5. 

Conferences

Elena Dimitrova gave conference talks at: 

• SIAM Conference on Applied Algebraic Geometry, invited talk, “Algebraic design of experiments for regulatory network identification.” Virtual. August 2021.

• Society for Mathematical Biology Annual Meeting, invited talk, “Revealing the canalizing structure of Boolean functions – algorithms and applications.” Virtual. June 2021.

Ryan Tully-Doyle gave conference talks at: 

• International Workshop in Operator Theory and its Applications at Chapman University, August 2021. 

• International Workshop in Operator Theory and its Applications at Lancaster University (virtual), August 2021. 

• Focus Program in Noncommutative Function Theory, Fields Institute, November 2021. 

Elsa Medina gave conference talks: 

• National Council of Teachers of Mathematics Fall Virtual Conference titled: “How Random is That?” Nov. 2021. 

• Teach Bilingual Learning Summit (virtual), titled: “Ideas for Making Mathematics More Accessible for Students from Diverse Backgrounds” in April 2021. 

Linda Patton gave a conference talk at: 

• American Mathematical Society (AMS) Sectional Meeting (virtual) in May 2021. Talk title: “Flat portions on the boundary of numerical ranges of 4-by-4 nilpotent matrices.” 

Amelie Shinck-Mikel gave a conference talk at: 

• 2022 Annual Association of Mathematics Teacher Educators Meeting, Henderson, NV, in February 2022. Talk title: “Lessons from the pandemic; Leveraging unique teaching experiences to inform mathematics secondary clinical practice.” 

Stathis Charalampidis gave conference talks at: 

• Colloquium, Mathematics Department, California Polytechnic State University, San Luis Obispo, November 19, 2021. Talk title: “Recent Advances in Nonlinear Waves: Theory and Computation'.' 

• 2nd Online Conference on Nonlinear Dynamics and Complexity, October 4-6, 2021. Talk title: “Formation of rogue waves in continuous and discrete model.” 

• SIAM Annual Meeting, Spokane, WA, July 19-23, 2021. Talk title: “Rogue waves in integrable and non-integrable systems: Existence, stability and dynamics'' 

• Application of Mathematics in Technical and Natural Sciences (AMiTaNS) conference, Albena, Bulgaria, June 24 - 29, 2021. Talk title: Bifurcation analysis tools for Nonlinear Complex Dynamical Systems'' 

• SIAM Conference on Applications of Dynamical Systems, Portland, OR, May 23-27, 2021. Talk title: “Rogue waves in continuous and discrete models: Existence, stability and dynamics.'' 

Grants

Ryan Tully-Doyle was awarded a National Science Foundation grant - DMS Analysis 2055098 “Representations of analytic functions in several variables and applications”