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Polymath 2023

Feb 19, 2023

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Featured Articles

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Math Stars Excel

Learn about how three Cal Poly students earned the best result out of any United States team in their problem category at an international math competition.

All in a Day's Work - Research and Publications

Apr 6, 2022

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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. 

Students Say It's 'Absolutely Amazing to Be Back in Person'

Apr 6, 2022

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Fall 2021 brought a return to in-person classes. Department club presidents reflect on the positive effects for the community of math majors.

Trinity Kobielusz, Math Club President

“It has been absolutely amazing to be back in person because it has allowed me to reconnect with old friends and also make new friends. I have enjoyed not sitting in front of a computer for all hours of the day and actually being able to talk to my peers in my classes. My level of stress has decreased, and I have been able to manage my time better. Attendance has significantly increased for Math Club since coming back in person. Everyone is eager to be involved and excited to come to our meetings.”

Adrienne Boone, Association for Women in Mathematics Club President

“I switched to the math major during the online spring 2020 quarter. As a result, my classes last year were filled with virtual strangers, so the absolute best part of being back has been getting to know the people outside of the computer! I’ve been able to do things I love with people who I love being around. Whether we’re having fun at the beach or stressing out in the math lounge, I don’t take any of it for granted anymore.

I am especially proud that the Association for Women in Mathematics Club has fostered such a supportive and welcoming environment despite the limitations of the pandemic. Running the club with four other amazing women has solidified my confidence and my love for mathematics. Our bi-weekly meetings and various events have introduced our members to inspiring speakers and provided a space for math-loving people of all identities and backgrounds to feel celebrated and heard. I am so grateful for the community I’ve found in mathematics, and I’m so excited for that community to grow next year.”

Networking and Career Opportunities

The return to campus also gave students unique opportunities to network and seek career advice from local companies. On Dec 1, the operations coordinator, Danielle Borelli, and a recent graduate from the California Cybersecurity institute came to visit. In January, the two Directors, Kim O’Neill and Dmytro Marushkevych, from the Data Science & Analytics Group of Razorfish came to give a talk to the math majors.
 

Passing on the Favor in Gratitude to Charlie Hanks

Apr 6, 2022

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Math alumnus Stephen Corcoran, above, and former Department
Chair Charles Hanks both served in the Coast Guard.

As Stephen Corcoran (Mathematics, B.S., ‘69; M.A., ‘75) tells the story, Charles Hanks was a strong presence in the Cal Poly Mathematics Department. He also played a significant role in Corcoran’s life beyond Cal Poly.

Corcoran came to Cal Poly as an aeronautical engineering major. All engineers took the same two-year calculus progression ending with Hanks’ differential equations course, MATH 318. Along the way, Corcoran also took linear algebra just for fun, and it hooked him on mathematics. He never looked back, not even to tell the Aeronautical Engineering Department that he was changing majors. 

“The deeper I got into mathematics, the more I enjoyed it,” Corcoran said. 

Though Corcoran didn’t use much math in his 26-year career in the Coast Guard — except for programming in COBOL when he improved the payroll system that paid reservists — Hanks, who was a captain in the Coast Guard Reserve, still influenced Corcoran’s career considerably. 

Corcoran joined the Coast Guard directly after graduation, then left in 1974 and decided to return to Cal Poly to pursue his master’s degree. To enroll, he needed approvals from the dean of the college and the Mathematics Department chair, which at the time was Hanks. When Corcoran presented himself, Hanks chewed him out for leaving the Coast Guard, approved his admission and offered him a job teaching agricultural mathematics. 

“Better than that, it just doesn’t get,” Corcoran said.

Corcoran finished his master’s degree and began working for the Burroughs Corporation selling computer systems to financial institutions in San Francisco. He often saw Captain Hanks, who came to the Bay Area for his weekend reserve duty. 

One weekend Hanks told Corcoran, “Make something out of your life, Corcoran. Go back in the Coast Guard.” 

Corcoran told him, “I applied and was rejected. I was just one of too many lieutenants with sea service seeking recall.”

Captain Hanks said, “Try again.” When he reapplied, the Coast Guard found it needed Corcoran. He suspected Hanks had something to do with their change of opinion.

This close relationship between faculty and students and the down-to-earth practicality that Hanks embodied define the Cal Poly experience for Corcoran. 

“The professors have their feet on the ground and make things real life,” Corcoran said. “We never had 300 students in an amphitheater class. To the extent possible, the Mathematics Department added enough sections to satisfy the need. If seats were needed for 300 students, somehow the department opened 10 sections. The students got the attention they deserved.”

When Corcoran attended Cal Poly, state funding for higher education was substantial, and college was the free education California was promising. Full-time tuition was $45 for fall quarter and $15 for spring. The difference was a sports fee for fall. Seeing how much state funding has decreased, he wanted to help students today who face much higher tuition costs.

“It’s no longer an education for all situation in California,” Corcoran said. 

When Corcoran learned of the Hanks Scholarship, he decided to change his annual contribution from a general contribution to the Mathematics Department to one Hanks Scholarship each year.

“It felt more satisfying to contribute to a particular individual,” Corcoran said. “It’s important to fund the Mathematics Department because of its foundational nature: the department supports the whole university, but there aren’t enough mathematics graduates to make as significant a financial impact as would be desirable. I decided if I could directly help one student, I would better appreciate the impact of my contribution.

“When it came down to putting numbers on paper, I decided to change it to two scholarships and perhaps pleasantly surprise someone. I did not know then that Dr. Hanks’ widow Marjorie had passed and the Mathematics Department was concerned for the future of the Hanks Scholarship. For the next five years at least, we will have two scholarships in Charlie Hanks’ name.”

Hanks’ generosity continues to inspire Corcoran.

“Charlie helped me along the way, likely more than I can know,” he said. “Perhaps I can continue the favor in his name and spirit.”

Supporting Mathematics Students

If you'd like to support mathematics students with a scholarship or a gift to the department, you can contact Morgen Marshall, senior director for advancement and external relations, or make a financial donation.

Letter from the Chair 2022

Apr 5, 2022

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Alumni and friends of the Mathematics Department

We’re back in the classroom! It’s been a while since that fateful day when everything went virtual, but the chalk dust is once again flying in building 38. I’m pleased to report that as of winter 2022, math courses are entirely face-to-face.  

While math faculty have all become semi-expert with Zoom and other web-based content delivery methods, the main lesson we’ve learned is that online instruction is a poor substitute for good, old-fashioned, face-to-face coursework. 

During the virtual experiment that COVID forced upon us, in-person courses were limited to labs and other activity-based experiences, so it wasn’t until fall 2021 that we were first allowed to return to the chalkboards. We are now near the forefront of Cal Poly departments for in-person offerings and frequently get thanked by students for going live. 

The beginning of the winter quarter was difficult as each math instructor managed multiple instances of COVID-related student absences. It undoubtedly would have been easier to simply teach the quarter online, so it is a testament to the faculty’s dedication to the live Cal Poly experience that we did the extra work needed to keep our classes in the classroom. 

By the time of this writing, things have stabilized nicely. All our usual activities are up and running: the undergraduate study lounge has reopened, students and faculty are traveling to research conferences, our student clubs are back in person, and we’re all looking forward to the math awards banquet and the faculty/student softball game. Hopefully spring quarter will be even smoother. 

Finally, we recently conducted a search for two new tenure-track faculty members. This search, chaired by Vince Bonini was fantastically successful, and we are happy to announce that Patrick Orson and Cal Poly alumnus Sean Gasiorak will join us in the fall. Watch this space for official introductions upon their arrival next academic year.

In closing, I'd like to once again thank everyone who has supported the department financially. Your gifts have a direct impact on the quality of our program, funding many of the initiatives which are so important to the major but take place outside the classroom. We are incredibly grateful for the flexibility and opportunity provided by your generous donations.

Please keep in touch and let us know what you’ve been up to. I’m happy to once again be able to say that we'd love to see you at the department office if you're ever on campus.

Math Professor Leads Cal Poly Chapter of Statewide Service Program

Apr 5, 2022

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Cal Poly has been selected as one of 45 higher education institutions to implement the statewide #CaliforniansForAll College Corps program on its campus, and math Professor Erin Pearse is helping lead the campus effort.

#CaliforniansForAll College Corps is an initiative by Gov. Gavin Newsom that aims to provide 6,500 college students statewide with service-learning opportunities over the span of two academic years to tackle challenges in climate action, K-12 education and food insecurity.

Thanks to partnerships built by Pearse through the Initiative for Climate Leadership and Resilience, students across campus will have the opportunity to work on climate action projects with community organizations. In true Learn by Doing fashion, students will plan and build the infrastructure that will reduce the carbon footprint of Central Coast communities from Santa Barbara to Santa Cruz.

College of Science and Mathematics media intern Devan Spiegel got all the details from Pearse in a recent episode of the Cal Poly Can podcast. Listen in and find out how students will become climate leaders and receive $10,000 toward their college education in return.

 

Polymath 2022

Apr 5, 2022

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Featured Articles

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Math Professor Leads Cal Poly Chapter of Statewide Service Program

Through the statewide #CaliforniansForAll College Corps, Cal Poly students will earn $10,000 toward their education by becoming climate leaders, and Math Professor Erin Pearse is leading the way.

Letter from the Chair 2021

Apr 7, 2021

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Alumni and friends of the Mathematics Department,

What a year it’s been! Ever since that fateful day in March 2020, all math classes have been conducted as virtual affairs. The change was rather abrupt and could have been a disaster but for the flexibility and ingenuity of math faculty and staff. We recognized right away that nothing can replace the collaborative face-to-face experience that is the centerpiece of our major. It required an incredible effort and sacrifice to reproduce our usual practices as much as possible online — but we rose to the challenge.

While we eagerly await a return to the chalkboards in Building 38, our pandemic operations have made me nothing but proud. Similar observations can be made about our students. Community building and the benefits of peer-to-peer instruction and collaboration — not to mention the encouragement of shared experiences — are difficult to manufacture over Zoom, but math majors are finding a way. Our students have certainly justified our high opinion of their abilities.

The usual activities in the department continue apace though modified by the pandemic. For example, honors during our Spring 2020 Awards Ceremony, usually a banquet, were conferred by many celebrity guests from within and beyond the department, including a special congratulatory shoutout from math Ph.D. Winnie Cooper. We had 25 students and seven faculty members participate in summer research projects with virtual meetings and presentations and I see many interesting senior projects and master’s theses come across my desk digitally. Faculty members' individual research projects also continue. Again, though constrained by circumstances, the department has performed admirably.

A big issue on (virtual) campus lately has been growing Cal Poly’s leadership as a data science and analytics innovator in research and education. The Math Department is part of this campus-wide effort and recently submitted a $1.3 million dollar grant proposal to the National Science Foundation to support data science course development. We look forward to what will happen next with this important undertaking.

Finally, I'd like to once again thank everyone who has supported the department financially. Your gifts have a direct impact on the quality of our program. For example, Math 351 Typesetting with LaTeX; Math 370 Putnam Exam Seminar; and Math 371 Math Modelling Seminar are important classes for the major but cannot be funded via the state budget in 2021-22. Thanks to donor support, though, we will still be able to run these classes next year. We are incredibly grateful for the flexibility and opportunity provided by your generous donations.

Please keep in touch and let us know what you’ve been up to. Once we're all back and live, we'd love to see you at the department office if you're ever on campus.

Student and Faculty Research and Publications 2021

Mar 25, 2021

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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
   

Polymath 2021

Mar 22, 2021

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Featured Articles

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Nothing Stops Mathematics

Not even a global pandemic could interrupt studies of Coarse Ricci Curvature, connectivity in the brain, and Gross-Pitaevskii equations, among others.