Recent News
In Memoriam
May 24, 2019
Howard Steinberg, Math Professor from 1970 to 1991
Howard Steinberg passed away on November 3, 2018. He was 89. Howard was born and raised in New York City and graduated from City College in engineering. After his career in engineering and aerospace development, he earned his master’s and doctoral degrees in applied mathematics in 1969 from the Courant Institute of New York University.
Steinberg was hired as an associate professor of mathematics at Cal Poly in 1970. He taught here until his retirement in 1991. While at Cal Poly, he oversaw the graduate math program. He loved teaching and still had contact with many students who had completed advanced degrees in math.
Upon retirement, Steinberg founded Howard Steinberg Photography. He was a member of the San Luis Obispo Museum of Art, the Sierra Club and the San Luis Obispo Land Conservancy.
His family was his priority. He is survived by his wife of 45 years, “Biz” Steinberg, three children and their spouses and five grandchildren. Steinberg’s Celebration of Life was held at the Santa Margarita Ranch Barn on December 9, 2018. Read Steinberg's full obituary.
Alberto Jiménez, Math Instructor from 2001 to 2013
Following a distinguished career in software programming, Alberto Jiménez retired to San Luis Obispo. He came out of retirement to teach for the Mathematics Department for 12 years. He taught multiple courses, from calculus to numerical analysis. Read Jiménez's full obituary.
Exams and Explorations
May 23, 2019
From the Putnam exam to research in conics, the readability of proofs and more, Cal Poly math majors increased their mathematical skills, excelled against some tough competition and created new mathematical knowledge doing research.
Cal Poly Places in top 10% at Putnam Exam Competition
The Cal Poly team of Joel Pion, Sam Lindbloom-Airey and Jason Brown placed 54th out of 568 institutions participating.
The best individual scores were:
- Joel Pion with 20 points and a rank of 619 out of 4,623 students participating
- Sam Lindbloom-Airey, 17 points, rank 708
- Nore Vellandi, 10 points, rank 1,157
- Jason Brown, 5 points, rank 1,437.5
- Weston Grewe, 4 points, rank 1,576.5
- Sean Gonzales, 2 points, rank 2,182.5
- Sergio Aguayo, 1 point, rank 2,720
- Kyle Rachman, 2 points
- Frederick Streetman, 2 points
- Logan Burrington, 1 point
- Kaitlyn Harechmak, 1 point
- Perrin Silveira, 1 point
Congratulations to our team and all of the students who did so well!
The national results are available on the Mathematical Association of America website (spoiler alert — Harvard won).
Summer Research Groups Investigate Conics, Matrices, Learning Proofs and More
Professors Bonini and Pearse with Conor Carroll, Catie Corwin, Uyen Dinh, Sydney Dye and Joshua Frederick
Erin Pearse and Vince Bonini supervised a student research team in the Faculty and Undergraduate Research Student Teams program at CSU Fresno during summer 2018. The team continued to work together during fall quarter at Cal Poly. The students received an outstanding poster award for their presentation at the Mathematical Association of America (MAA) student poster session at the 2019 Joint Mathematics Meetings. They are also working on a paper titled Coarse Ricci Curvature of Complete and Strongly Regular Graphs.
The research was supported by the National Science Foundation and the Frost Fund.
Professor Brussel with Joel Pion and Ryan Zesch
Elliptic curves are a deep area of mathematics with many surprising applications to real life, including cryptography and prime factorization. Pell conics are a special type of conic curve, such as a unit circle. They are the less studied little brother of elliptic curves, with many of the same properties and applications. Our work focused on describing the group structure of pell conics over various rings, and the adaptation to pell conics of some well-known elliptic curve encryption and prime factorization algorithms. This work — titled Curves, Conics and Cryptography — was presented as a poster at the MAA meeting in February.
Professor Champney with Surabhi Agrawal, Chad Collins and Julissa Magana
Chad Collins, Surabhi Agrawal and Julissa Magana worked on a summer project titled Examining Students' Perspectives on Analogies in Abstract Algebra. This research was an extension of Magana and Collins' senior project, as well as independent work that Collins started in winter 2018. The team collected data on and studied students’ use of analogies in making sense of new and difficult Math 481 material, and ultimately extended their findings to describe analogy types, design curricular activities and implications that could use analogies, and more.
Professor Champney with Joelle Saute and Kathryn Voltmer
Joelle Saute and Kathryn Voltmer worked on a summer research project titled Group Effectiveness and Questioning Processes in an IBL (Inquiry Based Learning) Math Classroom. This research was an extension of Saute’s senior project and her work to gain a more in-depth look at how group effectiveness and group questioning of self and peers may or may not be linked. The initial research was supported by a Cal Poly Baker/Koob grant.
Professors Grundmeier and Retsek with Shannon Cardoza and Tommy Giang
Thanks to support from the Frost Fund, this research group explored readability in the context of mathematical proof. Readability is an essential component of proof writing because a completely valid argument is useless if it is entirely incoherent to the reader. Definitions of readability in a mathematical context, however, are limited and vague.
Our work sought to pinpoint which characteristics of a proof contribute predominantly to its readability, specifically in the setting of introductory proofs courses. Additionally, mathematics education research has shown that proof assessment is a subjective process. Therefore we also sought to investigate the role that readability plays in proof assessment.
Professor Patton with Mackenzie Cox, Weston Grewe and Grace Hochrien
The research group worked on a project titled Numerical Ranges of 4 by 4 Nilpotent Matrices. The numerical range $W(A)$ of a matrix $A$ is a convex set in the complex plane. If $A$ is 4 by 4 and nilpotent, then $W(A)$ has at most two line segments on its boundary. This group found families of matrices that show every angle between these line segments is possible. We also found conditions guaranteeing symmetry about given lines through the origin. We used properties of an algebraic curve associated with $W(A)$. Weston and Professor Linda Patton are continuing this work to try to prove some conjectures motivated by our examples.
Additional research groups included:
- Professor Camp with Raymart Ballesteros, Tobias Iven and Brian Knight
- Professor Stankus with Grant Bernosky, Cameron Frederickson, Timothy Royston and Alexa White
- Professor Gu with Chase Peak and Jordan Rowley
Math Department Frost Summer Undergraduate Research Showcase Projects
- Optimal Transport, Coarse Ricci Curvature, and Some Applications
- Uyen Dinh (with FURST students, Dr. Bonini and Dr. Pearse)
- Curves, Conics, and Cryptography, Oh My!
- Joel Pion and Ryan Zesch (Dr. Brussel)
- Fingerprints of the Pleistocene Glacial Cycles
- Tobias Iven (Dr. Camp)
- Glacial Cycles and the 100 Kyr Problem
- Raymart Ballesteros and Brian Knight (Dr. Camp)
- Group Effectiveness and Questioning Processes in an IBL Math Classroom
- Joelle Saute and Kathryn Voltmer (graduate student) (Dr. Champney)
- Examining Students’ Perspectives on Analogies in Abstract Algebra
- Chad Collins, Surabhi Agrawal, and Julissa Magana (Dr. Champney)
- Readability in the Context of Introductory Proofs Courses
- Shannon Cardoza and Tommy Giang (Drs. Grundmeier and Retsek)
- Unitary Equivalence for Tensor Products of Linear Operators
- Chase Peak and Jordan Rowley (graduate student) (Dr. Gu)
- Flat Portions on the Numerical Range of a 4z4 Nilpotent Matrix
- Mackenzie Cox, Weston Grewe and Grace Hochrein (Dr. Patton)
- Recognizing Overlapping Handwritten Digits Using Neural Networks
- Cameron Frederickson, Grant Bernosky, Timothy Royston, and Alexa White (Dr. Stankus)
Bringing Math to the World
May 23, 2019
A panel of alumni met with current graduate students to share information on the career and educational options made possible by a graduate degree.
Cal Poly math faculty and students engage in teaching and learning mathematics in many ways outside the classroom. From increasing inquiry-based learning in higher education to helping lead the math club at a local elementary school to scholarly publications and presentations, the department is making an impact in the world of mathematics.
Faculty and Student Conferences, Workshops and Notable Research
In 2018, Danielle Champney and Todd Grundmeier led National Science Foundation (NSF)-supported workshops on inquiry-based learning in Torrance, California, and Washington, D.C., respectively. The workshops were part of a five-year, $2.8 million collaborative research project between Cal Poly and the University of Colorado Boulder that focuses on increasing the use of research-based teaching practices at the college level.
More than 50 college mathematics instructors from institutions across the U.S. and Canada attended the four-day workshops. To date, more than 400 faculty across the nation have participated in an inquiry-based learning workshop led by Cal Poly faculty.
Stan Yoshinobu, Katie Kahle and Winston Chang from the Academy of Inquiry Based Learning provided workshop administration and logistical support. Sandra Laursen from the Ethnography and Evaluation Research unit at the University of Colorado Boulder led the research and evaluation support.
Grundmeier and Elsa Medina offered a Noyce summer workshops for 25 mathematics teachers. The work is funded by an NSF Noyce Grant.
In 2018, Emily Hamilton and Joyce Lin organized a Mathematics Masters Career Panel for graduate students with alumni Shelby Burnett, who teaches at Cuesta College; Caleb Miller, who is currently a graduate student at University of Colorado Boulder; and James Hall, who works at Amazon. Panelists had lunch with the graduate students and held an open-question career panel for all advanced math majors and graduate students.
Goro Kato gave a talk titled “P-Adic Oka Coherence Theorem” in October and November 2018 at Shizuoka and Waseda universities.
Math majors Julissa Magana and Randolph Mercado facilitated the Pacheco Math Club (PMC) at Pacheco Elementary School in San Luis Obispo during the 2018-19 academic year. PMC is a weekly, after-school math club for 25 students in grades three through six. The program aims to promote a growth mindset in students, especially students who feel discouraged or need a boost in math.
The students and Pacheco Elementary teachers Danielle Elsea, Mercedes Pascual and Cindy Peters co-facilitated hands-on activities on topics such as place value, geometry, fractions, math games and math derived from stories. The activities shared a common focus of doing math in a low-stress, fun and supportive environment, which helped students develop a better understanding and connection to math. This project is funded by the College of Science and Mathematics and led by Rick Mayfield, director of learning and achievement for San Luis Coastal School District, and Professor Stan Yoshinobu.
Elsa Medina, Amélie Schinck-Mikel and liberal studies students Emily Mapa and Adriana Vazquez gave a presentation titled “Opening the Door to 3D Visualization through Multiple Representations” at the California Mathematics Council (CMC) Central Conference in March. Math credential students and liberal studies math concentration students Baylee Wickham, Nicole Linman, Robyn Amendola and Kelsey Genasci attended the CMC North Conference in December 2018.
In October 2018, Linda Patton gave an invited talk on joint work with Caixing Gu titled “A Composition Operator Norm Upper Bound on Multivariable Reproducing Kernel Hilbert Spaces” at the American Mathematical Society sectional meeting in San Francisco.
Patton also worked with math major Jason Brown to study subsets of the C-numerical range of a matrix $A$. The C-numerical range of a matrix A is a set (not necessarily convex) generated by all matrices unitarily equivalent to $A$. They studied the sets generated when the unitary matrices were restricted to certain subgroups.
Brown showed that some symmetry results for the C-numerical range also hold for the special subsets and described some cases when the subsets are simply connected. They worked on plotting these subsets as well as the entire C-numerical range; these plots involve difficult optimization. Brown presented his work at the Spring 2019 Mathematical Association of America meeting at AIM.
Mathematical Association of America’s Golden Section Meeting
Several students attended the Mathematical Association of America’s Golden Section Meeting, which covers northern California, Nevada and Hawaii. See below for photos of the students with the posters they presented.
Brian Knight and Raymart Ballesteros
Joel Pion and Ryan Zesch
Jason Brown
Faculty Publications
P. Ashwin, C. D. Camp, A. S. von der Heydt. “Chaotic and non-chaotic response to quasiperiodic forcing: limits to predictability of ice ages paced by Milankovitch forcing.” Dyn. Statis. Clim. Syst. (2018) 1-20, doi:10.1093/climsys/dzy002.
V. Bonini, S. Ma, and J. Qing. “Hypersurfaces with Nonnegative Ricci Curvature in Hyperbolic Space.” J. Calc. Var. (2019) 58-36, doi:10.1007/s00526-018-1471-2.
V. Bonini, S. Ma, and J. Qing. “On Nonnegatively Curved Hypersurfaces in Hyperbolic Space.” Math. Ann. 372 (2018) 1103-1120, doi.org/10.1007/s00208-018-1694-8.
V. Bonini, J. Qing, and J. Zhu. “Weakly Horospherically Convex Hypersurfaces in Hyperbolic Space.” Annals of Global Analysis and Geometry. 52(2) (2017) 201-212.
S. Burnett, A. Chandler, and L. J. Patton. “Symmetric numerical ranges of four-by-four matrices.” Involve 11(5)(2018) 803–826.
G. Kato. “Fate Changing Door Knock by a Great Mathematician.” Tokyo, Iwanami-Shoten, Jan. 2019.
E. Z. Medina and A. G. Schinck-Mikel. “Dog, Double Dog!” ComMuniCator, California Mathematics Council. March (2019).
Faculty Awards
Vince Bonini and Erin Pearse received a $49,000 grant from the NSF FURST program, which was a collaborative project with CSU Fresno.
Young Alumni Establish Scholarship to Advance STEM
May 23, 2019
Nick (Mathematics and Computer Science, ’02) and Katie (Statistics, ’01) Dellamaggiores started giving to Cal Poly the year after they graduated. Their support has grown over time, and they now fund a scholarship available to math, computer science and statistics majors. Below, the Dellamaggiores discuss what inspired them to give back.
Interview with the Dellamaggiores
What inspired you to start donating to Cal Poly so soon after you graduated?
We received tremendous value from our Cal Poly education and are very grateful for the practical experience we gained there and the job opportunities it has provided us. With the cost of education rising so significantly since we graduated, we felt that now is the right time to start helping and motivating the next generation in their pursuit of quality higher education.
What do you find rewarding about providing student scholarships?
We just love knowing that we’re helping great students in their academic journey. We also enjoy attending the yearly awards banquet to meet and converse with the next generation of students.
The name of your scholarship is "Scholarship for the Advancement of Science and Technology." How do you see your gift contributing to that advancement?
Math, statistics and computer science majors are eligible for the scholarships. Those happen to be the majors Katie and I graduated with. These fields provided us with a great foundation for our impactful careers in the technology industry. Today, these fields are even more relevant given the intense demand for data science, AI, software engineering and cryptography expertise in both industry and academia. We hope these scholarships will attract bright minds that will continue the advancement of STEM.
What Cal Poly experience has been most influential in your life?
We really enjoyed opportunities to practice Learn by Doing by working for on-campus departments. For example, Nick had an amazing internship with the Library Multimedia Group, where he gained experience building real software systems for on-campus clients. Katie had an opportunity to work with the Natural Resources Management Department doing data analysis on real-world data.
Letter from the Chair 2019
May 22, 2019
Since this is my first newsletter as department chair, let me take a moment to introduce myself. My name is Ben Richert, and I came to Cal Poly in 2003. In 2011 I became the undergraduate coordinator for the department and worked closely with the two previous chairs. I can say without reservation that I inherited a well-functioning department with a great reputation on campus from my predecessor, Joe Borzellino. Joe has recently taken on a new and much-needed role on campus as the director of enrollment management.
There is quite a bit of good news to share. First, the $110 million gift from William and Linda Frost continues to benefit the department. We support student-faculty research for 13 math students during the academic year. Baseball analytics, the Witt Ring, the Riemann Sphere and machine learning are among their research topics. This summer will see an additional 20 projects led by nine faculty advisors. These are unique opportunities for Cal Poly undergraduates to develop skills that prepare them to enter industry, graduate school or a credential program. And it’s just good clean fun!
There is also exciting news concerning our graduate program. Students earning a master’s in mathematics from Cal Poly have been successful applying to prestigious doctoral programs or attaining employment at community colleges. We plan to strengthen the path from our degree to positions in industry by adding the option of an applied math specialization.
Our vision involves expanding the applied coursework and developing internship partners. To help with the staffing side of these goals we recently conducted a fantastically successful search, and we are happy to announce that two new tenure-track colleagues in applied mathematics will join us next fall, Elena Dimitrova and Stathis Charalampidis. Watch this space for official introductions upon their arrival.
Finally, let me offer one observation from a newbie. Like the rest of the faculty, I was aware that much of what the department is able to accomplish is due to donations. With the vantage point provided by my new position, however, I am astounded and humbled by the generosity of our donors. On behalf of the faculty and students, let me again offer our sincerest thanks for helping the Mathematics Department meet its critical goals.
Please do keep in touch — we love to hear news, especially in person. If you're in town, please drop by the office to say hello.
Polymath 2019
May 22, 2019
Featured Articles
Exams and Explorations
From the Putnam exam to research in conics, the readability of proofs and more, Cal Poly math majors increased their mathematical skills, excelled against some tough competition and created new mathematical knowledge doing research.
Letter from the Chair
New chair Ben Richert introduces himself and reports on student and faculty accomplishments as well as changes to the graduate program.
An Early Start to Giving Back
Nick (Mathematics and Computer Science, ’02) and Katie (Statistics, ’01) Dellamaggiore started giving back to Cal Poly the year after they graduated.
Bringing Math to the World
From increasing inquiry-based learning in higher education to helping lead the math club at a local elementary school, faculty and students are making an impact in the world of mathematics.
In Memoriam
Bidding adieu to longtime professor Howard Steinberg and instructor Alberto Jiménez, who passed away in 2018.
Letter from the Chair - 2018
May 15, 2018
This year the department began to realize the benefits of the $110 million donation from Bill and Linda Frost to the College of Science and Mathematics. We supported travel to conferences for a record number of undergraduate students, and we can now offer students research stipends during the academic year in addition to the summer.
We’ve also made undergraduate research colloquia a regular part of our colloquium series. These opportunities have generated so much interest in student-faculty research that I believe we will soon offer such exceptional experiences as a regular part of our undergraduate mathematics program.
Melissa Sunata joined the department as our new administrative assistant during fall quarter, and Kristina Wong took over the administrative coordinator role held previously by Cami Reece, who retired in December. Faculty members Goro Kato and Todor Todorov have also announced their retirements at the end of this academic year. We wish them the best in enjoying the good life.
I’d like to once again thank those who have supported us through donations and gifts. We are grateful for the critical support you provide through your generosity. Your continued interest in helping the department meet its goals is very much appreciated by our students, faculty and staff.
I’ll close on a personal note. This year I began a new role as director of enrollment management. I’ve enjoyed working with a universitywide team to find creative solutions to the challenges surrounding enrollment management. Because my time commitment in this area will increase next year, I will be stepping down as department chair, and Ben Richert will take the helm in winter 2019.
It has been an honor and pleasure to lead the department for the last six years. I genuinely believe that we have one of the best and most highly respected departments on campus. I have great faith the department will continue to meet current challenges while realizing its aspirations for the future.
Please keep in touch and let us know what you’ve been up to. If you’re on campus, we’d love to see you at the department office.
Sincerely,
Joseph Borzellino
Department Welcomes New Staff
May 12, 2018
Melissa Sunata
Melissa Sunata was born and raised in Southern California and moved to Las Vegas, Nev., to attend University of Nevada, Las Vegas (UNLV). After graduating with a degree in secondary education and English, she worked for a non-profit organization developing student leadership programs at UNLV. After 9 years at UNLV, she moved to San Luis Obispo and became a stay-at-home mom to three wonderful children. In 2016, Sunata went back to school at Cal Poly for a master’s degree in educational leadership and administration with a focus on higher education. She graduated in summer 2017 and began working with the Mathematics Department. She enjoys serving students, getting to know staff and faculty, and discovering all that Cal Poly has to offer.
Kristina Wong
Kristina Wong grew up in Alameda, Calif. Shortly after completing her degree in kinesiology with a minor in environmental studies at Cal Poly, she joined the Kinesiology Department as a staff member in 2011. She enjoyed making the transition from student to staff and the opportunity to support student learning experiences — especially those promoting health and wellness in communities — as well as learning the about the intricacies of department and campus operations. After taking an extended leave from Cal Poly during the 2016-17 academic year to take care of her health, she is excited and grateful to be back in the College of Science and Mathematics with the Mathematics Department and to continue to support faculty, staff and students in their endeavors at Cal Poly and beyond.
Putnam Results
May 12, 2018
The official Cal Poly team of Zoe Cooperband, Sam Lindbloom-Airey and Perry Roeder placed in the top 15 percent at the annual William Lowell Putnam Mathematical Competition, the preeminent undergraduate mathematics competition in the United States and Canada, coming in at exactly 85.5 out of 575 institutions entered in the competition. Lawrence Sze coached the team this year.
The exam scores of the top Cal Poly finishers were: Zoe Cooperband with 18 points, placing 823 out of 4,638 students; Cruz Godar – 17 points, placing 856; Joel Pion – 12 points, placing 1,005; Perry Roeder – 11 points, placing 1,115.5; Sam Lindbloom-Airey, Michael Hehman, and Jason Brown all with 10 points, placing 1,274.5. A perfect score on the exam is 120, and the winning score was 90.
Congratulations to our team and all of our participants.
For full results, visit the Putnam website.
Students Expand the Frontiers of Mathematics with Faculty Mentors
May 11, 2018
Student researchers and their faculty mentors explored mathematical concepts ranging from quadratic infinite trees to the Game of Life.
Eric Brussel with Patrick Kerrigan
A Simple Continuous Analogue of the ‘Game of Life’
During summer 2017 Eric Brussel and physics major Patrick Kerrigan attempted to construct a simple continuous analogue of the somewhat infamous “Game of Life,” a discrete time and space cellular automaton devised by John Conway. In trying to make the reverse-quantum-leap, there were several difficulties with how to interpret some of the rules of the original game of life, and Kerrigan attempted to put his own twist on some of the things that have already been done by others. Immediately Brussel and Kerrigan were confronted by questions: what sort of metric should be used to determine whether a transition should occur? Indeed, what does a “transition” even look like in this new formulation?
In the end, finding a transition function that allowed for both propagation of “life” and not immediate system collapse was never found, but a few stable states were coaxed into existence with various additional techniques, for example the stable cell in the figure below. Perhaps a more systematic exploration of the parameters involved could shed more light on this situation and find more interesting objects.
This figure shows a stable “alive” cell, unable to move. This is a 1 spatial, 1 temporal dimension version of the ‘game,’ with the time parameter being the backwards direction, so that one can see the stable object persisting in time without moving on this plot. The periodic time displacements visible are from a driving oscillation that Kerrigan added to try to coax out some more movement, but ultimately this failed.
Danielle Champney with Julia Gladding, Nicole Linman, Kathryn Voltmer, Lacey Christopher Maria Ramirez-Camacho, Evelyn Fox and Francis Britschgi
Content-Based Mentorship Program
Lacey Christophersen, Maria Ramirez-Camacho and Kathryn Voltmer worked on extensions of previous summers' projects, completing the final design of a content-based mentorship program. Cal Poly is implementing the program, which is in its third cycle, with partner Da Vinci Science High School in Hawthorne, Calif. The team also developed three research studies. Christophersen and Voltmer also presented a poster on their work during the 2017 Learn by Doing: More than a Motto Conference, and Ramirez-Camacho presented a poster and gave a research talk to prospective and current students and parents at the Cal Poly Mustang Family Weekend Showcase.
Understanding Students' Mathematical Development
Julia Gladding and Nicole Linman developed and implemented a study designed to better understand students' mathematical development of three content-based strands that span from kindergarten through college. Their study included extensive development of tasks and protocols for collecting data on young students' mathematical thinking and understanding.
Their work transitioned into their senior project, and they were joined by Lindsay Nolte. The team of three has, in addition to pursuing their own research, developed a video library that showcases young students thinking along their identified strands, which coincides with the Math for Liberal Studies sequence of four courses offered to future teachers through the Mathematics Department.
The Effectiveness of a Classroom-Based System of Games
Statistics majors Francis Britschi and Evelyn Fox extended previous summers' research to design measures and means for studying the effectiveness of a classroom-based system of games being implemented in fifth grade classrooms. The classroom system is on its fourth cycle during the current academic year, and Britschi and Fox’s experimental design has guided data collection during this first non-pilot year of the system and curriculum.
Robert Easton with Chad Collins, Sam Lindbloom-Airey and Cruz Godar
A Tropical Analogue of the Classical Duality Map for Projective Plane Conics
Robert Easton led a group of Frost Research Fellows consisting of Chad Collins, Cruz Godar and Sam Lindbloom in an investigation into a tropical analogue of the classical duality map for projective plane conics. They ultimately showed that the straightforward tropical analogues of the duality do not lead to a true duality for tropical projective plane conics, but something closer to a partial duality.
Caixing Gu with Sean Gonzales, Perry Roeder and Codi Barnett
Quadratic infinite trees and 3-isometric composition operators.
Isometries are linear operators that preserve the length of vectors. In this project, we studied high order isometries. We focused on a class of composition operators that can be represented by infinite graphs. The branch growth properties of these graphs are closed related to the orders of the generalized isometries. If the graph has a quadratic growth, then we have a 3-isometry. By enumerating these graphs using several mathematical tools, we showed there are unaccountably many (unitarily non-equivalent) such 3-isometries. This is in contrast with the 2-isometries where there are only countably many such 2-isometries.
Erin Pearse and Tony Samuel with Elise Mihanovich, Elisabeth Esquivel, Blaine Quackenbush, Jordan Rowley, Matt West and Zoe Cooperband
The Topological Entropy of 1-Dimensional Dynamical Systems
Erin Pearse and Tony Samuel worked over the summer with Zoe Cooperband, Elisabeth Esquivel, Elise Mihanovich, Jordan Rowley, Blaine Quackenbush and Matt West. The research team studied the topological entropy of 1-dimensional dynamical systems (iteration of Lorenz maps). More specifically, they looked at a family of Lorenz maps with a single discontinuity and attempted to prove that entropy changes continuously as the point of discontinuity is varied.
Cooperband, Rowley, Quackenbush and West continued to work on the project through fall and winter quarters and presented their results at the Joint Mathematics Meeting poster session in January. The preprint is now complete and posted on arXiv.
Dylan Retsek with Scott Warnert
Abstract: Given a set S of functions we often ask
If ƒ and g are members of S and both enjoy property X, does ƒ◦g also enjoy property X?
When S is the set of functions from ℝ to ℝ and property X is continuity or differentiability, we answer this question affirmatively in calculus class.
In this project we considered the Hardy space Η² (ⅅ) of analytic functions on the open unit disk ⅅ in the complex plane whose Maclaurin coefficients are square-summable. Given analytic φ : ⅅ➞ⅅ, the composition operator Cφ on Η² (ⅅ); is then defined by Cφ = ƒ◦φ
Our program of research was to understand certain operator-theoretic properties of Cφ in terms of the geometric-function-theoretic properties of the map φ. In particular, the action of the operator Cφ on the reproducing kernels in Η² was fully classified for linear fractional symbols φ yielding some surprising results. The authors are currently preparing a manuscript for publication.
Student Teacher and Researcher (STAR) Program
Nick Rubio participated in the Student Teacher and Researcher (STAR) Program during summer 2017. He worked with researchers and other future teachers at the Biosphere 2 Lab at the University of Arizona in Tucson. Rubio studied trends in the California drought and learned about research techniques and some applied mathematics techniques, while spending time with fellow participants thinking about how to utilize his new skills in his future high school mathematics classroom. Rubio’s advisor at University of Arizona was Guo-Yue Niu.
Academy of Inquiry Based Learning
Danielle Champney, Todd Grundmeier, Dylan Retsek and Stan Yoshinobu continued their work on supporting inquiry-based learning in college mathematics. Professional Development and Uptake through Collaborative Teams (PRODUCT). This project focuses on A main goal of PRODUCT is to expand the professional development capacity of the mathematics profession in delivering inquiry-based learning (IBL) methods in college math courses.
Co-led by Yoshinobu and Sandra Laursen at the University of Colorado, Boulder, the PRODUCT team includes 19 math professors across the nation in addition to the Cal Poly faculty members. In summer 2018, the entire team will conduct three workshops in Los Angeles, Washington, D.C. and Chicago, and several shorter workshops at math departments and regional conferences in North America.
The project is funded by a $2.8 million National Science Foundation grant. More information is available on the Academy of Inquiry Based Learning website.
http://www.inquirybasedlearning.org/workshops/