# Recent News

## Letter from the Chair - 2017

Jun 13, 2017

It’s been a big year for the College of Science and Mathematics. You may have heard that Bill (Biochemistry, ’72) and Linda Frost recently made a historic gift of $110 million to the college. We’re very grateful to the Frosts for their generosity.

This gift will directly impact the Mathematics Department in a number of ways. It includes money for scholarships to attract the most academically talented high school students. Math students are eligible for these scholarships, which offer $20,000 a year for four years. Currently, there are four of these Frost Scholars in the department.

Summer research students will also benefit from the gift. You can read about the accomplishments of our summer research students in this newsletter.

This gift also includes the previously announced $20 million for the new Science and Agriculture Teaching and Research Complex, which will provide approximately 2,000 square feet of dedicated computational and collaboration space for student-faculty research in multiple disciplines, including mathematics. The building is scheduled to open in the 2021-22 academic year.

From what I’ve seen of preliminary design plans, this new building will be one of the most impressive on campus. Located across from the Baker Center in the open space between the English and Science North buildings, it will incorporate many of the latest innovations in architectural design.

The total cost for the science and mathematics facilities in the building is $25 million, and the college still needs to raise $2 million. In addition to providing needed funding, your donation to this building project will demonstrate to the Frosts that mathematics alumni are dedicated to Cal Poly. If you’re interested in supporting the building, you can read more information online, contact me, or contact the college.

We’re grateful for all the different ways our alumni give back to Cal Poly. In January, we were excited to host alumnus Don Gibson (Mathematics, ’80). As a student, Don competed as a Putnam Exam team member, was a member of Kappa Mu Epsilon, completed two internships with IBM, and was named Outstanding Graduating Senior for the School of Science and Mathematics. After graduating from Cal Poly, Don worked for Hewlett-Packard until his retirement in January 2011. At HP, Don worked in many capacities, which included conducting hundreds of interviews for technical positions. Don spoke to a packed room of math majors about his experience as a recruiter and passed on advice for students confronting job interviews for the first time. It was a pleasure to meet Don, as well as a wonderful experience for our students to connect with him and benefit from his expertise.

In closing, 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.

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

## Publications, Grants and Awards 2016-17

Jun 6, 2017

## Publications

A. Bertram and R. Easton. "The tropical Nullstellensatz for congruences." Advances in Mathematics. 308 (2016) 36-82, DOI 10.1016/j.aim.2016.12.004.

J. Borzellino and V. Brunsden. “On the notions of suborbifold and orbifold embedding.” Algebraic & Geometric Topology. 15 (5)(2015) 2789-2803.

E. Brussel, K. McKinnie and E. Tengan. “Cyclic length in the tame Brauer group of the function field of a p-adic curve.” American Journal of Mathematics. 138(2)(2016) 251-286.

C. Gu. “Algebraic properties of Cauchy singular integral operators on the unit circle.” Taiwanese Journal of Mathematics. 20 (1) (2016) 161-189.

C. Gu. “Reducing subspaces of weighted shifts with operator weights.” Bulletin of the Korean Mathematical Society. 53 (5) (2016) 1471-1481.

C. Gu, M. Chō and W. Y. Lee. “Elementary properties of infinity - isometries on a Hilbert space.” Linear Algebra and its Applications. 511 (2016) 378-402.

C. Gu, I.S. Huang, D. Kang and W. Y. Lee. “Normal singular Cauchy integral operators with operator-valued symbols.” Journal of Mathematical Analysis and Applications. 447 (1) (2017) 289-308.

E. Hamilton. “Double coset separability of abelian subgroups of hyperbolic n-orbifold groups.” Proceedings of the American Mathematical Society. 144(6) (2016) 2327–2336.

G. Kato. “Topos Theoretic Approach to Space and Time.” Space, Time and the Limits of Human Understanding. Springer, 2017.

J. Liese, B. Miceli and J. Remmel. “Connection coefficients between generalized rising and falling factorial bases.” Annals of Combinatorics. 19(2)(2015) 337-361.

A. Mendes and M. Romero. “A note on the kth tensor product of the defining representation.” Journal of Combinatorics. 7(4)(2016) 715-724.

B. Richert. “A proof of Evans’ convexity conjecture.” Communications in Algebra. 43(8)(2015) 3275-3281.

T. Samuel, K. Falk, T. Jäger, M. Keßeböhmer and J. Rademacher, ed. Diffusion on Fractals and Non-linear Dynamics: Discrete and Continuous Dynamical Systems Series S. 10 (2017).

R. Veeraraghavan, J. Lin, J. P. Keener, R. G. Gourdie and S. Poelzing. “Potassium Channels in the Cx43 Gap Junction Perinexus Modulate Ephaptic Coupling: An Experimental and Modeling Study.” Pflüger's Archiv - European Journal of Physiology. Aug 11 (2016) 1651-1661.

## Invited Talks

Tony Samuel gave two invited talks at the University of Bremen: “Continuity of entropy in one-dimensional Lorenz maps” and “Quasicrystals, Jarník sets and spectral metrics.” Samuel will conduct research at the Mittag Leffler Institute in Swededn in fall 2017.

Joe Borzellino traveled to Krakow, Poland, in fall 2016 to work with collaborator Tomek Rybicki of AGH University of Science and Technology and, while in Poland, attended the 50th Session of the Seminar Sophus Lie at the Mathematical Research and Science Center in Będlewo.

Joyce Lin traveled to Atlanta, Ga., for the Joint Mathematics Meetings in January 2017 to give an invited talk in the American Mathematical Society Special Session on Mathematics in Physiology and Medicine. Undergraduates Sidney Arthofer, Jeffrey Lee, Jojo Brooker, Nolan Schock, Kevin Sum and Caroline Yovanovich also attended.

## Grants

Joyce Lin received a joint National Science Foundation-National Institutes of Health grant to study ephaptic effects — a form of communication within the nervous system — in cardiac tissue. She will collaborate with Steven Poelzing at Virginia Tech’s Carilion Research Institute.

## Awards

Kappa Alpha Theta, a women’s fraternity founded in 1870, named Danielle Champney one of ten Outstanding Faculty Award recipients following the 2015-16 school year.

## Mathematical Competition Results 2016-17

Jun 6, 2017

## Cal Poly Fares Well at Putnam Exam

The 2016 Cal Poly Putnam Exam team of Zach Cooperband, Michael Boulos and Perry Roeder placed 70th out of 568 teams and was coached by Lawrence Sze. Cal Poly was the highest ranking team in the CSU. The team’s high score came from Zach Cooperband, who earned a score of 29, which gave him a ranking of 460.5 out of 4,164 participants. He was one of only two students in the CSU in the top 500. Michael Boulos and Sam Lindbloom-Airey scored 11 points each, Perry Roeder earned 9 points, and Nore Vellandi finished with 8 points. View the complete results online. Congratulations to the team and Coach Sze!

## Mathematical Contest in Modeling Team Finishes in Top 10 Percent

In January, six three-student teams competed in the Mathematical Contest in Modeling. The top Cal Poly team of Sidney Arthofer, Caroline Yovanovich and Aron Daw earned the rank of Meritorious, which is awarded to the top 10 percent of teams. Three Cal Poly teams achieved Honorable Mention, awarded to the top 50 percent of teams, and two teams were designated Successful Participants. The highly competitive field included 8,843 teams, only three percent of which were from the U.S. Congratulations to all the student competitors!

## Students Learn by Doing Summer Research

Jun 5, 2017

## Morgan Sherman with Jason Chew and Aron Daw

### The Rate of Convergence of the Kähler-Ricci Flow on the Complex Torus

The Kähler-Ricci flow is a flow of metrics on a complex manifold that satisfies a PDE which is a nonlinear analog of the heat equation. A solution is a flow of metrics which will tend to smooth out the irregularities in the curvature on the manifold. In our summer project we numerically approximated solutions to the PDE on the complex torus (which, for a given metric, will look like a deformed doughnut) in order to investigate the rate at which the metric converges to the flat metric. Our aim was to compare the rate of convergence with conjectured bounds and our results were consistent with these conjectures.

To tackle this project, the students first acquainted themselves with the notion of a complex manifold, which is, roughly speaking, a smooth geometrical space that can be described by coordinates consisting of complex numbers (a natural example is the complex plane itself). Then we were able to formulate the PDE of interest to us in the case of a torus (which can be realized as a complex manifold). We learned various techniques for numerically approximating the solution to a PDE, and, with extensive coding in MatLab, were able to generate a great deal of concrete examples of tori who were originally deformed due to an irregular curvature but would 'flow' in time toward a more smoothly dispersed curvature.

## Caixing Gu with Eunwoo Choi and Luan Dinh

### Higher Order Isometries on Finite Dimensional Banach Spaces

An isometry is a linear map that preserves the norm. Isometries on the finite dimensional inner product space are orthogonal matrices or unitary matrices. There are relatively few isometries if the norm of the finite dimensional vector space does not come from an inner product. In this project, we study a generalization of isometries — high order isometries. Numerical and symbolic experiments discovered many higher order isometries when the norm is closely related to an inner product norm. We would like to prove these numerical results in a future project.

## Linda Patton with Mollie Zechlin and Jing-Tian Isabella Ye

Mollie Zechlin and JingTian Isabella Ye worked with Professor Linda Patton to study unitary invariants for 4 by 4 matrices. There is a known list of 20 traces involving a matrix A and its conjugate transpose A*. Equality of these 20 traces for two matrices A and B is necessary and sufficient for the matrices to be unitarily similar. Our group made the additional assumption that the matrices are nilpotent. This assumption implies some of the traces are automatically zero so they can be eliminated from the list when checking unitary similarity. Our conjecture was that some of the other traces might be redundant in the nilpotent case. Although we were unable to definitively determine that, we did create examples showing that most of the traces could not be eliminated from the list.

## Joyce Lin with Jeffrey Lee

### Studying the Effects of Anisotropy on Action Potential Propagation in Cardiac Tissue

Jeffrey Lee worked with Joyce Lin to study the speed of action potentials, not simply along the surface of the heart, but also in the depth of the heart tissue. When an electrical signal passes through heart tissue, the muscles contract and allow blood to pump through the body. This electrical signal is called an action potential (AP). The speed of the AP has been studied as an indicator of arrhythmia — abnormal heart beats — and heart failure. We have excellent simulations of the AP, but given the complexities of the cardiac cells, this is only computationally feasible in a tissue sheet. How does this extend to a full three-dimensional heart? We were not able to complete this project during the summer, though Jeffrey found some interesting trends.

## Erin Pearse and Joyce Lin with Jon Lindgren

In the spirit of Learn By Doing, Jon Lindgren has been working with Erin Pearse and Joyce Lin to develop pedagogical materials using a 3D printer. These manipulatives are designed to enhance student learning in the calculus sequences and other upper level courses, providing hands-on visuals for abstract concepts.

## Paul Choboter and Joyce Lin with Sidney Arthofer and Caleb Miller

Nonlinear internal waves, a well-established feature of the coastal ocean, play an important role in various physical and biological processes, including vertical mixing. In our summer project, graduate student Caleb Miller and undergraduate student Sidney Arthofer worked with Paul Choboter and Joyce Lin and physics Professor Ryan Walter to explain the ability of a fully nonlinear mathematical model — the Dubreil-Jacotin-Long equation — to describe field observations with a strong background shear current. This interdisciplinary study utilizes mathematical techniques, numerical simulations, and field observations to answer important questions about internal wave characteristics and water column stability. This research was extended through the 2016-17 academic year, with undergraduate Jeffrey Lee joining the research group.

## Danielle Champney with Lacey Christophersen, Kathryn Voltmer, Brian Keating and Andrew Crosby

Math students Andrew Crosby, Brian Keating, Lacey Christopherson and Kathryn Voltmer spent the summer working closely with Danielle Champney studying data on the assessment of several unique classroom systems from fifth grade through college. Crosby and Keating also worked with alumnus Ben Woodford (B.S., Mathematics, ’12; Single Subject Credential, Mathematics, ’14) on designing curriculum on Growth Mindset for the New Tech High School teacher professional development program. Christophersen and Voltmer spent additional time thinking deeply about student engagement in fifth grade math. The team produced several papers and posters in progress based on the summer research.

## Jeffrey Liese with Jordan Brooker, Alfredo Ramirez and Kevin de Szendeffy

Professor Jeffrey Liese worked with students Jordan (Jojo) Brooker, Alfredo Ramirez and Kevin de Szendeffy studying the asymptotics of minimally overlapping permutations. A permutation p is said to be minimally overlapping if there no integer k>1 such that the first k integers of p are in the same relative order as the last k. Previous work included finding a bound on the probability that a random n-permutation is minimally overlapping as n tends to infinity.

This summer, the students worked on obtaining some exact results with the ultimate goal of precisely determining the aforementioned probability. Although this probability still remains unknown, the group was able to produce some partial results. In particular, they provided some explicit formulas for the number of permutations that overlap in certain specific ways. Perhaps future work on studying other types of overlaps could yield enough information to characterize the asymptotics of minimally overlapping permutations.

Zachary Cooperband also participated in summer research advised by Dave Camp.

## Alumna Appointed Princeton Post-Doctoral Fellow

Jun 5, 2017

Casey Kelleher (B.S., M.S., Mathematics, 2012) will graduate from the doctoral program at UC Irvine in June. She is advised by Richard Schoen, and her research area is geometric analysis with a focus on the Yang-Mills and harmonic map heat flows. Kelleher has been awarded a four-year appointment as a postdoctoral fellow at Princeton University beginning September 2017. She will be partially funded by an National Science Foundation fellowship, and Gang Tian will be her mentor.

Kelleher wasn’t originally planning to study mathematics but switched into the major with the encouragement of her mentors Linda Patton and Matthew White. Kelleher says Cal Poly’s faculty and staff went above and beyond in supporting her and fostering her enthusiasm for math through multiple independent studies with Linda Patton, Matt White, Vincent Bonini, Morgan Sherman and Robert Easton; a research project with Charles Camp; dedicated teaching in her courses; and countless one-on-one conversations.

## Engaging the World of Mathematics

Jun 5, 2017

## Inquiry-Based Learning

Professors Danielle Champney, Todd Grundmeier, Dylan Retsek and Stan Yoshinobu are collaborating on a $2.8 million National Science Foundation-funded project to expand the professional development capacity of the mathematics profession. This five-year project is in its second year, and during the summer of 2017 they will organize three Inquiry-Based Learning workshops in collaboration with 15 other facilitators across the nation.

## Robot Mentors

In June 2016, students from Da Vinci High School in Hawthorne, Calif., visited Cal Poly to showcase robots that they designed and built in response to a problem designed by Cal Poly math students Curtis Li and Alvaro Matias, engineering students Lucas Dodd and Vitto Monteverdi, and faculty advisor Danielle Champney. The Cal Poly team designed a two-month long project to build a robot that could rescue a trapped faculty member in the engineering quad by navigating several obstacles by remote control.

The Cal Poly team also served as mentors for the high school students for the duration of the project along with math student Brian Keating, and helped the high school students troubleshoot their mathematics, physics and engineering questions. During the academic year, the project expanded to grades 9-12. Math students Hayley Cushing, Maria Ramirez and Nick Rubio; engineering students Kara Hewson and Gloria Whang; and physics student Max Yarbrough mentored the high school students.

## All Things Noyce

### Noyce Workshop

Todd Grundmeier and Elsa Medina offered two three-day mathematics workshops for 47 Noyce Scholars during summer 2016. The workshop is designed to provide a support system for these future and current mathematics teachers and an opportunity for them to discuss the teaching and learning of mathematics. The workshop is funded by a National Science Foundation grant that provides $12,000 or $24,000 scholarships to future mathematics teachers who make a commitment to teach in a high needs school district. Noyce Scholars also receive $800 for attending the summer workshops.

### Noyce Summit

Elsa Medina and Noyce Scholar Ben Woodford (B.S., Mathematics, ’12; Single Subject Credential, Mathematics, ’14) presented the results of National Science Foundation-funded work by Medina and Todd Grundmeier in a presentation titled "A Model for Continued Support for Math Scholars" at the 2016 Noyce Summit in Washington, D.C. Woodford was selected from a nationwide pool to be part of a panel presentation at the conference and represented Cal Poly's Math Noyce program.

### Noyce Conference

Elsa Medina, Amelie Schinck-Mikel and undergraduates Maria Ramirez and Hayley Cushing gave a presentation titled "Using the Fold-and-Cut Theorem to Engage Students in Mathematics" at the Western Regional Noyce Conference held in Fresno, Calif.

## Future Teachers Attend Conferences

Math students Roxanne Windover, Julia Gladding and Maria Ramirez attended the 2016 December California Mathematics Council North conference for math teachers and educators.

Elsa Medina, Danielle Champney and four students who are preparing to become mathematics teachers attended the annual California Mathematics Council Conference held in Pacific Grove, Calif.

## Math Academy

The fifth annual Cal Poly Math Academy, directed by Elsa Medina and Amelie Schinck-Mikel, welcomed more than 40 Hispanic students from local high schools to campus this summer. For one week, students solved challenging mathematics problems through hands-on activities. Students also had the opportunity to explore the campus, heard from a campus police officer about forensic science, asked questions of members of the Society of Hispanic Professional Engineers, and toured the agricultural facilities. The academy, which is supported by the College of Science and Mathematics, aims to inspire students to pursue careers in science, technology, engineering and mathematics (STEM) fields and to recognize and enjoy the beauty of mathematics.

## Middle School Science Bowl

The Central Coast Middle School Science Bowl was held at Cal Poly on Saturday, February 25th. The Regional Science Bowl competition is an annual, fast-paced, question-and-answer contest in which students answer questions about Earth, physical, life, and general sciences, and math. Eighteen teams from eight middle schools participated.

Although Science Bowl tournaments have been taking place on the Central Coast for several years, this is the first time that this competition was held at Cal Poly. The competition was organized by Paul Choboter (Mathematics), Jenny Cruz (CESAME) and Jason Diodati (Templeton High School).

The event was generously supported by CESAME, and local community sponsors included IQMS in Paso Robles, MindBody in San Luis Obispo and RSH Construction in San Luis Obispo. The members of the winning team from St. John's Lutheran School in Bakersfield, Calif., received all-expenses paid trips to Washington, D.C., to participate in the National Science Bowl. The U.S. Department of Energy, Office of Science, manages the National Science Bowl and sponsors the finals competition.

## Simple Group Sends Large Cohort to Graduate School

Jun 3, 2016

Thanks to funding from a generous donor, a group of math and math-interested majors met weekly during 2014-15 and 2015-16 for in-depth, on-going discussions of mathematics-related subjects. The Simple Group — named after an enigmatic mathematical object — also hosted well-known guest speakers and held group GRE study sessions.

Though diving deeper into mathematics is the group’s main purpose — discussion topics included the nature of pi and Heegner numbers — it proved a great springboard for graduate school. Five students will attend prestigious doctoral programs at the University of Illinois at Chicago; University of Colorado, Boulder; UC Santa Barbara; UC Santa Cruz and UC Davis.

These successful graduate school applications are due in part to group study efforts on the Mathematics GRE exam, which significantly streamlined the problem-solving process. The fall GRE scores were among the highest ever recorded by Cal Poly math students, reaching as high as the top 10 percentile. This may be one of the most significant and long-lasting benefits of the Simple Group meetings because the department now has good ideas about how to prepare our majors for the exam.

The group is seeking funding to continue in the 2016-17 school year. For more information contact Joe Borzellino, department chair, at jborzell@calpoly.edu or 805-756-2206.

## Letter from the Chair - 2016

May 31, 2016

As I begin my second term as chair of the Mathematics Department, I have some big news to share with you. Thanks to a generous donor, the College of Science and Mathematics has the opportunity to partner with the College of Agriculture, Food and Environmental Sciences on a new research and teaching building. This facility will support undergraduate mathematics research with 1,800 square feet of computational and collaboration space.

Our students and faculty have needed this space for a long time. You can hear directly from them in this video.

Though much of the support for this privately-funded building is secured, the college still needs to raise $5 million. If you’re interested in supporting the building, you can read more information online, contact me at jborzell@calpoly.edu, or contact Ruzena Brar, the college's director of advancement, at rkbrar@calpoly.edu or 805-756-6534.

On a smaller scale, last year I mentioned that the Mathematics Department lab in Building 38 was substantially upgraded with new equipment and furniture that meets the needs of our applied math and mathematics education groups. This summer, the upgrade will be completed with a long overdue refresh of carpet and paint.

In the fall, we welcomed a new tenure-track faculty member, Anthony Samuel, an expert in fractal geometry and analysis. Tony joins us from the Universität Bremen in Germany as an assistant professor. Also, Kara Eversman has been promoted to the scheduling role in the department after spending a year with us as our front office staff person. In this newsletter, you can learn more about each of them, as well as the students’ and faculty’s many achievements.

Also this year, the department went through the thorough and important quinquennial program review process. I am happy to report that the review team affirmed that we are a collegial department comprised of outstanding faculty, staff and students, and one that offers a high quality mathematics program that embodies the Learn by Doing and teacher-scholar models. The team’s report also provided innovative ideas for educating the next generation of mathematicians.

In closing, I’d like to thank those who have supported us through your donations and gifts. Your generosity provides critical support for the students, faculty and staff of the department. It is very much appreciated.

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

jborzell@calpoly.edu

## Summer 2015 Research

May 27, 2016

## Danielle Champney with Chad Eckman, Alvaro Matias and Alex Cheng

Mathematics students Alvaro Matias, Chad Eckman and Alex Cheng worked with Danielle Champney on developing interdisciplinary science, technology, engineering and math (STEM) curriculum that could be adapted for multiple grades and age groups. The group focused on topics in mathematics, statistics, physics and engineering and developed several modules for implementation in middle school, high school and college courses.

Additionally, Eckman adapted one of these modules, which focuses on students' data-based decision making, and implemented it in a fifth grade classroom as part of his senior project in fall and winter. He and Champney are currently writing up the findings. Liberal studies student Colin Schaefer is building on these findings and implementing similar research strategies in another fifth grade classroom to further study how young students make data-driven decisions.

## Paul Choboter with Caleb Miller, Skyer Young and Tuyen Pham

Modern weather prediction relies on the careful incorporation of observational data into numerical simulations to improve accuracy. The process of merging data with a simulation is called data assimilation. The mathematics of data assimilation is well-developed and draws from variational calculus, optimization, control theory and statistics.

Data assimilation is used in simulations of ocean circulation as well, but ocean data is difficult to collect in large quantities, especially near the coast. This project seeks to answer the question: with a limited amount of data to assimilate in a coastal ocean model, where are the optimal locations to collect that data? Realistic simulations were run in several configurations, with synthetic data measured from one simulation and assimilated into a second simulation. The Regional Ocean Modeling System was used to perform the simulations. Preliminary results were reported at the Mathematical Association of America fall 2015 meeting, and the research is ongoing.

## Caixing Gu with Heidi Keas and Robert Lee

Caixing Gu and students Heidi Keas and Robert Lee worked on a project titled "The *n*-inverses of a matrix," which resulted in the submission of a manuscript with the same title in December 2015. The concept of a left *n-*inverse of a bounded linear operator on a complex Banach space was introduced recently. Previously, there have been results on products and tensor products of left *n*-inverses, and the representation of left *n*-inverses as the sum of left inverses and nilpotent operators was being discussed. In this paper, the group gave a spectral characterization of the left *n*-inverses of a finite (square) matrix. They also showed that a left *n*-inverse of a matrix *T* is the sum of the inverse of *T* and two nilpotent matrices.

## Tony Mendes with Thomas Taylor, Brian Jones and Shelby Burnett

Tony Mendes worked with students Shelby Burnett, Brian Jones and Thomas Taylor to study the following problem posed by the late Herb Wilf. Let *u _{k}*(

*n*) be the number of permutations of 1, 2,…,

*n*with no increasing subsequence of length

*k*+1 and let

*y*(

_{k}*n*) be the number of standard Young tableaux with

*n*cells with bottom row at most

*k*cells.

The problem was to find a sign reversing involution proof of the identity

when *k* is even.

Using the Robinson-Schenstead correspondence, we interpreted the problem as one involving red and blue paths drawn inside symmetric permutation matrices. (See attached figure for one of these matrices when *n* = 10.) The group hoped that this new interpretation could lead to new insights into the combinatorics of permutations. We were able to solve the problem in certain special cases, but a general solution to the problem remains elusive.

## Erin Pearse with Jon Lindren and Zach Zhang

Erin Pearse worked with mathematics student Jonathan Lindgren and engineering student Zach Zhang on the problems of reconstruction of missing data and denoising data. The team is developing an algorithm that converts a dataset (for example, a collection of images) into a network of connected points and then exploits the intrinsic geometry of the network to “fix” damaged points using linear algebra.

## Jonathan Shapiro with Buddy Galletti, Adam Mair and Christopher Hurley

Jonathan Shapiro worked with students Christopher Hurley, Adam Mair and Buddy Galletti. The group studied the numerical ranges of composition operators on the Hardy space. They examined the numerical ranges for composition operators whose symbols are automorphisms of the disk, paying particular attention to those whose symbols are elliptical automorphisms. They made several conjectures involving the continuity of the numerical range and the numerical radius. Some continuity results which showed that the numerical range of certain composition operators with elliptical automorphism as their symbols are not disks.

Other research groups were **Dave Camp with Darren Marotta and Ben Brown **and** Stepan Paul with Michael Blakeman, Matthew Varble and Madeleine Jacques.**

## New Faculty and Staff

May 26, 2016

## Kara Eversman

Kara Eversman was born and raised in Los Osos, Calif. After graduating from Cal Poly with a degree in animal science, she moved to Irvine, Calif., where she worked at a fertility clinic. After almost two years in Orange County, Eversman moved to the Bay Area and worked at another fertility clinic and a hospital. Three years later, she returned to the Central Coast and started working with the Cal Poly Mathematics Department in August 2014. Over the past year, she has enjoyed getting to know everyone in the department and helping students.

## Tony Samuel

Tony Samuel joined the mathematics faculty in fall 2015. He earned a B.Sc. from the University of St. Andrews in the U.K. in June 2005. After spending a year at the Department of Pure Mathematics and Mathematical Statistics of the University of Cambridge in the U.K., he returned to the University of St. Andrews and studied with Kenneth Falconer and Bernd Stratmann. In June 2011 he earned his doctorate in pure mathematics for his dissertation A Commutative Noncommutative Fractal Geometry and was honored with an EPSRC Doctoral Prize.

Samuel has held research fellowships at Australian National University and the University of St. Andrews, a guest lectureship at Humboldt-Universität zu Berlin in Germany, and a post-doctoral position at Universität Bremen, also in Germany. His research interests range from operator theory (non-commutative geometry), to dynamical systems, to stochastic, to fractal geometry, to graph theory. His research has been and continues to be supported by grants from the Australian Research Council, the Engineering and Physical Sciences Research Council in the U.K., the Deutsche Forschungsgemeinschaft in Germany, and the National Science Foundation.