Promise Prize Winners

#### 2020

The 2020 Benedict Freedman Prize for Mathematical Promise was shared by **BEN C. PAGANO and ANDREA G. STINE**.** **

Ben Pagano is a math major with a double minor in theater and computer science. In the summer of 2018, he worked with Professor Naimi to construct directed graphs with intrinsic knots and links of arbitrary complexity. The following summer, he worked with Professor Sundberg and fellow student Kate Grossmann to characterize extremal hypergraphs for the Erdős-Selfridge Theorem. Finally, in the summer of 2020, through a remote REU hosted by Georgia Tech, he worked with Professor Kuzbary and fellow students to try and prove that the string link concordance group is not solvable.

Andrea Stine is currently a graduate student in mathematics at the University of California - Riverside (where she has found not only does she love doing math, she loves teaching it as well!). She graduated from Occidental with a degree in mathematics in Spring 2020 after transferring to Occidental from Missouri State University. Andrea worked with Jay Daigle in the summer of 2018 on numerical monoids, and in particular, on delta sets.

#### 2019

The 2019 Benedict Freedman Prize for Mathematical Promise was awarded to **VENA A. ZHANG**, a double major in mathematics and computer science. She conducted research on factorization theory in numerical monoids, and analyzed how adding non-irreducible elements to the set of factors affects an invariant known as the delta set. This research combined combinatorial and number-theoretic and computer simulations to understand the algebraic structure of numerical monoids. Vena also excelled in her studies, and is the recipient of the Benedict Freedman Senior Prize in Mathematics.

#### 2017

The 2017 Benedict Freedman Prize for Mathematical Promise was awarded to **THAYER A. FISHER**, a Mathematics/Chinese double major with a minor in Computer Science. He aced all his math classes with a knack for creative problem solving. Thayer did summer research on "Phylogenetic topographer: systematic exploration of the phylogenetic likelihood surface" at the Fred Hutchinson Cancer Research Center in Seattle in 2016 which led to his honor project taken with Professor Lengyel. His research combined probability theory, statistical theory, biological modeling, and sophisticated computer science techniques and applications. Thayer was twice the highest scoring Oxy student taking the Putnam competition. Fisher is also the co-recipient of the Benedict Freedman Senior Prize in Mathematics.

#### 2016

The 2016 Benedict Freedman Prize for Mathematical Promise was awarded to **JESSE M. KREGER**. His work was on mathematical modeling of epidermal wound healing, an interest that was sparked during the MATH 392 Mathematical Models in Biology course. He also participated in the 2015 UCLA Applied Mathematics REU, where he completed a mathematical fluid dynamics project on the modeling of particle-laden slurries. This work was presented as a poster and oral presentation at the 2015 American Physical Society- Division of Fluid Dynamics conference. Jesse will be attending the math Ph.D. program at UC Irvine beginning in Fall 2016.

#### 2015

The 2015 Benedict Freedman Prize for Mathematical Promise was awarded to **EMILY J. HEATH**. She conducted research in the area of positional game theory, where she investigated extremal hypergraphs for the Erdős–Selfridge theorem, which is a pivotal result in the area of positional game theory. Specifically, together with Professor Sundberg, Emily characterized the economical extremal hypergraphs for the Erdős–Selfridge theorem. Emily began her research in this area with an independent study that she took in Spring 2013. She then spent the summer at Carleton College where she participated in the Summer Mathematics Program for Women Undergraduates. In Spring 2014, she attended the Budapest Semesters in Mathematics and returned in Summer 2014 where she did the bulk of her research with Professor Sundberg as part of the Summer Research Program (SRP) run by Occidental’s Undergraduate Research Center. Emily presented her results as a talk at the SRP summer conference in July 2014 and at the Nebraska Conference for Undergraduate Women in Mathematics in January 2015. She also presented her work as a poster at the Joint Mathematics Meetings in January 2015 where she received an award for an "Outstanding Presentation". Emily and Professor Sundberg compiled their research into a scholarly manuscript which was published in the journal Discrete Mathematics, Volume 339, Issue 9, 6 September 2016. Emily graduated summa cum laude from Oxy in 2015 with an overall GPA of 4.0. She is now attending the University of Illinois at Urbana-Champaign where she is pursuing her PhD in Mathematics and she is staying very active in the mathematics community and enthusiastically supporting and contributing to activities which promote the success of women in mathematics.

#### 2013

Senior mathematics major **HANNAH R. SCHWARTZ** received the 2013 Freedman Prize for Mathematical Promise. During the summer of 2012 Hannah worked on two problems in the field of spatial graph theory: finding new intrinsically knotted graphs and their relations to known intrinsically knotted; and finding out if K_9 has a linear linkless embedding. She found a few new intrinsically knotted graphs, one of which has one of the smallest known families for such graphs.

#### 2012

The 2012 Benedict Freedman Prize for Mathematical Promise was awarded to mathematics junior **JACOB ORTEGA-GINGRICH**. His work was on investigating and improving a mathematical model for cinematic box-office dynamics, known as the Edwards-Buckmire Model (EBM). He initially did this work as a rising sophomore during a 10-week summer research program supported by the Howards Hughes Medical Institute and Undergraduate Research Center at Occidental College in 2010. Jacob made significant modifications to the EBM and has been researching several different aspects of the modified EBM and other associated problems since then. This research is an interesting combination of applied mathematics and economics. A summary of some of his joint work with Profs. David Edwards (University of Delaware) and Ron Buckmire (Occidental College) has been submitted for publication. Jacob is an accomplished musician and intends to go to graduate school in the near future.

#### 2011

The 2011 Benedict Freedman Prize for Mathematical Promise was awarded to mathematics junior **NOAM GOLDBERG**. His work was on minor minimal intrinsically knotted graphs in S^3. He did this work as a rising sophomore during a 10-week summer research program supported by URC at Occidental College. He gave a presentation on his work at a National Council on Undergraduate Research annual conference. Noam's joint work with Profs. Thomas Mattman (CSU Chico) and Ramin Naimi (Occidental College) will be submitted for publication in the near future. Noam is in the 3-2 program and will spend his last two years of studies at Columbia University in New York.

#### 2010

The 2010 Benedict Freedman Prize for Mathematical Promise was awarded to math senior **ZHENGYI ZHOU**. Her honors senior thesis centered on ordinary differential equation modeling of traffic flow. She began that work in a summer research experience and had gone on to present parts of that work at various regional and national meetings, including the conference by the National Council on Undergraduate Research. Zhengyi was born and raised in Chengdu, China and came to Oxy after attending Raffles Junior College (for high school) in Singapore. Zhengyi double majored in Mathematics and Economics and earned honors in both fields. She is currently pursuing her PhD in Applied Mathematics at Cornell University.

#### 2005

The 2005 Benedict Freedman Prize for Mathematical Promise was shared by math seniors **DAVID COLLINS** and **PATRICK DIXON**. Both did undergraduate research during the summer of 2005 (supported by Occidental's Undergraduate Research Center). Patrick's work was in applied mathematics (Epidemiological Modeling of STDs in Adolescent Populations Using Graph Theory, faculty mentor: Ramin Naimi), while David's work was in pure mathematics (Winning Strategies and Other Properties of the Game of 3-Pile Euclid, faculty mentor: Tamas Lengyel).

David and Patrick each received a $250 prize, awarded at a ceremony in the spring of 2006. Following the ceremony, each gave a talk on their work.

#### 2004

Junior mathematics major **DAVID COLLINS **of Bakersfield received the 2004 Freedman Prize for Mathematical Promise. His research (Variations on a Theme of Euclid, faculty mentor: Tamas Lengyel) falls within a branch of mathematics known as combinatorial game theory. Collins’ work on developing winning strategies for variations of the game Euclid was published in INTEGERS, the Electronic Journal of Combinatorial Number Theory.

Collins plans to teach mathematics at the college or university level.

#### 2003

Senior **RADOSLAV M. KIROV** of Sofia, Bulgaria, received the 2003 Freedman Prize for Mathematical Promise. Radoslav, a double-major in Mathematics and Physics, did two summer research projects at Occidental College with Ramin Naimi -- one on elliptic curves, number theory, and triangles with rational sides; the other on list-coloring in k-choosable and k-monophilic graphs.

Rado was also impressive in his performance in the Putnam mathematics contest: he ranked 314th out of 2954 contestants!

#### 2002

Junior mathematics major **JOSEF TOBISKA **of Santa Ana was the recipient of the institution's 2002 Freedman Prize for Mathematical Promise. Tobiska was being honored for his work on combinatorics. His submitted work, Integer Partitions and their Application to Quantum Physics, was done with the help of his professor and mentor, Prof. Jennifer Quinn, who describes him as a student with a real knack for problem solving.

Specifically, Tobiska's research centers on integer partitions, in which whole numbers can be broken into a sum of other whole numbers. The integer partitions of three, for example, are 1+1+1, 2+1 and three. This simple idea can lead to many exciting mathematical problems that have far-reaching implications in such fields as physics, computer science and economics. Specifically, their work allowed them to formulate and prove a new theorem regarding the composite Fermion model of the Fractional Quantum Hall Effect.

Tobiska received his $500 prize at a Jan. 30, 2003 ceremony in which he also gave a 45-minute presentation on his research. He was selected for the Freedman Prize by a committee of Occidental mathematics faculty. Receiving honorable mentions were junior Daniel Ionita of Bucharest, Romania, and senior Radoslav Kirov of Sofia, Bulgaria.

#### 2001

**ROBERTO CARLOS PELAYO **is the winner of the first annual Benedict Freedman Prize for Mathematical Promise.

Professor Emeritus Benedict Freedman awarded the prize to ROBERTO CARLOS PELAYO '02 on Thursday, November 15, 2001 on the Branca Patio of the Johnson Student Center. Following the awarding of the prize, Bob made a brief presentation of his work.

Bob was awarded the prize for his investigation of probabilistic problems arising in the area called "graph colorings." One of the problems can be described informally as follows: Every student in a class is given two specific numbers (which may or may not be the same for each student) and is asked to randomly pick one of them. For a given seating arrangement and assignment of number choices to students, there is a certain probability that neighboring students will choose the same number. Working with Professor Ramin Naimi, Bob developed methods to find exceptional examples where, surprisingly, the probability can be larger than the case where all students are given the same two numbers.

Even for situations with ten or fewer students, the number of cases to check an example can tax the capacity of currently available computers. Bob developed a deep understanding of the problem and was able to choose instances which allowed him and his advisor to develop a necessary and sufficient condition for the seating arrangements where the surprising exceptions cannot occur.

Roberto Pelayo is a Los Angeles native and a graduate of Loyola High School where, among his many activities, he was President of the Math Club. Bob entered Occidental College in 1998 with forty Advanced Placement credits. Bob is now attending graduate school in Mathematics at Caltech with a 5 year James Irvine Fellowship.