Current Undergraduate Research Projects

Student: Mikayla Leggett
Mentor: Mario Bencomo
Dates: Spring 2024
Project:  Solving heat propagation problems via the finite element method

Students: Hassoon Sarwar, Nathan Theng
Mentor: Mario Banuelos
Dates: AY 2022-current
Project:  Structural Variation Detection Methods

Student: Nipun Amarasinghe
Mentor: Carmen Caprau
Dates: AY 2023-2024
Project: Category Theory and Tangle Invariants

Student: Victoria Wiest
Mentor: Carmen Caprau
Dates: AY 2023-2024
Project: Polynomial Invariants for 4-valent knotted graphs

Student: Jacob Caraccilo and Sarah Garner
Mentor: Mario Banuelos
Dates: Summer 2022-current
Project: Modeling Environmental Factors in Valley Fever Prevalence

Past Undergraduate Research Projects

Students: Sarah Garner and Isaiah Gonzalez
Mentor: Mario Banuelos
Dates: AY 2021-2024
Project:  Machine Learning Approaches to Epistasis

Student: Mikayla Leggett
Mentor: Mario Bencomo
Dates: Summer and Fall 2023
Project:  Spectral method solutions to the axi-symmetric, cylindrical heat equation, in the application of estimating internal temperatures of thermally processed foods

 

Student: Anthony Cortez
Mentor: Mario Bencomo
Dates: Spring 2023
Project:  Super-convergence of symmetric finite difference approximations to derivatives.

Student: Audrey Baumheckel
Mentor: Tamas Forgacs
Dates: AY 2021-2022
Project: An exploration of very triangular numbers. Forthcoming in the PUMP Journal of Undergraduate Research
Main Outcome: Baumheckel, A., & Forgács, T. (2023). An Exploration of Very Triangular Numbers. The PUMP Journal of Undergraduate Research, 6, 317-333. 

Student: Alann Rosas
Mentor: Tamas Forgacs
Dates: AY 2022-2023
Project: Towards the characterization of Hermite diagonal reality preserving operators.

Student: Nipun Amarasinghe
Mentor: Tamas Forgacs
Dates: AY 2022-2023
Project: Legendre multiplier sequences interpolated by quartic polynomials

Students: Emma Andrade, Nicholas Tom, and Sarah Garner
Mentor: Mario Banuelos
Dates: AY 2021-current
Project:  Machine Learning Approaches to Epistasis

Student: Cassandra and Megan Siechert
Mentor: Oscar Vega
Dates: AY 2022-2023
Project: Classical multiplier sequences over PIDs.

Student: Christy Nakad
Mentor: Oscar Vega
Dates: Fall 2022
Project: Non-classical multiplier sequences over small finite fields.

Students: Francisco Cruz and Cesar Gonzalez
Mentor: Khang Tran
Dates: AY 2022-2023
Project: Distribution measure of zeros of polynomials satisfying a three-term recurrence.

Student: Audrey Baumheckel and Conor Righetti
Mentor: Carmen Caprau
Dates: AY 2021-2022
Project: A polynomial invariant for colored classical and singular links.

Student: Olivia Soghomonian
Mentor: Marat Markin
Dates: Spring 2021, AY 2021-22
Project: Convergence in Banach Spaces with a Schauder Basis

Student: Anthony Cortez
Mentor: Marat Markin
Dates: AY 2021-22
Project: Dense Orbits of the Tent Map

Students: Katelyn Clark and Vathana To 
Mentor: Steve Chung
Dates: AY 2020-2021
Project: Financial volatility estimation using modern data mining techniques

Student: Grace Burton
Mentor: Oscar Vega
Dates: AY 2020-2022
Project: Multiplier sequences over F₂, F₃, and F₄

Student: Raul Reynoso and Luis Vega
Mentor: Oscar Vega
Dates: AY 2021-2022
Project: The mathematics of Tsuro

Students: Manuel Chacón and Gobind Puniani 
Mentor: Mario Banuelos
Dates: AY 2019-current
Project: The Role of Activation Functions in Deep Learning

Students: Dhan Bautista, Anthony Cortez
Mentor: Michael Bishop
Dates: AY 2020-2021
Project: Basics of Quantum Computation

Students: Joseph White
Mentor: Michael Bishop
Dates: AY 2020-2021
Project: Explorations into Quantum Gravity

Student: Amanda Liles
Mentor: Carmen Caprau
Dates: Fall 2020
Project: Braid Groups and Temperley-Lieb Algebra

Student: Jack Luong
Mentor: Khang Tran
Dates: 2019-2020 AY
Project: Zeros of polynomials generated from rook paths
Main Outcome: Accepted for publication in Z.Anal. Anwend. DOI 10.4171/ZAA/1698

Student:William Reimer
Mentor: Michael Bishop
Dates: AY 2019-2020
Project: Fractal Geometry
 
Student: Juhoon Chung
Mentor: Stefaan Delcroix
Dates: AY 2019-2020
Project: $n=a^2+k \cdot b^2$
 
Student: Jessica Yearton
Mentor: Stefaan Delcroix
Dates: Spring 2020
Project: $n=x^2+3y^2$

Students: Andres Zumba and Libby Farrell
Mentor: Khang Tran
Dates: AY 2018-19
Project: Zero Distribution of a Sequence of Polynomials with a three-term recurrence
Main Outcome: Presentation at the JMM 2018. 

Student: Sam Cleofas
Mentor: Steve Chung
Dates: AY 2018-2019
Project: Retention and Graduation at Fresno State

Student: Kam Chan 
Mentor: Steve Chung
Dates: AY 2018-2019
Project:  Bitcoin Market Analysis

Student: Scott Harbour 
Mentor: Steve Chung
Dates: AY 2018-2019
Project: Bayesian methodology.
Main Outcome: Presentations at 2018 JMM. 

xStudent: Maria Diaz and Yuliana Segura

Student: Andres Zumba
Mentor: Khang Tran
Dates: 2018-19 AY
Project: Zeros of polynomials with four-term recurrence and linear coefficients
Main Outcome: K. Tran, A. Zumba, Ramanujan J (2020). https://doi.org/10.1007/s11139-020-00263-0 

Student: Michael Dunia
Mentor: Michael Bishop
Dates: 2018-19 AY
Project: Minimum Length Scales from Quantum Gravity 

Student: Robert Duyst
Mentor: Agnes Tuska
Dates: 2018-19 AY
Project: Philosophy of Science and Mathematics Education
Main Outcome: Smittcamp Honors Program Research Paper, presentation in Math 191T Junior Seminar in Mathematics Education (Spring, 2019). 

Student: Erick Gonzalez 
Mentor: Oscar Vega
Dates: Spring 2018
Project: The commuting graph of a group
Main Outcome: E. Gonzalez. Commuting Graphs of Split Metacyclic Groups. The PUMP Journal of Undergraduate Research. 1 (2018). 62-67.

Student: Jack Luong and Josh Williamson
Mentor: Tamás Forgács
Dates: 2017-18 AY
Project: The convergence of series with recursively defined term
Main Outcome: T. Forgács, J. Luong and J. Williamson, A note on infinite series with recursively defined terms. Amer. Math. Monthly, 126 (3) (2019), pp. 269-274. DOI: 10.1080/00029890.2019.1555411

Students: Abigayle Dirdak and Daniel Hooker
Mentor: Khang Tran
Dates: AY 2017-18
Project: Zeros of polynomials generated by multiple quadratic factors
Main Outcome: Poster presentation at the JMM 2018.

Student: Miguel Baza
Mentor: Oscar Vega
Dates: AY 2017-18
Project: Multiplier sequences over finite fields

Students: Bradley Scott
Mentor: Oscar Vega
Dates: AY 2017-18
Project: Blocking sets of polygons and complements of hyperplane arrangements in finite projective planes

Student: Jagdeep Basi
Mentor: Oscar Vega
Dates: AY 2017-18
Project: Grim on complete multipartite graphs
Main Outcome: Barretto, S.; Basi, J.; Miyake, M. Grim on Complete Multipartite Graphs. The PUMP Journal of Undergraduate Research 1 (2018). 48-61.

Student: Jalen Harris
Mentor: Steve Chung
Dates: AY 2017-2018
Project: Bayesian GARCH vs. Frequentist GARCH.
Main Outcome: Chung, S., Harris, J., Yeung, D., and Newmark, C.. (2019). Volatility Modeling of the Foreign Exchange Rates under GARCH: A Comparison between Frequentist and Bayesian Methods. Journal of Data Science, 17(3), 591-610.

Student: Ariana Cavazos
Mentor: Carmen Caprau
Dates: 2017-18 AY
Project: An invariant of colored singular links
Main Outcome: Student's Presentations at Northern California Undergraduate Math Conference 2018 and Central California Research Symposium 2018.

Student: Abigayle Dirdak
Mentor: Carmen Caprau
Dates: Summer 2017
Project: Alexander- and Markov-type theorems for virtual trivalent braids 
Main Outcome: C. Caprau, A. Dirdak, R. Post and E. Sawyer. Alexander- and Markov-type theorems for virtual trivalent braids. J. of Knot Theory and its Ramifications 28, No. 1 (2019) 195003 (33 pages).  

Student: Samuel Barretto and Matthew Miyake
Mentor: Oscar Vega
Dates: AY 2016-17
Project: The study of Grim on complete multipartite graphs having a singleton as one of their partitions
Main Outcome: Barretto, S.; Basi, J.; Miyake, M. Grim on Complete Multipartite Graphs. The PUMP Journal of Undergraduate Research 1 (2018). 48-61.

Students: Summer Al-Hamdani, Alexandra Leon
Mentor: Tamas Forgacs
Dates: AY 2016-17
Project: Generating classical multiplier sequences using products of exponential factors
Main Outcome: AL-HAMDANI, Summer; LEON, Alexandra. On Classical Multiplier Sequences. The PUMP Journal of Undergraduate Research, [S.l.], v. 1, p. 14-29, Jan. 2018. ISSN 2576-3725.

Student: Andres Zumba
Mentor: Khang Tran
Dates: AY 2016-17
Project: Zeros of polynomials with four-term recurrence
Main Outcome: K. Tran, A. Zumba. Zeros of polynomials with four-term recurrence. Involve, a Journal of Mathematics Vol. 11 (2018), No. 3, 501-518.

Student: Christopher Bradbury
Mentor: Steve Chung
Dates: AY 2016-2017
Project: Advanced statistical methods

Student: Adam Jauregui 
Mentor: Steve Chung
Dates: AY 2015-2016
Project: Examining Fantasy football using Bayesian Analysis
Main Outcome: Presentation at 2016 JMM. 

Students: Andres Zumba
Mentor: Khang Tran
Dates: AY 2015-16
Project: Zeros of polynomial generated by the reciprocal of 1+t^2+zt^3
Main Outcome: Student's presentation in 37th Annual Central California Research Symposium

Student: Brennen Fagan 
Mentor: Doreen De Leon
Dates: AY 2015-16
Project: On the Immunization of Small Computer Networks

Student: Aramayis Orkusyan
Mentor: Doreen De Leon
Dates: AY 2015-16
Project: On the Immunization of Large Computer Networks

Student: Rebekha Zhou 
Mentor: Steve Chung
Dates: AY 2015-2016
Project: Examining diabetes using logistic regression

Student: John Fausone
Mentor: Steve Chung
Dates: AY 2015-2016
Project: Predicting customer calls

Students: Andrew De La Pena and Sarah McGahan
Mentor: Carmen Caprau
Dates: AY 2014-15
Project: Virtual singular braids and links
Main Outcome: C. Caprau, A. De La Pena and S. McGahan. Virtual singular braids and links. Manuscripta Mathematica (September 2016) 151, Issue 1, 147-175.

Students: Manuel Lopez and Majerle Reeves
Mentor: Doreen De Leon
Dates: 2014-15 AY
Project: Optimal immunization schemes for the flu vaccine

Students: Richard Adams and Janae Dixon
Mentor: Oscar Vega
Dates: 2014-15 AY
Project: Grim on large graphs
Main Outcome: Adams, R.;Dixon, J.; Elder, J.; Peabody, J.; Vega, O.; Willis, K. Combinatorial Analysis of a Subtraction Game on Graphs. International Journal of Combinatorics vol. 2016, Article ID 1476359, 8 pages, 2016. https://www.hindawi.com/journals/ijcom/2016/1476359/

Students: Elaina Aceves and Jennifer Elder.
Mentor: Carmen Caprau
Dates: 2013-14 AY
Project: A Yang-Baxter model for specializations of the Kauffman polynomial
Main Outcome: Presentation at the JMM in Baltimore, January 2014.

Students: Elaina Aceves and Jennifer Elder.
Mentor: Carmen Caprau
Dates: 2013-14 AY
Project: On invariants for spatial graphs
Main Outcome: E. Aceves and J. Elder. On invariants for spatial graphs. Rose-Hulman Undergraduate Mathematics Journal 16, No 2, Fall 2015, 17 pages. 

Students: Kelsey Friesen and Thoa Tran.
Mentor: Carmen Caprau
Dates: 2013-14 AY
Project: Invariants for virtual singular links
Main Outcome: Presentations (talk and poster) at the Central California Research Symposium, April 2014.
Best Oral Presentation by an Undergraduate Student Award.
Honorable Mention recognition for an Outstanding Poster Presentation.

Student: Serena McTeer
Mentor: Carmen Caprau
Dates: 2012-13 AY
Project: The category of sl(3) webs
Main Outcome: Presentation at the Central California Research Symposium, April 2013.

Students: Elaina Aceves and David Heywood
Mentor: Oscar Vega
Dates: Summer 2012
Project: Embedding of cycles in PG(n,q)
Main Outcome: Aceves, Elaina; Heywood, David; Klahr, Ashley; Vega, Oscar. Cycles in projective spaces. J. Geom. 105 (2014), no. 1, 111-117.

Student: Jamie Peabody
Mentor: Oscar Vega
Dates: Summer 2012
Project: Embeddings of cycle-related graphs in finite projective planes
Main Outcome: Peabody, Jamie; Vega, Oscar; White, Jordan. Cycles, wheels, and gears in finite planes. Contrib. Discrete Math. 8 (2013), no. 2, 75-87.
Poster presentation at the JMM in San Diego (Outstanding Poster Presentation Award winner), January 2013.

Student: James Stinecipher
Mentor: Ke Wu
Dates: Summer 2012
Project: Assessing the risk of liver cancer in Hepatitis B patients using Survival Analysis.
Main Outcome: Poster presentation at the Central California Research Symposium (Davin Youngclarke Award for Undergraduate Research Poster).

Student: Joel Smith
Mentor: Carmen Caprau
Dates: 2012-13 AY
Project: The singular Temperley-Lieb category
Main Outcome: Caprau, Carmen; Smith, Joel. The singular Temperley-Lieb category. ISRN Geom. 2014, Art. ID 321509, 9 pp.

Students: Elaina Aceves and Jennifer Elder.
Mentor: Carmen Caprau
Dates: 2012-13 AY
Project: Invariants for spatial graphs
Main Outcome: Poster presentation at the JMM in San Diego, January 2013. Talk at the JMM in Baltimore, January 2014.

Student: Benjamin Wright
Mentor: Oscar Vega
Dates: Fall 2012
Project: Representation of numbers and their powers in base b
Main Outcome: Poster presentation at the JMM in San Diego, January 2013.

Students: Megan Kuneli, Robyn McDonald, and Katherine Urabe
Mentor: Oscar Vega
Dates: 2011-12 AY
Project: The well-covered dimension of Cartesian products of graphs.
Main Outcome: Birnbaum, Isaac; Kuneli, Megan; McDonald, Robyn; Urabe, Katherine; Vega, Oscar. The well-covered dimension of products of graphs. Discuss. Math. Graph Theory 34 (2014), no. 4, 811-827.

Students: Jamie Peabody and Karen Willis
Mentor: Oscar Vega
Dates: 2011-12 AY
Project: A subtraction game on graphs
Main Outcome: Poster presentation at the JMM in Boston, January 2012.

Student: Katherine Urabe
Mentor: Tamas Forgacs
Dates: 2011-12 AY
Project: Investigations of Legendre multiplier sequences
Main Outcome: Blakeman, Kelly; Davis, Emily; Forgacs, Tamas; Urabe, Katherine. On Legendre Multiplier Sequences,  Missouri J. Math. Sci., 24 (2012), 7-23.
Poster presentation at the JMM in Boston (Outstanding Poster Presentation Award winner), January 2012.

Student: David Heywood
Mentor: Carmen Caprau
Dates: Spring and Fall 2012
Project: The SO(2n) Kauffman polynomial
Main Outcome: Caprau, Carmen; Heywood, David; Ibarra, Dionne. On a state model for the SO(2n) Kauffman polynomial. Involve 7 (2014), no. 4, 547-563.

Students: James Tipton and Benjamin Wright
Mentor: Tamas Forgacs
Dates: 2010-11 AY
Project: Multiplier sequences for non-orthogonal bases and simple sets in general
Main Outcome: Forgacs, Tamas; Tipton, James, Wright, Benjamin. Multiplier Sequences for Simple Sets of Polynomials, Acta Math. Hungar. 137 (2012), 282-295.

Student: James Tipton
Mentor: Carmen Caprau
Dates: 2010-11 AY
Project: Connections between graph theory and knot theory
Main Outcomes: Caprau, Carmen; Tipton, James. The Kauffman polynomial and trivalent graphs. To appear in Kyungpook Mathematical Journal.
Talk at the Central California Research Symposium (Outstanding Undergraduate Student Talk in Mathematical Sciences Award winner)

Students: Mario Banuelos and Michelle Hoshiko
Mentor: Tamas Forgacs
Dates: 2010-11 AY
Project: Multiplier sequences in finite fields
Main Outcomes: Talks at the CURM spring research conference, the Central California Research Symposium, the Pacific Coast Undergraduate Mathematics Conference, and the JMM in New Orleans. All given in 2011.

Student: Isaac Birnbaum
Mentor: Oscar Vega
Dates: 2010-11 AY
Project: The well-covered dimension of graphs.
Main Outcome: Birnbaum, Isaac; Kuneli, Megan; McDonald, Robyn; Urabe, Katherine; Vega, Oscar. The well-covered dimension of products of graphs. Discuss. Math. Graph Theory 34 (2014), no. 4, 811-827.

Students: Michelle Hoshiko and Lucy Montalvo
Mentor: Tamas Forgacs
Dates: Summer and Fall of 2009
Project: Highway speeding and policing
Main Outcome: Poster presentation at the JMM in San Francisco, January 2010.

Student: Ana-Cristina Jimenez
Mentor: Carmen Caprau
Dates: 2009-10 AY
Project: Studying knots via braids
Main Outcome: Poster presentation at the JMM in New Orleans (Outstanding Poster Presentation Award winner), January 2011.

Student: Dhiraj Holden
Mentors: Stefaan Delcroix and Oscar Vega
Dates: Summer and Fall 2010
Project: The Collatz conjecture
Main Outcome: Holden, Dhiraj. Results on the 3x+1 and 3x+d conjectures. Fibonacci Quart. 49 (2011), no. 2, 131-133

Student: Iliana Perez
Mentor: Tamas Forgacs
Dates: 2008-09 AY
Project: The cultural costs of international trade
Main Outcome: Talk at the annual meeting of the Missouri Valley Economic Association in St. Louis, MO in October, 2008.

Student: Ana-Cristina Jimenez
Mentor: Larry Cusick
Dates: 2008-09 AY
Project: Three strands, three crossings, one p-colorability
Main Outcome: Poster presentation at the JMM in San Francisco, January 2010.