About Me
My name is Raul Marquez III and I'm a first-year master's student majoring in mathematics at the University of Rio Grande Valley. Currently, I'm in the 4+1 program for the mathematics department, so I may receive a Bachelors and Masters of Science in a four-year program. I've attended an REU at William's College SMALL Program and the the UT Austin DRP Summer Program. Currently, I'm working as a research assistant on extremal set problems with Professor Alexey Glazyrin.
Published Papers
Arora, Palak & Bruda, Glenn & Fang, Bruce & Marquez, Raul & Miller, Steven & Prapashtica, Beni & Sharan, Vismay & Son, Daeyoung & Tang, Xueyiming & Waheed, Saad. (2025). Upper Bounds for the Lowest First Zero in Families of Cuspidal Newforms. Journal of Number Theory. 277. 10.1016/j.jnt.2025.02.012.
Link to PaperBruda, Glenn & Cooper, Joseph & Jaber, Kareem & Marquez, Raul & Miller, Steven. (2024). Variants of Conway Checkers and k-nacci Jumping. 10.48550/arXiv.2408.08856.
Link to PaperBruda, Glenn & Fang, Bruce & Gilman, Pico & Marquez, Raul & Miller, Steven & Prapashtica, Beni & Son, Daeyoung & Waheed, Saad & Wang, Janine. (2024). Stability of Matrix Recurrence Relations. 10.48550/arXiv.2408.12660.
Link to PaperBruda, Glenn & Fang, Bruce & Marquez, Raul & Miller, Steven & Prapashtica, Beni & Sharan, Vismay & Son, Daeyoung & Waheed, Saad & Wang, Janine. (2025). The Limiting Spectral Distribution of Various Matrix Ensembles Under the Anticommutator Operation. 10.48550/arXiv.2502.00505.
Link to PaperCashman, Caroline & Cooper, Joseph & Marquez, Raul & Miller, Steven & Shuffleton, Jenna. (2024). Hyper-bishops, Hyper-rooks, and Hyper-queens: Percentage of Safe Squares on Higher Dimensional Chess Boards. 10.48550/arXiv.2409.04423.
Link to PaperPrepared Talks at Conferences
Marquez, Raul. Elliptic Curves: Understanding Their Significance and the Point Addition Operation. Stephen F. Austin University. 18th Texas Undergraduate Mathematics Conference. October 28, 2023.
Conference WebpageMarquez, Raul. Upper Bounds for the Lowest First Zero in Families of Cuspidal Newforms. Prarie View Texas A&M. 104th Annual Meeting of the Texas Section of the Mathematical Association of America. March 29, 2025.
Conference WebpageMarquez, Raul. Upper Bounds for the Lowest First Zero in Families of Cuspidal Newforms. University of North Texas. 37th Automorphic Forms Workshop. May 3, 2025.
Conference WebpageCoursework
Graduate (UTRGV)
Complex Analysis (Fall 2025)
Algebra I (Fall 2025)
Numerical Analysis (Fall 2025)
Probality and Statistics (Spring 2025)
Discrete Mathematics (Spring 2025)
Partial Differential Equations (Spring 2025)
Linear Algebra (Fall 2024)
Undergraduate (UTRGV)
Basics of LIGO Data Analysis (Summer 2025)
Modern Algebra II (Spring 2025)
Real Analysis II (Spring 2025)
Topology (Fall 2024)
Applied Discrete Mathematics (Fall 2024)
Electromagnetism (Fall 2024)
Math Project (Fall 2024), Worked on PAWS Assignments on Root Systems
Modern Algebra I (Spring 2024)
Number Theory (Spring 2024)
Boundary Value Problems (Spring 2024)
Analysis I (Spring 2024)
Optics (Spring 2024)
Probability and Statistics (Fall 2023)
Physics for Scientists and Engineers III (Fall 2023)
Complex Variables (Fall 2023)
Modern Geometry (Fall 2023)
Intro to Math Proofs (Fall 2023)