Quantum Math Students | College of Sciences

Post Quantum Cryptography

Dr. Henry Chimal-Dzul

Sofía Carranza

I am a graduate student at the Department of Mathematics at UT San Antonio. My research, under the direction of Dr. Henry Chimal-Dzul, focuses on studying the Linear Equivalence Problem—a core hardness assumption underlying several code-based signature schemes currently under evaluation in the NIST PQC standardization process. In this problem, one is given two matrices that generate vector spaces with prescribed structural properties, and the task is to recover the linear transformations that map one space to the other. My goal is to develop and analyze new strategies to attack this problem, including approaches using machine learning techniques. With this approach we are seeking to strengthening or discovering weaknesses on the security of some code-based cryptosystem.

Quantum Information

Dr. José Morales

Mariano Alcalde

I collaborate with Professor José Morales on the theory of open quantum systems with environmental memory (non-Markovian dynamics). I use master-equation and phase-space methods, supported by numerical simulations, to study decoherence and information flow. I have also developed nanophotonics simulations for quantum optics and theoretical AMO models of collective light–matter interactions for applications in quantum information and thermodynamics. I am also interested in the foundations of quantum mechanics and the philosophy of physics.

Avery Tovar

My research focus is on open quantum systems, with an emphasis on the Wigner-Fokker-Planck (WFP) equation. I am developing a Monte Carlo solver that models the time evolution of quantum systems interacting with their environment. In this project, I transform the WFP into its stochastic differential form and integrate it using the Euler-Maruyama method, incorporating drift and diffusion terms, as well as a tunable friction parameter.

Mathematical Quantum Field Theory

Dr. Stephen Peña

Collin Sunes

I am a graduate student in the Department of Physics and Astronomy at UT San Antonio. My research with Dr. Stephen Peña focuses on the mathematical foundations of quantum theory, particularly within the framework of gauge field theory. I am interested in how geometry and symmetry principles underlie the structure of physical laws, and how gauge invariance provides a unifying language between classical and quantum descriptions. My work explores the mathematical consistency of gauge fields and their quantization, as well as connections between field theory, topology, and operator algebras. This research reflects my broader goal of understanding the deep correspondence between mathematics and physics, particularly in the realm of quantum field theory.