Isis A. Gallardo

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Biography

My name is Isis A. Gallardo. I was born in Tandil, Buenos Aires, Argentina. I hold a Licenciatura in Mathematics from UNICEN, a Master's in Mathematics from New Mexico State University (2019), and a PhD in Mathematics from the University of Denver (2024), where my dissertation focused on the algebraic structure of residuated lattices and ℓ-pregroups.
My research background is in ordered algebraic structures, universal algebra, and decidability — areas whose core design tension (finding structures expressive enough to ensure decidability, yet simple enough to admit explicit algorithms) maps directly onto open problems in post-quantum cryptography. I am currently transitioning to PQC, with a particular interest in how ring and parameter choices in lattice-based schemes such as ML-KEM and ML-DSA affect concrete security.

• CV- Curriculum Vitae

Current direction

I am currently pursuing graduate opportunities in post-quantum cryptography, with a focus on the algebraic structure of lattice-based schemes and their concrete security properties. I am working through foundational material in applied cryptography and have hands-on experience with quantum algorithms through the Erdős Institute's Quantum Computing Bootcamp (2025).

Portfolio

I have experience in several programming languages, such as Python, Fortran, R, and Qiskit, as well as technical writing and communications. Some of my work can be found here.

Research

My mathematical research spans algebraic logic, universal algebra, and residuated lattices. I am currently expanding into post-quantum cryptography, exploring connections between ordered algebraic structures and the hardness assumptions underlying lattice-based cryptographic schemes.

Publications

Conferences and talks

Teaching

Isis has experience teaching at the University of Colorado Boulder, the University of Denver, and New Mexico State University. I have planned, organized, and instructed several subjects, including: