About me

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Ilia Kuk
Ilia Kuk

About Me

Hi! I’m Ilia Kuk — an Applied Mathematics PhD student at The University of Arizona in Tucson, working at the intersection of nonlinear optics, quantum-inspired computation, and machine learning. I’m advised by Prof. Ildar R. Gabitov and collaborate across U of A research groups and the New Frontiers of Sound (NewFoS) Center.

Snapshot

  • 🎓 PhD (in progress) — Applied Mathematics, University of Arizona
  • 🔬 Research — nonlinear dynamics, integrable systems, inverse scattering, quantum-like computing and data-driven operator learning
  • 💻 Toolbox — Python (NumPy/PyTorch), Mathematica, LaTeX, a sprinkle of C/C++/CUDA, and an unreasonable amount of Neovim
  • 🌐 Web — building a clean, fast personal site to host notes, code, and demos
  • 📍 Based in — Tucson, AZ (where monsoons, mountains, and good tacos collide)

What I Work On

Quantum-Inspired Acoustics (a.k.a. Phibits)

I study classical acoustic metastructures that emulate quantum-like gate operations. Using precisely tuned phase modulation in aluminum-rod arrays with piezoelectric coupling, we realize analogs of quantum computational and explore algorithmic constructions within a deterministic, classical platform.

Integrable Systems for Communications

I develop methods around the Inverse Scattering Transform (IST) and related operator factorizations to recover signals in nonlinear optical fiber channels, including low-rank, pseudoinverse, and machine-learning-assisted reconstructions.

Data-Driven Operators

I experiment with Fourier Neural Operators and linear surrogates to approximate operators.

Tools & Preferences

  • Editor: Neovim
  • Compute: Python, PyTorch, SciPy, NumPy; occasional C/C++/CUDA for speed
  • Writing: LaTeX, TikZ
  • Plots: Matplotlib + SciencePlots
  • Style: precise, minimal, reproducible

Contact

If you like integrable structure, clean code, and experiments that actually close the loop with theory—let’s talk.