# Advanced studies

Why? How? These are our favorite questions. We are curious about the world and driven to create new technologies for the benefit of society. We want to understand what we see in the data. That is why we carry our fundamental research in numerical linear algebra, cryptology, quantum computing and quantum communication, and control theory.

Have you ever watched anything on the Internet? Or have you ever listened to music? For example, while driving an autonomous car or flying a plane (on autopilot)? And have you heard of machine learning? Sure you have! Well, matrix algorithms and linear algebra are behind it all.

**Numerical linear algebra** is the computational engine of modern science and technology. It’s a fascinating area of research bringing together many branches of mathematics. We are working on the new theory of matrix (meta)factorization, compression of AI models, and computational challenges of machine learning. We are looking for new algorithms for data reconstruction, matrix completion, compressed sensing, and sparse sensor placement. All that fuels our AI and cybersecurity systems.

**Cryptology**, classical and post-quantum cryptography algorithms and systems, information theory, number theory, discrete mathematics, error-correcting codes, linear codes, and, if that wasn’t enough for anyone, quantum mechanics. We are working on all this while developing our cyber security technologies. It is not a secret that we are having fun.

#Meta-factorization and encryption functions

**Quantum computing and quantum communication** are on the front lines of science and technology development, at the frontier of what we know and what we can learn about the world. We are working on the theory of quantum computing, we address the challenges of quantum state estimation, and we develop quantum key distribution technology. And we take a look at what the world is made of.

**We are working on:**

- Matrix meta-factorization theory
- Matrix completion algorithms
- Low-rank approximations
- Randomized numerical linear algebra
- DMD/SINDy
- Control theory
- AI models compression
- Sparse sampling
- Convergence of machine learning algorithms
- Generation of cryptographic keys
- Classical and post-quantum cryptography
- Quantum computing
- Measurement and estimation of quantum states
- Fundamentals of secure quantum communication