Anastasis develops and studies universal deep learning models capable of leveraging geometric structures in data science and time-series problems. He is now an Assistant Professor at McMaster University, Ontario, Canada.

## Research interests

Geometric Deep Learning

• Developed the first neural model which can proveably approximate any function while implementing exact constraint satisfaction with B. ZamanlooyI. DokmanicT. Liu.
• Developed a simple framework for building universal approximators between any differentiable manifold with L. Papon and E. Bilokopytov.
• Introduced the universal the first known class of UAP (Universal Approximation Property)-Invariant feature maps with C. Hyndman.
• Identified the first known homotopic obstructions to non-Euclidean universal approximation with L. Papon

Foundations of Data Science

• Developed the first probability-measure valued universal approximator and showed that it can approximate any regular conditional distribution.
• Introduced the first regret-optimal descent algorithms via control and variational approach to meta-optimization with P. Casgrain.
• Developed the first deep neural model capable of uniformly approximating any piecewise continuous function with finitely many pieces with B. Zamanlooy.

Mathematical Finance

• Introduced the first penalty for arbitrage-free learning with C. Hyndman.
• Introduce the fastest matrix completion algorithm for rapid low-rank + sparse decomposition of asset's covariance matrices with J. TeichmannC. HerreraF. Krach, and Google Research's P. Ruyssen.