List of faculty
members

Research in Cesana’s lab follows two main methodological directions:

1. Mathematical analysis of singular equations and ill-posed optimization problems, especially in elasticity theory and materials science.
2. Integration of analytical methods with Artificial Intelligence (AI) techniques, such as machine learning, neural networks, and genetic algorithms.

We focus on understanding how micro- and nano-scale features and instabilities in multifunctional materials influence the macroscopic behavior of materials and systems used in engineering.

From a modeling perspective, we address complex multi-physics and multi-scale phenomena. For example, in nanoswitches, we study how to optimize the ring-opening reaction rate (governed by quantum mechanics) alongside mesoscale properties like solution concentration (governed by thermodynamics). From a theoretical perspective, these problems involve singular Partial Differential Equations (PDEs) and Boundary Value Problems with highly oscillating solutions. We apply tools like variational analysis, relaxation, and Gamma-convergence to understand the effective behavior of materials such as soft crystals and shape-memory metal alloys, with particular attention to pattern formation and topological defects.

Recently, we have extended our methods using probability and statistics to study anomalies in areas like financial mathematics and blockchain technology/.