Research Statement
My research focuses on fundamental limits in information, machine learning, and optimization in high-dimensional and noisy systems.
My first research direction is in Information Theory, particularly sharp inequalities and conjectures that characterize the limits of information transmission through noisy channels. I am interested in identifying extremal structures, optimal information degradation, and universal principles governing communication systems.
My second direction studies the intrinsic geometry of data and machine-learning models. I develop Fisher width, a complexity measure based on information geometry, to investigate generalization, signal recovery, regularization, and the dynamics of learning algorithms.
My third direction exploits low-dimensional structure in optimization through random projections and adaptive decision subspaces, with applications to linear, conic, semidefinite, and more general constrained optimization problems.
I also work on Bregman geometry, curvature-adaptive optimization, information-theoretic bounds, Pareto geometry, and geometry-aware RBF optimization on manifolds. I am also interested in applications of Machine Learning and AI, as well as their limitations, challenges, and broader impact on science and society.
Prospective Students
I particularly enjoy working with students who have strong mathematical thinking and an interest in research. Students interested in pursuing a Bachelor, Master's thesis or PhD research with me are welcome to contact me at [myfullname]@gmail.com.
Students I have supervised have subsequently pursued Master's or PhD studies at leading universities, including the University of Bonn, University of Luxembourg, Technical University of Munich (TUM), and Université de Montréal.
Selected Projects
Flyspeck Project (funded by the U.S. National Science Foundation, NSF): development of a formal, computer-verifiable proof of the Kepler Conjecture (role: team member).
Smart Building Project (funded by Microsoft): optimization methods for improving energy efficiency in smart buildings (role: team member).
Quantile Regression in Large Energy Datasets I (funded by RTE): applied research on optimization and statistical methods for large-scale energy systems (role: team member).
Quantile Regression in Large Energy Datasets II (funded by the Siebel Energy Institute): applied research on optimization and statistical methods for large-scale energy systems (role: team member).