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Vu Khac Ky

I am currently a faculty member at FPT University. I graduated from the Honors Program at Hanoi National University in 2009, before moving to Germany for my Master's degree at TU Kaiserslautern. In 2012, I was the only PhD student in France to receive a doctoral research scholarship from Microsoft Research Cambridge and completed my PhD under the supervision of Professor Leo Liberti.

After receiving my PhD from École Polytechnique, I spent two years as a researcher at ITCSC in Hong Kong before returning to Vietnam. I joined FPT University in January 2019.

I was one of the main contributors to the Flyspeck project, a major project in formal mathematics that produced a computer-verifiable proof of the Kepler Conjecture, a problem that had remained open for about four centuries.

In 2026, Professor Tuan Tran and I proved the Courtade–Kumar conjecture, also known as the Most Informative Boolean Function conjecture, a long-standing open problem in information theory. I am also interested in related open problems in Boolean function analysis and information theory, including the Hellinger, Refined MLS, and FEI conjectures.

More recently, I have become interested in practical applications of AI, as well as its fundamental limitations, ethical challenges, and broader impact on science, education, and society.

Teaching Courses

Discrete Mathematics - MAD101
Mathematics for Engineering - MAE101
Mathematics for Machine Learning - MAI391
Probability and Statistics - MAS291
Programming Fundamentals C - PRF192

Publications:

1. Thomas Hales, Mark Adams, Gertrud Bauer, Dat Tat Dang, John Harrison, Truong Le Hoang, Cezary Kaliszyk, Victor Magron, Sean McLaughlin, Thang Tat Nguyen, Truong Quang Nguyen, Tobias Nipkow, Steven Obua, Joseph Pleso, Jason Rute, Alexey Solovyev, An Hoai Thi Ta, Trung Nam Tran, Diep Thi Trieu, Josef Urban, Ky Vu, Roland Zumkeller: A formal proof of the Kepler conjecture, Forum of Mathematics, Pi 5, e2 (2017).

2. Claudia D’Ambrosio, Ky Vu, Carlile Lavor, Leo Liberti & Nelson Maculan: New error measures and methods for realizing protein graphs from distance data, Discrete and Computational Geometry, 57(2): 371 - 418 (2017).

3. Ky Vu: Random projections for high-dimensional optimization problems, 4OR - A Quarterly Journal of Operations Research, 15(3) (2017).

4. Ky Vu, Claudia D’Ambrosio, Youssef Hamadi, Leo Liberti: Surrogate-based methods for black-box optimization, International Transactions in Operational Research, 24(3): 393 - 424 (2017).

5. Leo Liberti, Ky Vu: Barvinok's naive algorithm in Distance Geometry, Operations Research Letters ,Volume 46, Issue 5, (2018).

6. Ky Vu, Pierre-Louis Poirion & Leo Liberti: Random projections for linear programming, Mathematics of Operations Research 43 (4), 1051-1071 (2018).

7. Ky Vu, Pierre-Louis Poirion & Leo Liberti: Gaussian random projections for Euclidean membership problems, Discrete Applied Mathematics 253, 93 - 102 (2019).

8. Ky Vu, Pierre-Louis Poirion, Claudia D’Ambrosio & Leo Liberti: Random projections for quadratic programs over a Euclidean ball, Integer Programming and Combinatorial Optimization, 442 - 452 (2019).

9. Claudia D’Ambrosio, Leo Liberti, Pierre-Louis Poirion & Ky Vu: Random projections for quadratic programs, Mathematical Programming 183, 619 - 647 (2020).

10. Leo Liberti, Pierre-Louis Poirion & Ky Vu: Random projections for conic programs, Linear Algebra and its Applications, 626, 204 - 220 (2021).

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 extremal problems that characterize the limits of information transmission through noisy channels. I am interested in identifying optimal structures and universal principles governing noisy information systems.

My second direction studies the intrinsic geometry of data and learning models. I develop Fisher width, a complexity measure based on information geometry, to study generalization, signal recovery, regularization, and learning dynamics.

My third direction investigates how low-dimensional structure can be exploited in optimization through random projections and adaptive decision subspaces, with applications to linear, conic, semidefinite, and general constrained optimization.

I also work on Bregman geometry, curvature-adaptive optimization, information-theoretic bounds, Pareto geometry, and geometry-aware RBF optimization on manifolds, as well as broader questions concerning the applications, limitations, and societal impact of Machine Learning and AI.

News:

My student Nhat Mai was accepted to the Master program at Bonn University (Germany).
My student Vuong Quang was accepted to the Master program at Technical University of Munich (Germany).
My student Luong Chung was accepted to the Master program at University of Montreal (Canada).

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