PhD Student
My research interests are focused on the control-theoretical aspects of free boundary problems arising in fluid mechanics, and more recently, deep learning from a mathematical control perspective.

Borjan Geshkovski is a PhD Student at Universidad Autónoma de Madrid (UAM). He earned a MSc in Mathematics at the University of Bordeaux, during which he did an internship on the topic “Obstacle problems: theory and Applications” within the DyCon team.

Currently, he is studying for a PhD in Control Theory under the supervision of Prof. Enrique Zuazua (FAUUniversity of Deusto and Universidad Autónoma de Madrid).

  • MSc in Applied Mathematics (2016 – 2018). Université de Bordeaux, France
  • BSc in Applied Mathematics and Computer Science (2012 – 2016). Université de Bordeaux, France

Master’s Thesis. Obstacle Problems: Theory and Applications

Advisor: Prof. Enrique Zuazua
Abstract: In this master thesis, we present a study of the analytical and optimal control properties for the elliptic and parabolic obstacle problems. The obstacle problem is one of the simplest and most physically relevant free boundary problems. From a mathematical perspective, similar questions as for classical partial differential equations (well-posedness, regularity, optimal control) are addressed, as well as the conception of appropriate numerical schemes and computer simulations of the these problems. This work was supported by the Advanced Grant DyCon (Dynamic Control) of the European Research Council Executive Agency (ERC).

Master's Thesis PDF


Null-controllability of perturbed porous medium gas flow

B. Geshkovski Null-controllability of perturbed porous medium gas flow., ESAIM:COCV, vol. 26, No. 85 (2020). DOI: 10.1051/cocv/2020009 Abstract: In this ...
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Turnpike in Lipschitz-nonlinear optimal control

Esteve C., Geshkovski G., Pighin D., Zuazua E. . Turnpike in Lipschitz-nonlinear optimal control (2020) Abstract. We present a new ...
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Large-time asymptotics in deep learning

Esteve C., Geshkovski B., Pighin D., Zuazua E. Large-time asymptotics in deep learning (2020). hal-02912516 Abstract. It is by now well-known ...
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Controllability of one-dimensional viscous free boundary flows

B. Geshkovski, E. Zuazua Controllability of one-dimensional viscous free boundary flows Abstract: In this work, we address the local controllability ...
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Awarded the “Best Review and Presentation Prize” at the second ConFlex workshop held in Bilbao, from February 11 to 21, 2019

coming soon!

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