Research


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My research interests are focused on Combinatorial Optimization problems both from the perspective of constructing efficient algorithms and proving complexity bounds. The core of my research is applying methods from Real Algebraic Geometry to construct and analyze Semi-algebraic Proof Systems that, in turns, provide unified algorithmic frameworks (e.g. Sum-of-Squares algorithm). To prove strength and limitations of such Semi-algebraic Proof Systems I use various techniques from Linear Algebra, Fourier Analysis of Boolean Functions and Approximation Theory. During my PhD time I was working on Robust Optimization and this topic stays close to my heart. In free time I enjoy exploring random walks in graphs.

Grants


10.2019-09.2021 FLEXIBILITY, Swiss National Science Foundation, Switzerland, 47'000 CHF, Single PI.

02.2018-01.2022 AMBIZIONE, Theory and Applications of Linear and Semidefinite Relaxations for Combinatorial Optimization Problems, Swiss National Science Foundation, Switzerland, 540'620 CHF, Single PI.

04.2014-03.2017 OPUS, Algorithms for robust discrete optimization, The National Science Center, Poland, 114'626 CHF.

08.2013-07.2018 NMS-CH (SCIEX), Approximation Algorithms for Machine Scheduling, Scientific Exchange Programme, Switzerland, 50'000 CHF, Single PI.

09.2013-08.2014 ETIUDA, Planning and scheduling problems with uncertain parameters, The National Science Center, Poland, 20'000 CHF, Single PI.

10.2012-09.2013 GRANT PLUS, Planning and scheduling problems with uncertain parameters, Marshal Office of the Lower Silesia, Poland, 14'045 CHF, Single PI.