# Vít Musil

## About

I am a postdoc at Faculty of informatics, **Masaryk University**, Brno, Czechia.

In September 2018, I completed my PhD at the Faculty of Mathematics and Physics of the
**Charles University** under the supervision of Luboš Pick.

In 2018-2020, I was a postdoc at Dipartimento di Matematica e Informatica 'Ulisse Dini', **University of Florence**, Italy, and at Mathematical institute of the **Czech Academy of Sciences**.

## Research interest

**Mathematical Analysis**function spaces and inequalities, with applications in PDE’s, approximation theory, interpolation

**Computer Science**combinatorial algorithms in deep learning, adversarial patrolling games

## Publications

#### Journal Articles

- Cianchi, Andrea and Musil, Vít and Pick, Luboš,
**Optimal Sobolev embeddings for the Ornstein-Uhlenbeck operator**,*Journal of Differential Equations*, 2023, , eprint. - Musil, V. and Pick, L. and Takáč, J.,
**Optimality problems in Orlicz spaces**,*Advances in Mathematics*, 2023, , eprint. - Cianchi, Andrea and Musil, Vít and Pick, Luboš,
**Sharp exponential inequalities for the Ornstein-Uhlenbeck operator**,*Journal of Functional Analysis*, 2021, , eprint. - Lang, Jan and Musil, Vít and Olšák, Miroslav and Pick, Luboš,
**Maximal Non-compactness of Sobolev Embeddings**,*The Journal of Geometric Analysis*, 2021, , eprint. - Cianchi, A. and Musil, V. and Pick, L.,
**Moser inequalities in Gauss space**,*Mathematische Annalen*, 2020, , eprint. - Cianchi, A. and Musil, V. and Pick, L.,
**On the Existence of Extremals for Moser-Type Inequalities in Gauss Space**,*International Mathematics Research Notices*, 2020, , eprint. - Edmunds, D. E. and Mihula, Z. and Musil, V. and Pick, L.,
**Boundedness of classical operators on rearrangement-invariant spaces**,*Journal of Functional Analysis*, 2020, , eprint. - Cianchi, A. and Musil, V.,
**Optimal domain spaces in Orlicz-Sobolev embeddings**,*Indiana Univ. Math. J.*, 2019, , eprint. - Lang, J. and Musil, V.,
**Strict s-Numbers of Non-compact Sobolev Embeddings into Continuous Functions**,*Constructive Approximation*, 2019, , eprint. - Musil, V.,
**Fractional maximal operator in Orlicz spaces**,*J. Math. Anal. Appl.*, 2019, , eprint. - Musil, V. and Oľhava, R.,
**Interpolation theorem for Marcinkiewicz spaces with applications to Lorentz gamma spaces**,*Math. Nachr.*, 2019, , eprint. - Bakşi, Ö. and Khan, T. and Lang, J. and Musil, V.,
**Strict $s$-numbers of the Volterra operator**,*Proc. Amer. Math. Soc.*, 2018, , eprint. - Musil, V.,
**Optimal Orlicz domains in Sobolev embeddings into Marcinkiewicz spaces**,*J. Funct. Anal.*, 2016, , eprint.

#### Proceedings Papers

- Klaška, D. and Kučera, A. and K\rur, V. and Musil, V. and Řehák, V.,
**Optimizing Local Satisfaction of Long-Run Average Objectives in Markov Decision Processes**, 2024, eprint. - Paulus, A. and Martius, G. and Musil, V.,
**LPGD: A General Framework for Backpropagation through Embedded Optimization Layers**, 2024, eprint. - Klaška, D. and Kučera, A. and Kurečka, M. and Novotný, P. and Řehák, V.,
**Synthesizing Resilient Strategies for Infinite-Horizon Objectives in Multi-Agent Systems**, 2023, , eprint. - Klaška, D. and Kučera, A. and Musil, V. and Řehák, V.,
**Mean Payoff Optimization for Systems of Periodic Service and Maintenance**, 2023, , eprint. - Sahoo, S.S. and Paulus, A. and Vlastelica, M. and Musil, V. and Kuleshov, V. and Martius, G.,
**Gradient Backpropagation Through Combinatorial Algorithms: Identity with Projection Works**, 2023, eprint. - Brázdil, T. and Klaška, D. and Kučera, A. and Musil, V. and Novotný, P. and Řehák, V.,
**On-the-fly Adaptation of Patrolling Strategies in Changing Environments**, 2022, , eprint. - Klaška, D. and Kučera, A. and Musil, V. and Řehák, V.,
**General Optimization Framework for Recurrent Reachability Objectives**, 2022, eprint. - Klaška, D. and Kučera, A. and Musil, V. and Řehák, V.,
**Minimizing Expected Intrusion Detection Time in Adversarial Patrolling**, 2022, eprint. - Klaška, D. and Kučera, A. and Musil, V. and Řehák, V.,
**Regstar: Efficient Strategy Synthesis for Adversarial Patrolling Games**, 2021, eprint. - Paulus, A. and Rolínek, M. and Musil, V. and B., Amos and Martius, G.,
**CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints**, 2021, , eprint. - Rolínek, M. and Musil, V. and Paulus, A. and Vlastelica, M. and Michaelis, C. and Martius, G.,
**Optimizing ranking-based metrics with blackbox differentiation**, 2020, , eprint. - Rolínek, M. and Swoboda, P. and Zietlow, D. and Paulus, A. and Musil, V. and Martius, G.,
**Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers**, 2020, , eprint. - Vlastelica, M. and Paulus, A. and Musil, V. and Martius, G. and Rolínek, M.,
**Differentiation of blackbox combinatorial solvers**, 2020, , eprint.

#### Preprints

- Kerman, R. and Musil, V.,
**Increasingly global convergence of Hermite series**. - Mihula, Z. and Malý, J. and Musil, V. and Pick, L.,
**Maximal noncompactness of embeddings into Marcinkiewicz spaces**, eprint. - Musil, V. and Pick, L. and Takáč, J.,
**Almost compact embeddings between Orlicz and Lorentz spaces**.