About Me

I am a researcher in numerical linear algebra and connected topics, currently living in Geneva, Switzerland.

My interest for mathematics began in my family with my granduncle Jiří Outrata during the secondary school. He introduced me to university-level mathematics and we continued to work together well into my bachelor's years at the Charles University in Prague. However, in later years of my bachelor studies, the influence of the lecturers and professors shifted my main interest to the numerical linear algebra and we agreed with Zdeněk Strakoš to work on my Bachelor’s thesis together. At that time I was also offered a position in the research team of Tomáš Gergelits, which allowed me to attend conferences already as a bachelor student.

The summer of 2016 was quite busy as I was awarded the funding to complete a three month summer research internship at the University of Bath and I also had to defend my Bachelor's thesis immediately after returning. Nevertheless, I enjoyed that summer fully and I was entering my Master studies deeply satisfied. I also reaffirmed that I want to work in academia if possible and decided to focus my energy towards my studies to perform above expectations to make myself in this way more attractive for a future PhD supervisor. In addition, I decided to broaden my field of interest by pursuing a new topic in my Master’s thesis under Miroslav Tůma. I kept my dedication and motivation throughout the studies and I graduated summa cum laude in September 2018.

During the final year of my master‘s studies, I approached Martin Gander hoping he would have had an open position. I wrote to him in particular because we met in person at the ALGORITHMY 2015 conference during my bachelor studies. It was already back then when I knew I would be extremely lucky to ever get a chance to collaborate with him, based on both academical and personal impression and he kindly offered to lead my PhD studies. Together we applied for the Swiss Government Excellence Scholarship to support my stay in Geneva and in 2019 our proposal was awarded the scholarship. I have been thrilled to collaborate with the numerical analysis team of the university and foremost with Martin Gander for the last four years.


Skills and Languages

  Czech (native)     English (fluent)     French (conversational)     German (passive)  
  Python     Matlab     LaTeX     Jupyter    

CV

Available upon request.

Research


Krylov methods     Domain decomposition methods     Related topics     ORCiD

Krylov methods

I've worked with and on Krylov methods both in Prague and Geneva. My first topic of interest was GMRES and its convergence behavior and eventually became my Bachelor thesis topic, under the supervision of Zdeněk Strakoš. The work was an (incomplete) overview of the deep results about GMRES convergence behavior and we finished by looking on polynomial methods in general on infinite-dimensional spaces and in what sense we should think about the approximations of the solution and the operators when we discretize and use a Krylov method, e.g., GMRES. As a result, I obtained a solid theoretical background in theory and analysis of Krylov methods and GMRES in particular.

I continued to be interested in these method and worked on a preconditioner for CG in my Master thesis with Miroslav Tůma. We focused on problems where the system matrix is dually sparse. In particular we considered a block matrix with general rectangular block structure such that considerable amount of the blocks are zero and a lot of the non-zero ones are data-sparse (i.e., either low-rank or well-approximable by some hierarchical format). As a result, I learned techniques to deal both with structurally sparse matrices (elimination tree, graph prunning, ...) as well as with the data-sparse ones, e.g., hierarchical formats (such as HODLR, H, ...() but also low-rank approximation techniques (CUR approximation, randomized techniques, ...).

Domain decomposition methods methods

During my PhD I've transitioned to domain decomposition methods and the Schwarz methods in particular, navigated by Martin Gander. We started with optimized Schwarz methods withdata-sparse transmission conditions as a natural progression given my Master's background. This topic turned out to be very challenging to analyze, especially in contrast to structurally sparse transmission conditions. However the numerical results are very promising for the standard model problems. This naturally lead to further study of convergence behavior and convergence bounds in particular for the algebraic formulations of Schwarz methods.

Realted topics

With Martin Gander we have looked at the newly proposed block GMRES preconditioner for systems coming out of implicit Runge-Kutta discretizations of paraboplic PDEs - originaly the work of Victoria Howle and her group. We tried to understand why does it work so tremendously well for most problems and obtained some interesting results.

With Martin Gander and Lukáš Jakabčin we worked on Schur complement approximation qualities, focusing on the Schur complement on a truncated mesh and its relation to the Schur complement on unbounded domain.

Me and my granduncle Jiří Outrata have done some research in set-valued convex optimization but I deviated from this line of research already during my bachelor studies in Prague.

Teaching experience

Most of my teaching experience has been truly positive and pleasant as I enjoy interacting with younger students. Most of the times I was in charge (not necessarily solely) of preparing and presenting the exercises (often heavily inspired by previous runs of the course) and/or correcting these and giving feedback to students.

  • Linear Algebra
    • (fr-en) University of Geneva, Fall 2019, prof. Bart Vandereycken
    • (cz) Charles University in Prague, Fall 2017, prof. Libor Barto
  • Analysis
    • (fr-en) University of Geneva, Fall 2019 - Fall 2021, prof. Pavol Ševera
    • (cz) Prague University of Economics and Business, Fall 2016 - Fall 2017, prof. Lukáš Krump
  • Numerical Analysis
    • (fr) University of Geneva, Fall 2020 - Spring 2022, prof. Gilles Vilmart
  • Maxwell Equations and Scientific Computing
    • (fr-en) University of Geneva, Spring 2020, prof. Martin Gander
  • Low-rank Models in Scientific Simulation and Machine Learning
    • (en) University of Geneva, Fall 2019, prof. Bart Vandereycken

More about me

The goal of this page is for you (be it a student or a (potential) collaborator) to get some insight into what I am like outside the academia. If we meet at lunch (or elsewhere), we could talk about dozen of things completely unrelated to anything written below but maybe these can serve as humble suggestions.
Currently I'm living with my wife Lea and our cat Čičík in Geneva. In my free time I like to do sport activities, I climb and boulder regularly in Planet Climbing and also bike a decent amount. I used to play florbal as a goalie back in highschool but also did some handball, baseball, basketball and (beach) volleyball.
I enjoy following cultural and political issues and more general discussions about learning, thinking and mind, in all of which I have found the podcaster and philosopher Sam Harris extremely helpful and influential.
From tme to time I relax playing games - either with Lea, our friends or on my own. Our/my favourite titles include Terra Mystica, Puerto Rico, Wingspan, Dominion, Magic The Gathering, Code Names and Dixit but also Stellaris, It Takes Two, League of Legends or Diablo 2. Me and Lea also like to read and watch together - we enjoyed the Eragon and also the Wool sagas but we also spent hours watching The Office or Red Dwarf series or listening to the audiobooks of Terry Prachett.