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# Victor Falgas Ravry

Associate Professor in Mathematics. Main research interests: extremal combinatorics and discrete probability.

Research qualifications: Docent

## Works at

MIT-huset, plan 3, Matematik och matematisk statistik, MIT.B.343 Umeå universitet, 901 87 Umeå

Short bio

• 2004-2008, MMath, University of Cambridge, UK
• 2008-2012, PhD University of London, UK
• 2012-2014, Kempe research fellow, Umeå Universitet
• 2014-2016, Assistant professor, Vanderbilt University, USA
• 2016- , Associate professor, Umeå University
• 2019-, Docent, Umeå University

Research areas

I work in extremal combinatorics and discrete probability, especially extremal graph and hypergraph theory and random graphs.

Extremal combinatorics is concerned with a certain kind of optimisation problems. In essence, it is the mathematics of making the best choice possible in a discrete context and showing no better choice exists. More helpfully perhaps, a typical problem in extremal combinatorics is to maximise or minimise a parameter inside a finite structure subject to some restrictions. For instance: what is the smallest number of weighings on a pair of scales needed to identify a counterfeit coin? how do you win high-dimensional versions of tic-tac-toe? what is the most robust graph you can build with a given number of edges?

While such problems may look like mere puzzles at first glance, they have a great variety of applications within mathematics, statistics and computer science, in particular when it comes to designing optimal structures or algorithms with respect to some parameter or constraint. Progress in extremal combinatorics often occurs at a methodological level: to solve one particular problem, one must develop a new technique which then turns out to be applicable in many other situations. Extremal combinatorics is a highly active and exciting area of research, which has seen some major developments in recent years, and in which there are still a great many open problems to be solved.

My work in discrete probability for its part focusses on random graph models. Motivation for studying such models stems from a desire to gain a rigorous understanding of the behaviour of real-world networks such as social networks, communication networks or neural networks. While these networks may be governed by deterministic principles, they are too large and too complex to be analysed directly. A solution is to model them mathematically as random graphs, encoding statistical information about the real-world network as a probability distribution for a random graph. The typical behaviour of the random graph then provides a good approximation for the actual behaviour of the network. This paradigm underpins the field of statistical physics, which has widespread applications in economics, computer science, biology, physics and chemistry. Again, this area of research is very much alive and active, with a wealth of major advances and new open questions emerging in the past few year

Other information

• Since 2020, I am head of the Master's programmes in Mathematics and Mathematical Statistics.
• Since 2022, I am deputy head of the Bachelor's programme in Mathematics.
• I am one of the organisers the Discrete Mathematics Seminar and the yearly Midwinter Workshop in Discrete Probability, as well as of an upcoming workshop on extremal graphs and hypergraphs at the Mittag-Leffler Institute.
• For the period 2022-2025, my research is supported by a Swedish Research Council Project Grant (VR 2021-03687)
• Previously for the period 2017-2021 my research was supported by a Swedish Research Council Starting Grant (VR 2016-03488).
European journal of combinatorics (Print), Elsevier 2024, Vol. 118
Falgas-Ravry, Victor
Combinatorica
Falgas-Ravry, Victor; Markström, Klas; Räty, Eero
Journal of Graph Theory, John Wiley & Sons 2023, Vol. 104, (1) : 104-132
Falgas-Ravry, Victor; Hancock, Robert; Strömberg, Johanna; et al.
Random structures & algorithms (Print), John Wiley & Sons 2023, Vol. 62, (4) : 887-910
Falgas-Ravry, Victor; Pfenninger, Vincent
Journal of the London Mathematical Society, John Wiley & Sons 2023, Vol. 107, (5) : 1660-1691
Falgas-Ravry, Victor; Pikhurko, Oleg; Vaughan, Emil; et al.
Advances in Applied Probability, Cambridge University Press 2023, Vol. 55, (4) : 1254-1300
Falgas-Ravry, Victor; Sarkar, Amites
Random structures & algorithms (Print), John Wiley & Sons 2022, Vol. 60, (4) : 594-630
Behrstock, Jason; Falgas-Ravry, Victor; Susse, Tim
Journal of combinatorial theory. Series B (Print), Academia Press 2022, Vol. 154 : 1-48
Day, A. Nicholas; Falgas-Ravry, Victor; Treglown, Andrew
Combinatorics, probability & computing, Cambridge University Press 2021, Vol. 30, (2) : 200-227
Day, A. Nicholas; Falgas-Ravry, Victor
Journal of combinatorial theory. Series B (Print), Elsevier 2021, Vol. 151 : 482-508
Day, A. Nicholas; Falgas-Ravry, Victor
Combinatorics, probability & computing, Cambridges Institutes Press 2021, Vol. 30, (2) : 175-199
Falgas-Ravry, Victor; Markström, Klas; Zhao, Yi
Random structures & algorithms (Print), John Wiley & Sons 2020, Vol. 57, (4) : 1007-1049
Day, A. Nicholas; Falgas-Ravry, Victor; Hancock, Robert
Advances in Applied Probability, Cambridge University Press 2020, Vol. 52, (2) : 433-462
Falgas-Ravry, Victor; Larsson, Joel; Markström, Klas
Random structures & algorithms (Print), John Wiley & Sons 2020, Vol. 57, (4) : 1097-1133
Falgas-Ravry, Victor; Markström, Klas; Treglown, Andrew; et al.
Random structures & algorithms (Print), Wiley-Blackwell 2019, Vol. 54, (4) : 676-720
Falgas-Ravry, Victor; O'Connell, Kelly; Uzzell, Andrew
International mathematics research notices, Oxford University Press 2018, (5) : 1411-1441
Behrstock, Jason; Falgas-Ravry, Victor; Hagen, Mark; et al.
The Electronic Journal of Combinatorics, N.J. Calkin and H.S. Wilf 2018, Vol. 25, (2)
Falgas-Ravry, Victor; Lo, Allan
Journal of Graph Theory, Vol. 88, (3) : 411-427
Falgas-Ravry, Victor; Markström, Klas; Verstraëte, Jacques
The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17), Elsevier 2017 : 407-413
Falgas-Ravry, Victor; Pikhurko, Oleg; Vaughan, Emil; et al.
The Electronic Journal of Combinatorics, Vol. 23, (3)
Falgas-Ravry, Victor; Markström, Klas
SIAM Journal on Discrete Mathematics, Vol. 30, (4) : 1899-1917
Falgas–Ravry, Victor; Zhao, Yi
Electronic Communications in Probability, Vol. 20, (50) : 1-6
Björklund, Johan; Falgas-Ravry, Victor; Holmgren, Cecilia
Combinatorics, probability & computing, Vol. 24, (3) : 528-550
Falgas-Ravry, Victor
SIAM Journal on Discrete Mathematics, Vol. 29, (3) : 1504-1539
Falgas-Ravry, Victor; Marchant, Edward; Pikhurko, Oleg; et al.
Journal of Combinatorics, Vol. 5, (3) : 335-354
Falgas-Ravry, Victor; Kittipassorn, Teeradej; Korándi, Dániel; et al.
The Electronic Journal of Combinatorics, Electronic Journal of Combinatorics 2013, Vol. 20, (4) : Article number: P28-
Falgas-Ravry, Victor
Electronic Journal of Probability, Vol. 18, (paper 83) : 1-22
Falgas-Ravry, Victor
Combinatorics, probability & computing, NEW YORK, NY, USA: Cambridge University Press 2013, Vol. 22, (1) : 21-54
Falgas-Ravry, Victor; Vaughan, Emil R.
Advances in Applied Probability, Applied Probability Trust 2012, Vol. 44, (3) : 617-634
Falgas-Ravry, Victor; Walters, Mark
The Electronic Journal of Combinatorics, Newark: The Electronic Journal of Combinatorics 2012, Vol. 19, (3) : P40-
Ravry, Victor Falgas; Vaughan, Emil R.
The Electronic Journal of Combinatorics, Electronic Journal of Combinatorics 2011, Vol. 18, (1) : P95-
Falgas-Ravry, Victor

### Research projects

1 January 2022 until 31 December 2025
1 January 2017 until 31 December 2021

Thesis supervision

I am happy to supervise both bachelor's and master's theses in discrete mathematics and probability theory. I have a wide selection of possible topics to suggest to students. If interested, please send me an email or come by my office for a chat!