# Victor Falgas Ravry

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

## Works at

MIT-huset, plan 3, Matematik och matematisk statistik, B341 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 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 very active and exciting area of research, which has seen some major developments in recent years, and in which there are a great many open problems yet 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.

Other information

• From 2020, I am responsible for the Master's programmes in Mathematics and Mathematical Statistics.
• Since Fall 2016, I run the Discrete Mathematics Seminar.
• For the period, 2017-2020 my research is supported by a Swedish Research Council Starting Grant (VR 2016-03488).
2019
Random structures & algorithms (Print), Wiley-Blackwell 2019, Vol. 54, (4) : 676-720
Falgas-Ravry, Victor; O'Connell, Kelly; Uzzell, Andrew
2018
International mathematics research notices, Oxford University Press 2018, (5) : 1411-1441
Behrstock, Jason; Falgas-Ravry, Victor; Hagen, Mark; et al.
2018
The Electronic Journal of Combinatorics, Vol. 25, (2)
Falgas-Ravry, Victor; Lo, Allan
2018
Journal of Graph Theory, Vol. 88, (3) : 411-427
Falgas-Ravry, Victor; Markström, Klas; Verstraëte, Jacques
2017
The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17), Elsevier 2017 : 407-413
Falgas-Ravry, Victor; Pikhurko, Oleg; Vaughan, Emil; et al.
2016
The Electronic Journal of Combinatorics, Vol. 23, (3)
Falgas-Ravry, Victor; Markström, Klas
2016
SIAM Journal on Discrete Mathematics, Vol. 30, (4) : 1899-1917
Falgas–Ravry, Victor; Zhao, Yi
2015
Electronic Communications in Probability, Vol. 20, (50) : 1-6
Björklund, Johan; Falgas-Ravry, Victor; Holmgren, Cecilia
2015
Combinatorics, probability & computing, Vol. 24, (3) : 528-550
Falgas-Ravry, Victor
2015
SIAM Journal on Discrete Mathematics, Vol. 29, (3) : 1504-1539
Falgas-Ravry, Victor; Marchant, Edward; Pikhurko, Oleg; et al.
2014
Journal of Combinatorics, Vol. 5, (3) : 335-354
Falgas-Ravry, Victor; Kittipassorn, Teeradej; Korándi, Dániel; et al.
2013
Electronic Journal of Probability, Vol. 18, (paper 83) : 1-22
Falgas-Ravry, Victor
2013
The Electronic Journal of Combinatorics, Electronic Journal of Combinatorics 2013, Vol. 20, (4) : Article number: P28-
Falgas-Ravry, Victor
2013
Combinatorics, probability & computing, NEW YORK, NY, USA: Cambridge University Press 2013, Vol. 22, (1) : 21-54
Falgas-Ravry, Victor; Vaughan, Emil R.
2012
Advances in Applied Probability, Applied Probability Trust 2012, Vol. 44, (3) : 617-634
Falgas-Ravry, Victor; Walters, Mark
2012
The Electronic Journal of Combinatorics, Newark: The Electronic Journal of Combinatorics 2012, Vol. 19, (3) : P40-
Ravry, Victor Falgas; Vaughan, Emil R.
2011
The Electronic Journal of Combinatorics, Electronic Journal of Combinatorics 2011, Vol. 18, (1) : P95-
Falgas-Ravry, Victor

### Research projects

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!