Professor of Mathematics
University of Bath

t.c.rogers@bath.ac.uk

Department of Mathematical Sciences
University of Bath
Bath, BA2 7AY
+44(0)1225 38 6008
4 West 5.13

Research

I am interested in understanding and predicting the behaviour of complicated random events and processes, in particular when there are network or spatial structures involved. Most of my work is around to the idea of emergence: how large scale order can be created out of the random interactions of individual particles or organisms. The problems I work on come from a wide range of sources, including...

Fish
Collective Behaviour

Phenomnea such as flocking, schooling and lane formation arise from interactions between individuals and shape the large-scale properties of groups and crowds. In recent work I have been exploring how randomness in decision making can enhance collective dynamics:




Network
Networks and Epidemics

How fast can epidemics and information spread through networks? Which nodes will be reached first, and which are the most prolofic transmitters? These questions can be answered by adapting techniques from statistical physics:



Ants
Ecology and Evolution

Over many generations, the cumulative effect of many random interactions can shape a population in surprising ways. How can we predict the emergence of traits such as altruism? How can we be sure where one species ends and another starts?



Spectra
Random Matrix Theory

I am still working on problems I first encountered during my PhD on the distribution of eigenvalues of random matrices (useful in models of complex interacting systems). In a recent Topical Review with Fernando Metz and Izaak Neri we give an introduction to this fascinating field:



Publications

Google Scholar ORCiD
Bath Research Portal

  1. Lane nucleation in complex active flows
    KA Bacik, BS Bacik, T Rogers
    Science 379 (6635), 923-928 (2023)
  2. Stochastic drift in discrete waves of nonlocally interacting particles
    A Sontag, T Rogers, CA Yates
    Physical Review E 107 (1), 014128 (2023)
  3. Density fluctuations in stochastic kinematic flows
    P Milewski, T Rogers, J Worsfold
    SIAM Journal on Applied Mathematics (2023)
  4. Aggregate fluctuations in adaptive production networks
    Michael D König et al.
    Proceedings of the National Academy of Sciences, 119, 38 (2022)
  5. Misinformation can prevent the suppression of epidemics
    Andrei Sontag, Tim Rogers, Christian A Yates
    Royal Society Interface, 19, 188 (2022)
  6. Fluctuation spectra of large random dynamical systems reveal hidden structure in ecological networks
    Yvonne Krumbeck, Qian Yang, George Constable, Tim Rogers
    Nature Communications 12 (1), 1-14 (2021)
  7. Synchronized oscillations in growing cell populations are explained by demographic noise
    Enrico Gavagnin et al.
    Biophysical Journal 120 (8), 1314-1322 (2021)
  8. Heterogeneous node responses to multi-type epidemics on networks
    Sam Moore, Tim Rogers
    Proceedings of the Royal Society A 476, 2243, 20200587 (2020)
  9. Noise-induced schooling of fish
    Jitesh Jhawar et al.
    Nature Physics, 1-6 (2020)
  10. Predicting the Speed of Epidemics Spreading in Networks
    Sam Moore, Tim Rogers
    Physical Review Letters 124 (6), 068301
  11. Fitness differences suppress the number of mating types in evolving isogamous species
    Yvonne Krumbeck, George W. A. Constable, Tim Rogers
    Royal Society Open Science (2020)
  12. Universal hypotrochoidic law for random matrices with cyclic correlations
    Pau Vilimelis Aceituno, Tim Rogers, Henning Schomerus
    Phys Rev E (2019)
  13. New framework for automated article selection applied to a literature review of Enhanced Biological Phosphorus Removal
    Minh Nguyen Quang, Tim Rogers, Jan Hofman, Ana B. Lanham
    PLOS One (2019)
  14. Spectral Theory of Sparse Non-Hermitian Random Matrices
    (Topical Review) Izaak Neri, Fernando Metz, Tim Rogers
    Journal of Physics A: Mathematical and Theoretical (2019)
  15. The invasion speed of cell migration models with realistic cell cycle time distributions
    Enrico Gavagnin, Matthew J. Ford, Richard L. Mort, Tim Rogers, Christian A. Yates
    Journal of Theoretical Biology (2018)
  16. The Nested Kingman Coalescent: Speed of Coming Down from Infinity
    Airam Blancas Benítez, Tim Rogers, Jason Schweinsberg, Arno Siri-Jégousse
    Annals of Applied Probability (2018)
  17. The effect of population abundances on the stability of large random ecosystems
    Theo Gibbs, Jacopo Grilli, Tim Rogers, Stefano Allesina
    Phys Rev E (2018)
  18. Noise-driven bias in the non-local voter model
    Kevin Minors, Tim Rogers, Christian A Yates
    Europhysics Letters (2018)
  19. A re-entrant phase transition in the survival of secondary infections on networks
    Sam Moore, Peter Mörters and Tim Rogers
    Journal of Statistical Physics (2017)
  20. Demographic noise slows down cycles of dominance
    Qian Yang, Tim Rogers, and Jonathan Dawes
    Journal of Theoretical Biology (2017)
  21. Heterogeneous micro-structure of percolation in sparse networks
    Reimer Kühn and Tim Rogers
    Europhysics Letters (2017)
  22. Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift: a constructive approach with examples from theoretical biology
    Todd Parsons and Tim Rogers
    Journal of Physics A (2017) "Highlight of 2017"
  23. A phase transition in excursions from infinity of the "fast" fragmentation-coalescence process
    Andreas Kyprianou, Steven Pagett, Tim Rogers and Jason Schweinsberg
    Annals of Probability (2017)
  24. Universality in a class of fragmentation-coalescence processes
    Andreas Kyprianou, Steven Pagett, and Tim Rogers
    AIHP (2017)
  25. Dual-specificity phosphatase 5 controls the localized inhibition, propagation, and transforming potential of ERK signaling
    Andrew M. Kidger, Linda K. Rushworth, Julia Stellzig, Jane Davidson, Christopher J. Bryant, Cassidy Bayley, Edward Caddye, Tim Rogers, Stephen M. Keyse, and Christopher J. Caunt
    PNAS (2017)
  26. Demographic noise can reverse the direction of deterministic selection
    George Constable, Tim Rogers, Alan McKane and Corina Tarnita
    PNAS (2016)
  27. Modularity and stability in ecological communities
    Jacopo Grilli, Tim Rogers and Stefano Allesina
    Nature Communications, 7, 12031 (2016)
  28. Network Inoculation: Heteroclinics and phase transitions in an epidemic model
    Hui Yang, Tim Rogers and Thilo Gross
    Chaos, Volume 26, Issue 8 10.1063/1.4961249
  29. From empirical data to time-inhomogeneous continuous Markov processes
    Pedro Lencastre, Frank Raischel, Tim Rogers, and Pedro G. Lind
    Phys. Rev. E 93, 032135 (2016)
  30. Scale-invariant geometric random graphs
    Zheng Xie and Tim Rogers
    Phys. Rev. E 93, 032310 (2016)
  31. Assessing node risk and vulnerability to epidemics on networks
    Tim Rogers
    Europhys. Lett. 109, 28005 (2015) "Editor's Choice"
  32. Modes of competition and the fitness of evolved populations
    Tim Rogers, Alan McKane
    Phys. Rev. E 92, 032708 (2015) "Editor's Suggestion"
  33. Growth-induced breaking and unbreaking of ergodicity in fully-connected spin systems
    Richard Morris, Tim Rogers
    J. Phys. A: Math. Theor. 47 342003 (2014)
  34. Current noise-removal methods can create false signals in ecogenomic data
    Axel G Rossberg, Tim Rogers, Alan J McKane
    Full text Proc. R. Soc. B: Biol. (2014) 281, 1783
  35. Null models for dynamic centrality in temporal networks
    Tim Rogers
    Journal of Complex Networks (2014)
  36. Stochastic pattern formation and spontaneous polarisation: the linear noise approximation and beyond
    Alan J McKane, Tommaso Biancalani, Tim Rogers
    Bull. Math. Biol. 76, 4, pp 895-921 (2014)
  37. Consensus time and conformity in the adaptive voter model
    Tim Rogers, Thilo Gross
    Phys. Rev. E 88, 030102(R) (2013)
  38. Are there species smaller than 1mm?
    Axel G Rossberg, Tim Rogers, Alan J McKane
    Open access Proc. R. Soc. B: Biol. (2013) 280, 1767
  39. Stochastic dynamics on slow manifolds
    George W A Constable, Alan J McKane, Tim Rogers
    J. Phys. A: Math. Theor. 46, 295002 (2013)
  40. Voter models with conserved dynamics
    Fabio Caccioli, Luca Dall'Asta, Tobias Galla, Tim Rogers
    Phys. Rev. E. 87, 052114 (2013)
  41. Spontaneous genetic clustering in populations of competing organisms
    Tim Rogers, Alan J McKane, Axel G Rossberg
    Phys. Biol. 9, 066002 (2012)
  42. Stochastic oscillations of adaptive networks:application to epidemic modelling
    Tim Rogers, William Clifford-Brown, Catherine Mills, Tobias Galla
    J. Stat. Mech. P08018 (2012)
  43. Noise-induced metastability in biochemical networks
    Tommaso Biancalani, Tim Rogers, Alan J McKane
    Phys. Rev. E 86, 010106 (Rapid Communications) (2012)
  44. Jamming and pattern formation in models of segregation
    Tim Rogers, Alan J McKane
    Phys. Rev. E 85, 041136 (2012)
  45. Demographic noise can lead to the spontaneous formation of species
    Tim Rogers, Alan J McKane, Axel G Rossberg
    Europhys. Lett. 97, 40008 (2012) "Editor's Choice"
  46. A unified framework for Schelling's model of segregation
    Tim Rogers, Alan J McKane
    J. Stat. Mech. P07006 (2011)
  47. Maximum-entropy moment-closure for stochastic systems on networks
    Tim Rogers
    J. Stat. Mech. P05007 (2011)
  48. Universal sum and product rules for random matrices
    Tim Rogers
    J. Math. Phys. 51, 093304 (2010)
  49. Spectral density of random graphs with topological constraints
    Tim Rogers, Conrad Pérez Vicente, Koujin Takeda, Isaac Pérez Castillo
    J. Phys. A: Math. Theor. 43 195002, (2010)
  50. Cavity approach to the spectral density of non-Hermitian sparse matrices
    Tim Rogers, Isaac Pérez Castillo
    Phys. Rev. E. 79, 012101 (2009)
  51. Cavity approach to the spectral density of sparse symmetric random matrices
    Tim Rogers, Koujin Takeda, Isaac Pérez Castillo, Reimer Kühn
    Phys. Rev. E. 78, 031116 (2008)
spherical law

PhD Thesis:


New Results on the Spectral Density of Random Matrices
King's College London (2010)

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Group

Are you interested in using mathematics to study complex real-world phenomena? I have many more research questions than I have time to work on, so I am always looking for enthusiastic people to work with. Opportunities include:
  • Summer research projects
  • Masters dissertations
  • PhD projects
  • Postdoctoral researchers and fellows
  • International visitors
Contact me to find out more.

Current and former postdocs:


Karol
Karol Bacik

Funded by EPSRC New Horizons, working on pedestrian dynamics.



Sam
Samuel Johnston

Funded by EPSRC, working on fragmentation-coalescence processes.




Current and former PhD students: