Nathanaël Berestycki
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1 Nathanaël Berestycki Academic Positions Professor of Probability, University of Cambridge since 2015 Reader in Probability, University of Cambridge Lecturer, University of Cambridge Fellow of King s college, Cambridge since 2009 Postdoctoral fellow, University of British Columbia & PIMS Research Interests Probability theory, geometry and analysis. More precisely: Brownian motion, random geometry, Liouville quantum gravity, Gaussian free field, SLE, branching and coalescing systems and relation to partial differential equations, random walks on groups, mixing times. Education Joint PhD (Cornell 2005 and ENS Paris 2006). Advisors: R. Durrett and J.F. Le Gall. [Jury: J. Bertoin, R. Durrett, M. Ledoux, J.F. Le Gall, Y. Le Jan, and W. Werner.] DEA, Paris VI 2002 Ecole Normale Supérieure (Cachan) Invited Lecture Courses Chicago summer school in probability. Title of lectures: Introduction to the GFF and Liouville quantum gravity July 2016 Darmstadt spring school in probability. Title of lectures: Introduction to the GFF and Liouville quantum gravity April 2016 Marseille. Title of lectures: Random walks on random graphs October 2015 Clay institute / LMS modern developments in probability, Title of lectures: Introduction to the GFF and Liouville quantum gravity July 2015 Probability and Representation Theory, Edinburgh Title of lectures: Mixing times and representation theory February 2014 Ecole Polytechnique (Paris) Title of lectures: Mixing times. October 2011 Young European Probabilists, Eindhoven, Title of lectures: Recent progress in coalescent theory. March 2009 IMPA, Rio de Janeiro, Title of lectures: Recent progress in coalescent theory. January 2009 Selected Invited Lectures British Mathematical Colloquium, morning speaker April 2016 Clay Institute: Advances in Probability Sept Front Propagation and Particle Systems, Banff August 2014 Spin Glasses and Related Topics, Banff July 2014 School and Workshop on Random Interacting Systems, Bath, June 2014 Mathematical biology, particle systems and reaction-diffusion, Toulouse March 2014
2 Random Walks on Groups, IHP, Paris, January 2014 German Probability and Statistics Days, Mainz March 2012 Plenary speaker, Stochastic Processes and Applications, Oaxaca (Mexico) June 2011 Branching processes and coalescent processes, Beijing, April 2011 Random Structure and Dynamics, Oxford April 2011 Northeast Probability Seminar, New York, November 2010 Discrete probability and geometry: the mathematics of Oded Schramm, Jerusalem, Dec Selected Invited Seminars Helsinki colloquium (10/15), Rainwater seminar Seattle (09/15), UBC (09/15), KTH Stockholm (09/15), Duke (11/14), Warwick colloquium (11/14), Oxford (10/13), Bristol (10/13), Warwick (05/13) London Analysis seminar (03/13), Geneva (11/12), Warwick (05/12), U. Washington (04/12), Paris VI (12/11), ENS (12/11), Paris V (11/11), Marseille (11/11), Orsay (10/11), Polytechnique (10/11), ENS Paris (09/11), Frankfurt (05/11), ENS Lyon (04/11), ETH Zürich (10/10), Warwick (06/10), Paris VI (03/10), Bath (03/10), UBC (09/09), Warwick (02/09), UCL (colloquium) (01/09), ETH Zürich (11/08), Bristol (10/08), Microsoft Research (08/08), Weizmann Institute (06/08), Oxford (Stochastic Analysis Seminar) (05/08), Toronto, (04/08), Weizmann Institute of Science (06/07), Technion (05/07), Ecole Polytechnique (02/07), Oxford (Math. Genetics) (02/07), Indiana U. (colloquium) (01/09), U.C. Davis (colloquium) (01/07), Wisconsin (12/06), UCSD (colloquium and seminar) (12/06), UBC (11/06), Chicago (10/06), Cornell (Summer School) (07/06), Wisconsin (10/06), Berkeley (03/06), Oregon State (colloquium and seminar) (02/06), ENS Lyon (01/06), Marseille (01/06), UBC (10/05), Pittsburgh (colloquium) (03/05), Wisconsin (02/05), Microsoft Research (02/05), UCSD (01/05), Paris X (01/05), Marseille Provence (01/05), Delaware (12/04), NYU Courant Institute (02/04). PhD students Richard Pymar (graduated 2011), Lee Zhuo Zhao (graduated 2013), Bati Sengul (graduated 2014), Ed Mottram (graduated 2014), Henry Jackson (current), Ellen Powell (current), Mo-Dick Wong (current). Postdoctoral Associates Ariel Yadin (Herschel Smith Fellow, ), Arnab Sen ( ), Laure Dumaz ( ), Gourab Ray (current), Benoit Laslier (current). Honours, Grants Early-career fellowship from EPSRC, value 1.2M st recipient of Bernoulli Society Outstanding Expository Paper Prize 2012 Plenary speaker at Stochastic Processes and Application 2011 ESF grant for Geometry and Analysis of Random Processes, value e13, EPSRC Programme grant, New frontiers in Random Geometry. Co-PI with Geoffrey Grimmett and James Norris, value 1.65M EPSRC First grant EP/G055068/1 (ranked top), value 290, IMS Laha travel award 2004
3 Organisation of Conferences I was the principal organiser of a semester at the Newton Institute in Spring 2015 on Random Geometry. Co-organisers: Itai Benjamini, Jean-François Le Gall, Scott Sheffield. Geometry and Analysis of Random Processes (Easter UK Probability meeting), Cambridge. April 2013 Extremes in branching Brownian motion and random walks, with Louigi Addario-Berry and Nina Gantert Oberwolfach, September 2013 The geometry of discrete random structures, with Christina Goldschmidt (funded by EPSRC) Warwick, June 2012 Other Services Member of the Editorial board of: Annals of applied probability, to begin Electronic Journal of Probability, since Springer Briefs in Mathematical Physics, since Mathematical Proceedings of the Cambridge Philosophical Society, since Theoretical Population Biology. (Resigned 2012). I have served as a PhD examiner in Cambridge, Oxford, Bath, ENS Lyon, Paris Dauphine. Refereeing for: Transactions of AMS, Annals of Probability, J. Theoretical Probability, EJP, PTRF, J. Stat. Physics, Annals of Applied Probability, Bernoulli, Electronic J. Combinatorics, Discrete Mathematics, Random Structures and Algorithms, Bulletin of Math Biology, Annales de l IHP, Duke Math. Journal, SODA. Grant proposal reviews for: NSA (United states), ISF (Israel), ANR (France), NWO (Netherlands), NSERC (Canada), Royal Society (UK), EPSRC (UK). Publications 1. N. Berestycki and R. Durrett, (2006). A phase transition in the random transposition random walk. Probab. Theory Rel. Fields, 136, N. Berestycki (2006). The hyperbolic geometry of random transpositions. Ann. Probab., Vol. 34(2), N. Berestycki and J. Pitman. Gibbs distributions for random partitions generated by a fragementation process. J. Stat. Phys. 127(2), (2007). 4. J. Berestycki, N. Berestycki and J. Schweinsberg. Beta-coalescents and continuous stable random trees. Ann. Probab., 35, (2007). 5. J. Berestycki, N. Berestycki and J. Schweinsberg. Small-time behavior of beta-coalescents. Ann. Inst. H. Poincaré (B): Probab. Stat. 44(2), (2008). 6. N. Berestycki and R. Durrett, (2008). Limiting behavior for the distance of a random walk. Electr. J. Probab. 13, N. Berestycki. Recent progress in coalescent theory. Ensaios Matematicos, Vol. 16 (2009). 8. J. Berestycki and N. Berestycki. Kingman s coalescent and Brownian motion. Alea, 6, (2009).
4 9. J. Berestycki, N. Berestycki and V. Limic. The Λ-coalescent speed of coming down from infinity. Ann. Probab., 38, (2010). 10. N. Berestycki, A. Etheridge, and M. Hutzenthaler. Survival, extinction and ergodicity in a spatially continuous population model. Markov Proc. Rel. Fields, 15, (2009). Special issue Inhomogeneous random systems. 11. I. Benjamini and N. Berestycki. Random paths with bounded local time, J. Eur. Math. Soc. 12(4), (2010). 12. I. Benjamini and N. Berestycki. An integral test for the transience of Brownian paths with limited local time. Ann. Inst. H. Poincaré (B): Probab. Stat., 47, (2011). 13. N. Berestycki, O. Schramm and O. Zeitouni. Mixing times of random k-cycles and coagulationfragmentation chains. arxiv: Ann. Probab. 39(5), (2011). Special volume in memory of Oded Schramm. 14. O. Angel, N. Berestycki, and V. Limic. Global divergence of spatial coalescents. arxiv: Probab. Theory Rel. Fields, 152, (2012). 15. J. Berestycki, N. Berestycki and J. Schweinsberg. Survival of near-critical branching Brownian motion. J. Stat. Phys. 143( 5), , (2011). 16. N. Berestycki. Emergence of giant cycles and slowdown transition in random transpositions and k-cycles. Electr. J. Probab. 16, (2011). 17. N. Berestycki, R. Pymar. Effect of scale on long-range random graphs and chromosomal inversions. Ann. Appl. Probab., 22, (2012). 18. J. Berestycki, N. Berestycki and J. Schweinsberg. The genealogy of branching Brownian motion with absorption. Ann. Probab., 41(2), (2013). 19. N. Berestycki, A. Etheridge and A. Veber. Large-scale behaviour of the spatial Λ-Fleming- Viot process. arxiv: Ann. Inst. H. Poincaré, 49(2), (2013). 20. J. Berestycki, N. Berestycki, and V. Limic. A small-time coupling between Λ-coalescents and branching processes. Ann. Appl. Probab., 24, 2, (2014). 21. N. Berestycki, N. Gantert, P. Mörters and N. Sidorova. Galton Watson trees with vanishing martingale limit. J. Stat. Phys., 155, 4, (2014). 22. N. Berestycki and G. Kozma. Cycle structure of the interchange process and representation theory. Bull. Soc. Math. France, to appear. 23. J. Berestycki, N. Berestycki, and V. Limic. Asymptotic sampling formulae for Λ-coalescents. Ann. Inst. H. Poincaré, to appear. 24. J. Berestycki, N. Berestycki and J. Schweinsberg. Critical branching Brownian motion with absorption: survival probability. Probab. Theor. Rel. Fields, to appear. 25. N. Berestycki, Diffusion in planar Liouville quantum gravity. To appear in Ann. Inst. H. Poincaré (B). 26. J. Berestycki, N. Berestycki and J. Schweinsberg. Critical branching Brownian motion with absorption: particle configurations. To appear in Ann. Inst. H. Poincaré (B). 27. N. Berestycki and L. Zhuo Zhao. The shape of multidimensional Brunet-Derrida particle systems. To appear in Ann. Appl. Probab.
5 28. N. Berestycki, C. Garban and A. Sen. Coalescing Brownian flows: a new approach. To appear in Ann. Probab. 29. N. Berestycki and A. Yadin. Condensation of random walks and the Wulff crystal. arxiv. 30. N. Berestycki, C. Garban, R. Rhodes and V. Vargas. KPZ formula derived from Liouville heat kernel. arxiv. 31. N. Berestycki and B. Sengul. Cutoff for conjugacy-invariant random walks on the permutation group. arxiv. 32. N. Berestycki, S. Sheffield and X. Sun. Equivalence of Liouville measure and Gaussian free field. arxiv. 33. N. Berestycki, B. Laslier and G. Ray. Critical exponents on Fortuin Kasteleyn weighted planar maps. 34. N. Berestycki, Eyal Lubetzky, Yuval Peres and Allan Sly. Random walks on the random graph. 35. N. Berestycki. An elementary approach to Gaussian multiplicative chaos. Last modified: October 25, 2015.
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