Curriculum Vitæ

Nils BERGLUNDBorn 14 December 1969 in Lausanne, SwitzerlandSwedish citizenFrench and german (mother tongues), english

Professional address

Institut Denis PoissonUniversité d’Orléans, Université de Tours, CNRS – UMR 7013Bâtiment de Mathématiques, Route de Chartres, BP 6759F-45067 Orléans Cedex 2nils.berglund@univ-orleans.frhttps://www.idpoisson.fr/berglund

Education and career

Education

• 2004: Habilitation in Mathematics, University of Toulon, “Equations différentiellesstochastiques singulièrement perturbées”.Reviewers: Gérard Ben Arous, Anton Bovier, Lawrence E. Thomas.Jury: Jean-François Le Gall, Etienne Pardoux, Pierre Picco, Claude-Alain Pillet.

• 1998: PhD at Institut de Physique Théorique, ETH Lausanne, “Adiabatic DynamicalSystems and Hysteresis”.Adviser: Hervé Kunz.Reviewers: Jean-Philippe Ansermet, Serge Aubry, Oscar E. Lanford III.

• 1993: Diploma in Physics at ETH Lausanne.Diploma thesis: “Billiards magnétiques”. Direction: Hervé Kunz.

• 1988–1993: Physics studies at ETH Lausanne.

Positions held

• Since September 2007: Full professor (Professeur des universités), University ofOrléans.Member of MAPMO (CNRS, UMR 7349, Fédération Denis Poisson).

• September 2001 – August 2007: Assistant professor (Maître de Conférence), Mathe-matics department, University of Toulon. Member of CPT (CNRS, UMR 6207).

• October 2000 – September 2001: Postdoc with teaching, Departement Mathematik,ETH Zürich.

• April – September 2000: TMR fellow at Weierstraß-Institut für Angewandte Analysisund Stochastik (WIAS), Berlin.

• April 1999 – March 2000: Postdoc, Swiss National Fund, Georgia Institute of Tech-nology, Atlanta.

• September 1998 – March 1999: TMR fellow at Weierstraß-Institut für AngewandteAnalysis und Stochastik (WIAS), Berlin.

• 1994 – 1998: Assistant at Institut de Physique Théorique, ETH Lausanne.

2 January 22, 2019

Award“Prix des doctorats 1999” of ETH Lausanne.

Funded projects

• Local correspondent for ANR project MANDy, Mathematical Analysis of NeuronalDynamics, Budget for Orléans: 25’000.– Euro (September 2009 – August 2012)

• Principal investigator of research project “ACI Jeunes Chercheurs, Modélisation sto-chastique de systèmes hors équilibre”, French Ministry of Research, Budget: 70’000.–Euro (August 2004 – April 2008).

Invited stays (> 1 week), Sabbaticals

• July 2018: 10 days stay at WIAS, Berlin• February – August 2017: Sabbatical (Chercheur délégué au CNRS), at MAPMO, Or-

léans (UMR 7349) and Institut Henri Poincaré, Paris.• January 2017, December 2015: 1 week stays at University of Warwick.• February – August 2015: Sabbatical (Chercheur délégué au CNRS), at MAPMO, Or-

léans (UMR 7349).• March 2015: 2 weeks stay at TU Vienna.• One-month stays at CRC 701, Universität Bielefeld (once a year from 2007 to 2014).• One-month stays at the Weierstraß-Institut für Angewandte Analysis und Stochastik

(WIAS), Berlin (2001, ’02, ’03, ’04, ’05, ’06).• March – September 2006: Sabbatical (Chercheur délégué au CNRS), at Centre de

Physique Théorique Marseille-Luminy (CPT, UMR 6207).• March – September 2005: Sabbatical (Chercheur délégué au CNRS), WIAS Berlin

and CPT Marseille.• April 1999: Invited stay with Jacques Laskar, Bureau des Longitudes, Paris.

Peer review activitiesReferee for Alea, Annales Faculté Toulouse, Annales Institut Henri Poincaré, Annals ofProbability, Archive for Rational Mechanics and Analysis (ARMA), Chaos, Comm. Mathe-matical Physics (CMP), Comm. Nonlinear Science Numerical Simul., Comm. Pure andApplied Mathematics (CPAM), Discrete Contin. Dyn. Syst. A, Electron. J. DifferentialEquations, Inverse Problems, J. Computational Dynamics, J. Dynam. Diff. Eq., J. Mathe-matical Biology, J. Mathematical Neuroscience, J. Nonlinear Science, J. Phys. A, J. Statist.Physics, J. Theoretical Probability, Mathematics Computers Simulation, New J. Phys.,Nonlinear Analysis, Nonlinear Dynamics, Nonlinearity, Physica A, Physica D, PhysicalBiology, Probability Theory Related Fields (PTRF), SIAM J. Appl. Dynamical Systems(SIADS), SIAM J. Appl. Math. (SIAP), SIAM J. Scient. Comp. (SISC), Stochastic Process.Appl. (SPA), Syst. Contr. Letters.

Reviewer of grant proposals for ANR (France), NSF (United States) and NWO (Nether-lands).

Curriculum Vitæ – Nils Berglund 3

List of publications

Monograph

[33] N. Berglund, B. Gentz, Noise-Induced Phenomena in Slow–Fast Dynamical Systems.A Sample-Paths Approach (Springer, Probability and its Applications, 276 + xivpages, 2005)https://www.idpoisson.fr/berglund/book.html

Refereed papers

[32] M. Baudel, N. Berglund, Spectral theory for random Poincaré maps, SIAM J. Math.Anal. 49:4319–4375 (2017).

[31] N. Berglund, C. Kuehn, Model Spaces of Regularity Structures for Space-FractionalSPDEs, J. Statistical Physics 168:331–368 (2017).

[30] N. Berglund, G. Di Gesù, H. Weber, An Eyring–Kramers law for the stochastic Allen–Cahn equation in dimension two, Electronic J. Probability 22:1–27 (2017).

[29] N. Berglund, C. Kuehn, Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions, Electronic J. Probability 21:1–48 (2016).

[28] N. Berglund, S. Dutercq, Interface dynamics of a metastable mass-conserving spa-tially extended diffusion, J. Statistical Physics 162:334–370 (2016).

[27] N. Berglund, Noise-induced phase slips, log-periodic oscillations, and the Gumbeldistribution, Markov Processes Relat. Fields 22:467–505 (2016).

[26] N. Berglund, S. Dutercq, The Eyring-Kramers law for Markovian jump processeswith symmetries, J. Theoretical Probability 29:1240–1279 (2016).

[25] N. Berglund, B. Gentz, C. Kuehn, From random Poincaré maps to stochastic mixed-mode-oscillation patterns , J. Dynamics Differential Equations 27:83–136 (2015).

[24] N. Berglund, B. Gentz, On the noise-induced passage through an unstable periodicorbit II: General case, SIAM J. Math. Anal. 46:310–352 (2014).

[23] N. Berglund, B. Gentz, Sharp estimates for metastable lifetimes in parabolic SPDEs:Kramers’ law and beyond, Electronic J. Probability 18:no. 24,1–58 (2013).

[22] N. Berglund, Kramers’ law: Validity, derivations and generalisations, Markov Pro-cesses Relat. Fields 19:459–490 (2013).

[21] N. Berglund, D. Landon, Mixed-mode oscillations and interspike interval statisticsin the stochastic FitzHugh–Nagumo model, Nonlinearity 252:2303–2335 (2012).

[20] N. Berglund, B. Gentz, C. Kuehn, Hunting French Ducks in a Noisy Environment, J.Differential Equations 252:4786–4841 (2012).

[19] N. Berglund, B. Gentz, The Eyring-Kramers law for potentials with nonquadraticsaddles, Markov Processes Relat. Fields 16:549–598 (2010).

4 January 22, 2019

[18] N. Berglund, B. Gentz, Anomalous behavior of the Kramers rate at bifurcations inclassical field theories, J. Phys. A: Math. Theor. 42:052001 (9 pages) (2009).

[17] J.-P. Aguilar, N. Berglund, The effect of classical noise on a quantum two-level sys-tem, J. Math. Phys. 49:102102 (23 pages) (2008).

[16] N. Berglund, B. Fernandez, B. Gentz, Metastability in interacting nonlinear stochas-tic differential equations I: From weak coupling to synchronisation, Nonlinearity20:2551–2581 (2007).

[15] N. Berglund, B. Fernandez, B. Gentz, Metastability in interacting nonlinear stochas-tic differential equations II: Large-N regime, Nonlinearity 20:2583–2614 (2007).

[14] N. Berglund, B. Gentz, Universality of first-passage- and residence-time distribu-tions in nonadiabatic stochastic resonance, Europhys. Lett. 70:1–7 (2005).

[13] N. Berglund, B. Gentz, On the noise-induced passage through an unstable periodicorbit I: Two-level model, J. Statist. Phys. 114:1577–1618 (2004).

[12] N. Berglund, B. Gentz, Geometric singular perturbation theory for stochastic dif-ferential equations, J. Differential equations 191:1–54 (2003).

[11] N. Berglund, B. Gentz, Metastability in simple climate models: Pathwise analysisof slowly driven Langevin equations, Stoch. Dyn. 2:327–356 (2002).

[10] N. Berglund, B. Gentz, Beyond the Fokker–Planck equation: Pathwise control ofnoisy bistable systems, J. Phys. A 35:2057–2091 (2002).

[9] N. Berglund, B. Gentz, The effect of additive noise on dynamical hysteresis, Non-linearity 15:605–632 (2002).

[8] N. Berglund, B. Gentz, A sample-paths approach to noise-induced synchronization:Stochastic resonance in a double-well potential, Ann. Appl. Probab. 12:1419–1470(2002).

[7] N. Berglund, B. Gentz, Pathwise description of dynamic pitchfork bifurcations withadditive noise, Probab. Theory Related Fields 122:341–388 (2002).

[6] N. Berglund, T. Uzer, The averaged dynamics of the hydrogen atom in crossedelectric and magnetic fields as a perturbed Kepler problem, Found. Phys. 31:283–326 (2001).

[5] N. Berglund, Control of dynamic Hopf bifurcations, Nonlinearity 13:225–248 (2000).

[4] N. Berglund, H. Kunz, Memory Effects and Scaling Laws in Slowly Driven Systems,J. Phys. A 32:15–39 (1999).

[3] N. Berglund, H. Kunz, Chaotic Hysteresis in an Adiabatically Oscillating DoubleWell, Phys. Rev. Letters 78:1691–1694 (1997).

[2] N. Berglund, A. Hansen, E.H. Hauge, J. Piasecki, Can a Local Repulsive PotentialTrap an Electron?, Phys. Rev. Letters 77:2149–2153 (1996).

[1] N. Berglund, H. Kunz, Integrability and Ergodicity of Classical Billiards in a Mag-netic Field, J. Stat. Phys. 83:81–126 (1996).

Curriculum Vitæ – Nils Berglund 5

Book chapters

[34] N. Berglund, B. Gentz, Stochastic dynamic bifurcations and excitability, in C. Laing,G. Lord (Eds.), Stochastic Methods in Neuroscience (Oxford University Press, Ox-ford, 2009)

[35] N. Berglund, Bifurcations, scaling laws and hysteresis in singularly perturbed sys-tems, in B. Fiedler, K. Gröger, J. Sprekels (Eds.), Equadiff ’99 (World Scientific,Singapore, 2000)

[36] N. Berglund, K.R. Schneider, Control of dynamic bifurcations, in D. Aeyels, F.Lamnabhi-Lagarrigue, A. van der Schaft (Eds.), Stability and Stabilization of Non-linear Systems (Lecture Notes in Contr. and Inform. Sciences 246, Springer, Berlin,1999)

Proceedings

[37] N. Berglund, Stochastic dynamical systems in neuroscience, Oberwolfach Reports8:2290–2293 (2011). Proceedings of the miniworkshop Dynamics of StochasticSystems and their Approximation, Oberwolfach, Germany, August 2011.

[38] N. Berglund, Dynamic bifurcations: hysteresis, scaling laws and feedback control,Prog. Theor. Phys. Suppl. 139:325–336 (2000). Proceedings of the conference“Let’s face chaos through nonlinear dynamics”, Maribor, Slovenia, June/July 1999.

[39] N. Berglund, Classical Billiards in a Magnetic Field and a Potential, Nonlinear Phe-nomena in Complex Systems 3:61–70 (2000). Proceedings of the conference “Let’sface chaos through nonlinear dynamics”, Maribor, Slovenia, June/July 1996.

[40] N. Berglund, On the Reduction of Adiabatic Dynamical Systems near EquilibriumCurves (1998). Proceedings of the conference “Celestial Mechanics, SeparatrixSplitting, Diffusion”, Aussois, France, June 1998.

Diploma thesis, Phd thesis, habilitation thesis

[41] N. Berglund, Equations différentielles stochastiques singulièrement perturbées,Habilitation , University of Toulon (2004).https://www.idpoisson.fr/berglund/hdr.html

[42] N. Berglund, Adiabatic Dynamical Systems and Hysteresis,Phd thesis 1800, ETH Lausanne (1998).https://www.idpoisson.fr/berglund/these.html

[43] N. Berglund, Billards magnétiques, Diploma thesis, ETH Lausanne (1993).

Popularisation

[44] Résoudre des équations en comptant des arbres, Images des Mathématiques, CNRS,2018

[45] Les diagrammes de Feynman, parts 1–3, Images des Mathématiques, CNRS, 2016

6 January 22, 2019

[46] Mayonnaise et élections américaines, Dossier Pour la Science, 2016

[47] Probabiliser, Images des Mathématiques, CNRS, 2015

[48] Des canards dans mes neurones, Images des Mathématiques, CNRS, 2015

[49] Qu’est-ce qu’une Équation aux Dérivées Partielles Stochastique ?, Images des Ma-thématiques, CNRS, 2014

[50] Le climat et ses aléas, Microscoop CNRS, Hors-série 22, 2013

[51] Notre univers est-il irréversible ?, Images des Mathématiques, CNRS, 2013

[52] Hasard et glaciations, Mathématiques de la Planète Terre, 2013

[53] La probabilité d’extinction d’une espèce menacée, Images des Mathématiques,CNRS, 2013

[54] Rangez-moi ces bouquins !, Images des Mathématiques, CNRS, 2012

Lecture notes

1. An introduction to singular stochastic PDEs: Allen–Cahn equations, metastability andregularity structures (Sarajevo Stochastic Analysis Winter School, 2019, 95 pages)

2. Martingales et calcul stochastique, Master 2 Recherche (MAPMO, 2012, 125 pages)3. Processus aléatoires et applications, Master 2 Pro (MAPMO, 2011, 123 pages)4. Probabilités et Statistiques, Licence 3 (MAPMO, 2010, 63 pages)5. Théorie des Probabilités, Licence MASS (USTV, 2006, 76 pages)6. Introduction aux equations différentielles stochastiques (CPT, 2005, 22 pages)7. Geometrical Theory of Dynamical Systems (ETHZ, 2001, 85 pages)8. Perturbation Theory of Dynamical Systems (ETHZ, 2001, 111 pages)

https://www.idpoisson.fr/berglund/teaching.html

Teaching

• 2007-2018: University of Orléans (lectures):

– Master of mathematics, 2nd year: Martingales and stochastic calculus– Master of mathematics, 2nd year: Stochastic processes– Master of mathematics, 2nd year: Preparation to French “Agrégation” exams– Master of mathematics, 2nd year: Financial mathematics– Master of mathematics, 1st year: Probability theory– Master of mathematics, 1st year: Financial mathematics– Master of economics, 1st year: Data analysis– Master of economics, 1st year: Qualitative data analysis– Bachelor of economics, 3rd year: Linear optimisation– Bachelor of mathematics, 3rd year: Probability and statistics– Bachelor of mathematics and computer science, 1st year: Algebra

• 2001-2007: University of Toulon:

– Lectures:

Curriculum Vitæ – Nils Berglund 7

* Master of mathematics, 2nd year: Mathematical physics

* Master of mathematics, 1st year: Probability theory

* Master of mathematics, 1st year: Mathematical physics

* Bachelor of economics, 3rd year: Probability

* Engineering school, 3rd year: Stochastic processes

* Engineering school, 2nd year: Financial mathematics

* Bachelor in mathematics/computer science, 1st year: Algebra

* Bachelor in physics, 1st year: Matrices

– Exercise classes:

* Master in mathematics, 1st year: Algebra

* Bachelor in economics, 3rd year: Probability

* Bachelor in mathematics/computer science, 2nd year: Analysis, geometry,series

* Bachelor in biology, 2nd year: Probability and statistics

* Bachelor in biology, 1st year: Calculus

• 2000-2001: ETH Zürich (lectures):

– Geometrische Theorie dynamischer Systeme– Störungstheorie dynamischer Systeme

• 1994-1998: ETH Lausanne (exercise classes):

– General mechanics– General relativity and cosmology– Nonlinear phenomena and chaos– Electrodynamics

Thesis supervision

• PhD students:

– Manon Baudel (2014–2017)– Sébastien Dutercq (2011–2015)– Damien Landon (2008–2012)– Jean-Philippe Aguilar (2005–2008)

• Diploma students:

– Sébastien Dutercq (2011)– Kanal Hun (2009)– Damien Landon (2008)– Antoine Loyer (2005, in collaboration with Barbara Gentz, Berlin)– Jean-Philippe Aguilar (2005)– Evelyne Vas (2004, in collaboration with Emmanuel Buffet, Dublin)

Habilitation committee

• Jonathan Touboul (Collège de France, June 2015)

8 January 22, 2019

Doctoral committees

• Christian Wiesel (University of Bielefeld, July 2018): reviewer• Maximilian Engel (Imperial College London, January 2018): reviewer• Boris Nectoux (Ecole des Ponts Paris, November 2017): reviewer• Christophe Poquet (Université Paris Diderot, October 2013): reviewer• Julian Tugaut (Université Nancy 1, July 2010): reviewer• Bénédicte Aguer (Université Lille 1, June 2010): reviewer• Guillaume Voisin (Orléans, December 2009): president of jury• Laurent Marin (Orléans, November 2009)

Research interests

• Probability theory: Stochastic differential equations, stochastic partial differen-tial equations, stochastic exit problem, metastability, large deviations, potentialtheory, regularity structures

• Dynamical Systems: Singular perturbation theory, dynamic bifurcations, mixed-mode oscillations, spatially extended systems, Hamiltonian systems, symplecticmaps

• Applications: Statistical physics, classical and quantum open systems, neuro-science, climate models

My research interests mainly lie at the intersection of different fields, such as prob-ability theory and dynamical systems. These intersections lead to interesting new ap-proaches and results. For instance, with Barbara Gentz I have developed new methodsfor the quantitative analysis of stochastic differential equations with several timescales,based on a combination of stochastic analysis and singular perturbation theory.

My current research projects mainly deal with the following themes:

• Metastability in spatially extended systems: Characterisation of metastabletransitions (transition time, optimal transition path) in systems of coupled oscil-lators and stochastic partial differential equations. These problems require theextension of known results to infinite-dimensional situations and situations withbifurcations.

• Applications in the neurosciences: The creation of action potentials (“spiking”)in neurons is often modeled by slow–fast ordinary and stochastic differential equa-tions. A particularly interesting feature is the phenomenon of excitability, in whichsmall deterministic or stochastic perturbations can trigger spikes. The distributionof interspike time intervals is still poorly understood in irreversible cases.

International collaborations

• Hervé Kunz (Lausanne), Alex Hansen, Eivind Hauge (Trondheim), Jaroslav Piasecki(Warsaw): Billiards.

• Hervé Kunz (Lausanne): adiabatic dynamical systems.

Curriculum Vitæ – Nils Berglund 9

• Klaus Schneider (Berlin): control theory.• Turgay Uzer (Atlanta): Hamiltonian systems.• Barbara Gentz (Berlin/Bielefeld): stochastic differential equations.• Bastien Fernandez (Marseille): spatially extended systems.• Christian Kuehn (Vienna/Munich): fast–slow dynamical systems, regularity struc-

tures.• Giacomo Di Gesù (Paris/Vienna), Hendrik Weber (Warwick): stochastic partial differ-

ential equations.

These collaborations have been partly funded by the Swiss National Fund, the Euro-pean Union (TMR Project), the Forschungsinstitut Mathematik (FIM) at ETH Zürich, theEuropean Science Foundation (ESF), and the Deutsche Forschungsgemeinschaft (DFG).

Administration

Committees

• Since 2017: Adjoint director of Graduate School MIPTIS, Orléans–Tours.• 2014-2017: Head of outreach committee - Mathematics, University of Orléans.• 2014: External member of appointment committee, University of Poitiers.• 2013: External member of appointment committee, University of Tours.• 2012-2018: President of appointment committee, mathematics, Orléans.• 2010: External member of appointment committee, University of Poitiers.• 2010: External member of appointment committee, University Paris 7.• Since 2009: Elected member of appointment committee, mathematics, Orléans.• Since 2008: Elected member of institute committee, MAPMO–CNRS.• Since 2008: Member of thesis committee Orléans–Tours.• 2004-2007: Member of appointment committee, mathematics, University of Toulon.• 2005-2007: External member of appointment committee, mathematics, University

Aix-Marseille I.• 2005-2007: Nominated member of institute committee, CPT–CNRS.• 2004-2007: Responsible for teaching attribution, department of mathematics, Uni-

versity of Toulon.

Organisation of seminars and conferences

• “Stochastic Partial Differential Equations”, CIRM, Marseille (May 2018).• “Journées de Probabilités 2013”, Orléans (June 2013).• “Third meeting of the GDR Quantum Dynamics”, Orléans (February 2011).• “Fourth Workshop on Random Dynamical Systems”, Bielefeld (November 2010), with

Barbara Gentz.• Conference “Stochastic Models in Neuroscience”, CIRM, Marseille-Luminy (January

2010), with Simona Mancini and Michèle Thieullen (Paris 6).• Responsible for institute seminar, MAPMO (since 2008), with Simona Mancini and

Aurélien Alvarez (since 2011), and Luc Hillairet (since 2013).• Conference “Maths and billiards” (Orléans, March 2008), with Stéphane Cordier

(Orléans) and Emmanuel Lesigne (Tours).

10 January 22, 2019

• Closing meeting of the ACI Jeunes Chercheurs “Modélisation stochastique de sys-tèmes hors équilibre” (Orléans, February 2008).

• “Journées de Probabilités 2007”(La Londe, September 2007), with K. Bahlali, Y.Lacroix (Toulon), P. Picco (Marseille).

• Minisymposium “Recent developments in the stochastic exit problem” at the inter-national conference ICIAM07 (Zürich, July 2007), with Samuel Herrmann (Nancy).

• International conference QMath9 (Giens, September 2004), with J. Asch, J.-M. Bar-baroux, J.-M. Combes, J.-M. Ghez (Toulon), A. Joye (Grenoble).

• Colloquium “Equations Différentielles Stochastiques”, University of Toulon (2003),with K. Bahlali, P. Briet (Toulon), P. Picco (Marseille).

• “Séminaire de Dynamique Quantique et Classique”, CPT (2002).

Talks and conferences (since 1999)

Some slides are available at

https://www.idpoisson.fr/berglund/restalks.html

Invited talks at conferences

• 12-13.11.2018. Stochastics Meeting Lunteren, Trace process and metastability,Metastable dynamics of stochastic PDEs (Invitation: Frank den Hollander).

• 20.9.2018. “Advances in Computational Statistical Physics”, CIRM, Marseille, Traceprocess and metastability (Invitation: Tony Lelièvre, Gabriel Stoltz, Grigorios Pavli-otis).

• 5.6.2018. “Simulation and probability: recent trends”, Centre Henri Lebesgue, Rennes,Metastable Markov chains, trace process and spectral theory (Invitation: FrédéricCérou, Mathias Rousset, Fabien Panloup).

• 6.12.2017. “Random Dynamical Systems”, Lorentz Center, Leiden, Theory and ap-plications of random Poincaré maps (Invitation: Ale Homburg, Jeroen Lamb, MartinRasmussen).

• 28.7.2017. “39th Conference on Stochastic Processes and their Applications”, Mos-cow, Metastability for interacting particles in double-well potentials and Allen–CahnSPDEs (Invitation: Cédric Bernardin, Patricia Gonçalves).

• 24.7.2017. “39th Conference on Stochastic Processes and their Applications”, Mos-cow, A “thermodynamic” characterization of some regularity structures near the sub-criticality threshold (Invitation: Lorenzo Zambotti).

• 17.6.2017. “9th Workshop on Random Dynamical Systems”, Bielefeld, Metastabilityin stochastic Allen-Cahn PDEs (Invitation: Barbara Gentz).

• 24.5.2016. “Journées de Probabilités 2016”, Le Mans, EDPs stochastiques et méta-stabilité (Invitation: Anis Matoussi, Alexandre Popier).

• 20.4.2016. “Workshop on Metastability”, Eurandom, Eindhoven, Metastability ofstochastic Allen–Cahn PDEs (Invitation: Roberto Fernandez, Francesca Nardi, JulienSohier).

• 8.4.2016. “SIAM Conference on Uncertainty Quantification”, EPF Lausanne, The-ory and Applications of Random Poincaré Maps (Invitation: Xiaoying Han, Habib N.Najm).

Curriculum Vitæ – Nils Berglund 11

• 2.2.2016. “Computational statistics and molecular simulation”, Paris, Sharp esti-mates on metastable lifetimes for one- and two-dimensional Allen–Cahn SPDEs (In-vitation: Arnaud Guyader, Tony Lelièvre, Gabriel Stoltz).

• 5.11.2015. “8th Workshop on random dynamical systems”, Bielefeld, Regularitystructures and renormalisation of FitzHugh–Nagumo SPDEs in three space dimen-sions (Invitation: Barbara Gentz, Peter Imkeller).

• 8.7.2015. “Equadiff 2015”, Lyon, On FitzHugh–Nagumo SDEs and SPDEs (Invita-tion: Hans Crauel, Ale Jan Homburg).

• 16.6.2015. ENS Lyon, “Statistical mechanics and computation of large deviationrate functions”, Metastability in systems of coupled multistable SDEs (Invitation:Freddy Bouchet).

• 20.3.2015. Paris, Institut des Systèmes Complexes, ANR project meeting, A tool-box to quantify effects of noise on slow-fast dynamical systems (Invitation: MathieuDesroches).

• 12.12.2014. “7th Workshop on random dynamical systems”, Bielefeld, Extreme-value theory and the stochastic exit problem (Invitation: Barbara Gentz).

• 18.11.2014. “Multi-scale models, slow-fast differential equations, averaging in ecol-ogy”, Centre Bernoulli, Lausanne, Noise-induced transitions in slow–fast dynamicalsystems (Invitation: Mathieu Desroches).

• 28.7.2014. “37th Conference on Stochastic Processes and their Applications”, Bue-nos Aires, Some rigorous results on interspike interval distributions in stochasticneuron models (Invitation: Jonathan Touboul).

• 8.7.2014. “10th AIMS Conference on Dynamical Systems, Differential Equationsand Applications”, Madrid, A group-theoretic approach to metastability in networksof interacting SDEs (Invitation: Georgi Medvedev).

• 28.1.2014. “Inhomogeneous Random Systems”, Institut Henri Poincaré, Paris, Noise-induced phase slips, log-periodic oscillations and the Gumbel distribution (Invitation:Giambattista Giacomin).

• 31.10.2013. “6th Workshop on random dynamical systems”, Bielefeld, From randomPoincaré maps to stochastic mixed-mode-oscillation patterns (Invitation: BarbaraGentz).

• 6.6.2013. “Workshop on Slow-Fast Dynamics: Theory, Numerics, Application to Lifeand Earth Sciences”, CRM, Barcelona, Random Poincaré maps and noise-inducedmixed-mode-oscillation patterns (Invitation: Mathieu Desroches).

• 8.2.2013. “5ème Rencontre du GDR Dynamique Quantique”, Lille, Irreversible diffu-sions and non-selfadjoint operators: Results and open problems (Invitation: StephanDe Bièvre, Gabriel Rivière).

• 5.10.2012. “5th Workshop on Random Dynamical Systems”, Bielefeld, Some appli-cations of quasistationary distributions to random Poincaré maps (Invitation: Bar-bara Gentz).

• 5.7.2012. “Random models in neuroscience”, Université Paris 6, Some results on in-terspike interval statistics in conductance-based models for neuron action potentials(Invitation: Michèle Thieullen).

• 21.3.2012. “Critical Transitions in Complex Systems”, Imperial College London,Sample-path behaviour of noisy systems near critical transitions (Invitation: JeroenLamb, Greg Pavliotis, Martin Rasmussen).

• 12.12.2011. EPSRC Symposium Workshop “Multiscale Systems: Theory and Ap-

12 January 22, 2019

plications”, Warwick Mathematics Institute, Canards, mixed-mode oscillations andinterspike distributions in stochastic systems (Invitation: Martin Hairer, Greg Pavli-otis, Andrew Stuart).

• 2.11.2011. “Stochastic Dynamics in Mathematics, Physics and Engineering”, ZiF,Bielefeld, Does noise create or suppress mixed-mode oscillations? (Invitation: Bar-bara Gentz, Max-Olivier Hongler, Peter Reimann).

• 22.8.2011. “Dynamics of Stochastic Systems and their Approximation”, Mathema-tisches Forschungszentrum Oberwolfach, Stochastic dynamical systems in neuro-science (Invitation: Evelyn Buckwar, Barbara Gentz, Erika Hausenblas).

• 21.7.2011. ICIAM 2011, Vancouver, On the Interspike Time Statistics in the Stochas-tic FitzHugh–Nagumo Equation (Invitation: Jinqiao Duan, Barbara Gentz).

• 26.1.2011. “Inhomogeneous Random Systems”, Institut Henri Poincaré, Paris, TheKramers law: Validity, derivations and generalizations (Invitation: Christian Maes).

• 2.12.2010. “Open quantum systems”, Institut Fourier, Grenoble, Metastability in aclass of parabolic SPDEs (Invitation: Alain Joye).

• 19.11.2009. 3rd Workshop “Random Dynamical Systems”, Universität Bielefeld,Metastability for Ginzburg-Landau-type SPDEs with space-time white noise (Invi-tation: Barbara Gentz).

• 14.5.2009. “Deterministic and Stochastic Modeling in Computational Neuroscienceand Other Biological Topics”, CRM, Barcelona, Stochastic models for excitable sys-tems (Invitation: Antony Guillamon).

• 12.3.2009. “Journées Systèmes Ouverts”, Institut Fourier, Grenoble, Metastabilityfor the Ginzburg–Landau equation with space-time noise (Invitation: Alain Joye).

• 18.11.2008. 2nd Workshop “Random Dynamical Systems”, Universität Bielefeld,Metastability in systems with bifurcations (Invitation: Barbara Gentz).

• 19.6.2008. Workshop “Applications of spatio-temporal dynamical systems in biol-ogy”, Laboratoire Dieudonné, Nice, Metastability in a system of coupled nonlineardiffusions (Invitation: Elisabeth Pécou).

• 30.11.2007. Workshop “Random Dynamical Systems”, Universität Bielefeld, Meta-stable lifetimes and optimal transition paths in spatially extended systems (Invita-tion: Barbara Gentz).

• 23.2.2007. Workshop “Multiscale Analysis and Computations in Stochastic Differ-ential Equation Modelling 2007”, University of Sussex, Noise-induced phenomena inslow–fast dynamical systems (Invitation: Greg Pavliotis).

• 12.10.2006. Conference “Chaos and Complex Systems”, Novacella, Desynchronisa-tion of coupled bistable oscillators perturbed by additive noise (Invitation: MarcoRobnik).

• 27.6.2006. AIMS conference “Dynamical Systems and Differential Equations”, Poi-tiers, Metastability and stochastic resonance in slow–fast systems with noise (Invita-tion: Jianzhong Su).

• 9.6.2005. Stochastic Partial Differential Equations and Climatology, ZIF, UniversitätBielefeld, Geometric singular perturbation theory for stochastic differential equa-tions (Invitation: Friedrich Götze, Yuri Kondratiev, Michael Röckner).

• 31.5.2005. Period of Concentration, Stochastic climate models, Max-Planck Institut,Leipzig, Geometric singular perturbation theory applied to stochastic climate models(Invitation: Peter Imkeller).

• 19.5.2005. Period of Concentration, Metastability, ageing, and anomalous diffusion,

Curriculum Vitæ – Nils Berglund 13

Max-Planck Institute, Leipzig, Metastability in irreversible diffusion processes andstochastic resonance (Invitation: Anton Bovier).

• 22.6.2004. Coupled Map Lattices 2004 , Institut Henri Poincaré, Paris, Special ses-sion on effect of noise on synchronization (Invitation: Bastien Fernandez).

• 28.4.2004. European Geophysical Union meeting (EGU04), Nice, Universal proper-ties of noise-induced transitions (Invitation: Daniel Scherzer).

• 31.5.2003. 4th European Advanced Studies Conference, Novacella, On the noise-induced passage through an unstable periodic orbit (Invitation: Marko Robnik).

Invited talks at seminars

• 18.7.2018. Bielefeld, Bielefeld Stochastic Afternoon, Metastable Markov chains,trace process and spectral theory (Invitation: Barbara Gentz).

• 9.7.2018. FU and WIAS Berlin, Oberseminar Nonlinear Dynamics, Metastable dy-namics of Allen-Cahn SPDEs on the torus (Invitation: Bernold Fiedler and MathiasWolfrum).

• 6.7.2018. TU Berlin, Symposium of the Collaborative Research Center 910, Theoryand applications of random Poincaré maps (Invitation: Mathias Wolfrum).

• 19.1.2018. Imperial College London, Applied PDEs Seminar, Sharp estimates formetastable transition times in Allen-Cahn SPDEs on the torus (Invitation: Greg Pavli-otis).

• 21.12.2017. Lyon, Séminaire de Probabilités commun ICJ/UMPA, Une approche“mécanique statistique” aux structures de régularité près du seuil de sous-criticalité(Invitation: Fabio Toninelli).

• 2.11.2017. Warwick, Statistical Mechanics Seminar, Metastability in stochastic Allen–Cahn PDEs (Invitation: Daniel Ueltschi, Hendrik Weber).

• 9.5.2017. Paris, Séminaire du LPMA, Une approche “mécanique statistique” auxstructures de régularité près du seuil de sous-criticalité (Invitation: Lorenzo Zam-botti).

• 3.5.2017. IHP, Paris, Stochastic Dynamics Out of Equilibrium, General Seminar,Metastability in stochastic PDEs (Invitation: Giambattista Giacomin, Stefano Olla,Ellen Saada, Herbert Spohn, Gabriel Stoltz).

• 22.3.2017. TU Wien, DK Seminar, Metastability of stochastic Allen–Cahn equationson the torus (Invitation: ).

• 19.1.2017. Warwick, Statistical Mechanics Seminar, A “thermodynamic” character-isation of some regularity structures near the subcriticality threshold (Invitation:Daniel Ueltschi, Hendrik Weber).

• 7.10.2016. Utrecht, Marc Kac Seminar, Metastable dynamics of Allen–Cahn equa-tions (Invitation: Roberto Fernandez, Wouter Kager).

• 15.6.2016. École des Ponts ParisTech, Séminaire du CERMICS, Regularity struc-tures and renormalisation of FitzHugh–Nagumo SPDEs in three space dimensions(Invitation: Giacomo Di Gesù).

• 10.5.2016. Augsburg, Mathematisches Kolloquium, Sharp asymptotics for metastabletransition times in one- and two-dimensional Allen–Cahn SPDEs (Invitation: LisaBeck).

• 11.4.2016. EPF Lausanne, Séminaire de Probabilités, Regularity structures andrenormalisation of FitzHugh–Nagumo SPDEs in three space dimensions (Invitation:

14 January 22, 2019

Robert Dalang).• 17.12.2015. TU Darmstadt, Oberseminar Stochastik, Synchronisation, noise-induced

phase slips and the Gumbel distribution (Invitation: Volker Betz).• 9.12.2015. Warwick, Probability Seminar, An Eyring–Kramers formula for one-

dimensional parabolic SPDEs with space-time white noise (Invitation: Hendrik We-ber).

• 13.11.2015. Strasbourg, Séminaire de Calcul stochastique, Structures de régularitéet renormalisation d’EDPS de FitzHugh–Nagumo (Invitation: Nicolas Juillet).

• 26.3.2015. Le Havre, Séminaire du LMAH, Phénomènes induits par le bruit dans lessystèmes dynamiques lent–rapides (Invitation: Benjamin Ambrosio).

• 12.3.2015. LMA Poitiers, Séminaire de probabilités, statistique et applications, Dis-tribution de spikes pour des modèles stochastiques de neurones et chaînes de Markovà espace continu (Invitation: Hermine Biermé).

• 4.3.2015. TU Vienna, Institute for Analysis und Scientific Computing, An Eyring–Kramers formula for parabolic SPDEs with space-time white noise (Invitation: Chris-tian Kuehn).

• 5.12.2014. LMPT Tours, Séminaire de probabilités et théorie ergodique, Distribu-tion de spikes pour des modèles stochastiques de neurones et chaînes de Markov àespace continu (Invitation: Kilian Raschel).

• 16.4.2014. Ruhr-Universität Bochum, Synchronization, noise-induced phase slipsand extreme-value theory (Invitation: Christof Külske).

• 13.3.2014. Évry, Séminaire de Probabilités et mathématiques financières, Problèmede sortie stochastique à travers une orbite instable (Invitation: Dasha Loukinaova).

• 9.12.2013. IRMAR, Université de Rennes, Séminaire de Probabilités, Chaînes deMarkov à espace continu, distributions quasi-stationnaires, et diffusions irréversibles(Invitation: Jean-Christophe Breton).

• 1.2.2013. Rhein-Main Kolloquium Stochastik, Gutenberg-Universität Mainz, Quan-tifying neuronal spiking patterns using continuous-space Markov chains (Invitation:Reinhard Höpfner).

• 2.11.2012. Heriot-Watt University, Edinburgh, Quantifying the effect of noise onneuronal spiking patterns (Invitation: Sébastien Loisel, Gabriel Lord).

• 7.2.2012. Séminaire de Probabilités, Institut de Mathématiques de Toulouse, Os-cillations multimodales et chasse aux canards stochastiques (Invitation: ClémentPellegrini).

• 5.5.2011. Groupe de travail modélisation, LPMA, Paris 6, Oscillations multimodalesdans les équations différentielles stochastiques (Invitation: Gianbattista Giacomin).

• 15.3.2011. Groupe de travail Neuromathématiques et modèles de perception, IHP,Paris, Geometric singular perturbation theory for stochastic differential equationswith applications to neuroscience (Invitation: Alessandro Sarti).

• 14.3.2011. Groupe de travail mathématiques et neurosciences, IHP, Paris, Chasseaux canards en environnement bruité (Invitation: Michèle Thieullen).

• 11.2.2011. Laboratoire Dieudonné, Nice, Chasse aux canards en environnementbruité (Invitation: Jean-Marc Gambaudo, Bruno Marcos).

• 18.1.2011. Institut du Fer à Moulin, Paris, Quantifying the effect of noise on oscilla-tory patterns (Invitation: Jacques Droulez).

• 12.11.2010. Séminaire de probabilités, EPF Lausanne, Metastability in a class ofparabolic SPDEs (Invitation: Charles Pfister).

Curriculum Vitæ – Nils Berglund 15

• 18.6.2010. IGK-Seminar, Bielefeld, Stochastic differential equations in neuroscience(Invitation: Sven Wiesinger).

• 1.4.2010. Groupe de travail systèmes dynamiques, LJLL, Paris 6, Systèmes lents-rapides perturbés par un bruit — Applications dans les neurosciences (Invitation:Jean-Pierre Françoise, Alain Haraux).

• 26.6.2009. Journée en l’honneur d’Hervé Kunz, EPF Lausanne, Métastabilité dansdes équations de Ginzburg–Landau avec bruit blanc spatiotemporel (Invitation: Vin-cenzo Savona).

• 27.11.2008. Groupe de Travail Modélisation de l’Evolution du Vivant, Ecole Poly-technique, Paris/Palaiseau, Equations différentielles stochastiques lentes–rapides (In-vitation: Sylvie Méléard).

• 27.10.2008. Theoretical Physics Seminar, KU Leuven, Kramers rate theory at bifur-cations (Invitation: Christian Maes).

• 24.6.2008. Séminaire de physique mathématique, Lille, L’effet d’un bruit classiquesur un système quantique à deux niveaux (Invitation: Stephan de Bièvre).

• 27.5.2008. Séminaire de probabilités, Paris 6 & 7, Métastabilité dans un systèmede diffusions couplées (Invitation: Jean Bertoin).

• 10.3.2008. Séminaire de probabilités Nord-Ouest, Angers, Métastabilité dans unsystème de diffusions couplées (Invitation: Loïc Chaumont).

• 13.6.2007. Seminar on Stochastic Analysis, University of Warwick, Metastability ina chain of coupled nonlinear diffusions (Invitation: Martin Hairer).

• 18.4.2007. Berliner Kolloquium Wahrscheinlichkeitstheorie, WIAS Berlin, Metastabi-lity in a chain of coupled nonlinear diffusions (Invitation: Anton Bovier).

• 2.4.2007. Séminaire de Probabilités, Université Rennes 1, Metastabilité dans unsystème de diffusions non-linéaires couplées (Invitation: Ying Hu, Florent Malrieu).

• 10.1.2007. Oberseminar Math. Statistik & Wahrscheinlichkeitstheorie, UniversitätBielefeld, Metastability in a system of interacting nonlinear diffusions (Invitation:Barbara Gentz).

• 7.12.2006. Séminaire de probabilités, Nancy, Synchronisation de diffusions cou-plées (Invitation: Samy Tindel).

• 15.11.2006. Seminar on Stochastic processes, Zürich, Metastability in a system ofinteracting diffusions (Invitation: Erwin Bolthausen).

• 10.3.2006. Séminaire de probabilités, LATP Marseille, Synchronisation de diffusionscouplées (Invitation: Laurent Miclo).

• 18.11.2003. Institut Fourier, Grenoble, Passage sous l’effet d’un bruit à travers uneorbite périodique instable (Invitation: Alain Joye).

• 29.10.2003. WIAS Berlin, On the noise-induced passage through an unstable peri-odic orbit (Invitation: Barbara Gentz).

• 8.11.2002. LATP, Marseille, Théorie géométrique des perturbations singulières pouréquations différentielles stochastiques (Invitation: Yvan Velenik).

• 26.6.2002. Humboldt-Universität zu Berlin, Geometric singular perturbation theoryfor stochastic differential equations (Invitation: Peter Imkeller).

• 8.5.2001. EPFL, Résonance stochastique et hystérèse (Invitation: Charles Pfister).• 21.3.2001. CPT Marseille, Résonance stochastique et synchronisation induite par

bruit (Invitation: Claude-Alain Pillet).• 14.11.2000. Institut Fourier, Grenoble, L’effet de bruit additif sur les bifurcations

dynamiques (Invitation: Alain Joye).

16 January 22, 2019

• 18.10.2000. WIAS Berlin, Dynamic pitchfork bifurcations with additive noise (Invi-tation: Barbara Gentz).

• 5.9.2000. Universität Augsburg, The effect of additive noise on dynamic pitchforkbifurcations (Invitation: Fritz Colonius).

• 23.9.1999. University of Victoria, BC, Hysteresis and scaling laws in dynamic bifur-cations (Invitation: Florin Diacu).

• 6.5.1999. Bureau des Longitudes, Paris, Bifurcations dynamiques (Invitation: Jac-ques Laskar).

• 24.2.1999. Universität Augsburg, Control of dynamic Hopf bifurcations (Invitation:Fritz Colonius).

Minicourses

• January 2019. Sarajevo, Stochastic Analysis Winter School, An introduction to sin-gular stochastic PDEs: Allen–Cahn equations, metastability and regularity structures(Invitation: Frank Proske, Abdol-Reza Mansouri and Oussama Amine).

• November 2015. Nice, Laboratoire Dieudonné, 2 lecture, Modèles neuronaux etstructures de régularité (Invitation: François Delarue).

• October 2011. CIRM, Marseille Luminy, 5 lectures, Bifurcations in stochastic sys-tems with multiple timescales (Invitation: Olivier Faugeras).

• April 2011. IGK, Bielefeld, 5 lectures, Stochastic differential equations with multipletimescales (Invitation: Barbara Gentz).

Talks at local seminars

• 5.10.2017. Séminaire du MAPMO, Orléans, Résoudre des EDPS en comptant desarbres.

• 1.12.2016. Séminaire du MAPMO, Orléans, Métastabilité, théorie du potentiel etdéterminants de Carleman–Fredholm : une introduction.

• 6.2015. Tours, Séminaire tournant de probabilités et statistiques, Théorie des valeursextrêmes et problème de sortie stochastique.

• 16.4.2015. Séminaire du MAPMO, Orléans, Introduction aux EDPS et aux structuresde régularité .

• 2.2013. Groupe de travail probabilités, Orléans, Markov loops, paths and fields I-III .• 14.12.2010. Evaluation AERES, Orléans, Quantifying the effect of noise on oscilla-

tory patterns.• 10/12.2008. Groupe de travail de probabilités, Orléans, Métastablité .• 15.11.2007. Journée de la Fédération Denis Poisson, Orléans, EDS lentes-rapides,

métastablité et résonance stochastique.• 2/3.2007. Groupe de travail Systèmes Ouverts, CPT Marseille, Grandes déviations

et processus d’exclusion I-III .• 10.11.2006. Open Systems Days, Marseille, Métastabilité dans une chaîne classique

bruitée.• 17.11.2003. Colloquium Equations Différentielles Stochastiques, Université de Tou-

lon, Modèles climatiques stochastiques.• 14.11.2003. Séminaire de Travail en Physique Mathématique, CPT Marseille, L’éva-

sion stochastique à travers une orbite périodique instable.

Curriculum Vitæ – Nils Berglund 17

• 2.10.2003. Colloquium Equations Différentielles Stochastiques, Université de Toulon,Mouvement Brownien, intégration stochastique.

• 13.6.2003. Séminaire de Travail en Physique Mathématique, CPT Marseille, Equa-tions différentielles stochastiques singulièrement perturbées.

• 6.12.2002. Séminaire de Travail en Physique Mathématique, CPT Marseille, Equa-tions différentielles singulièrement perturbées.

• 25.1.2002. Colloquium du Groupe 3, CPT Marseille, Atome d’hydrogène en champscroisés.

• 6.6.2001. Seminar on Stochastic Processes, ETH/Universität Zürich, Stochastic res-onance and hysteresis.

• 30.11.2000. Talks in Mathematical Physics, ETH Zürich, Slowly time-dependent sys-tems with additive noise: delay and resonance phenomena.

• 10.12.1999. Séminaire de Physique Théorique, EPFL, Atome d’hydrogène en champscroisés.

• 11.1999. Physics Colloquia, Georgia Tech, Adiabatic Dynamical Systems and Hys-teresis.

Other talks at conferences

• 23.6.2017. Journées de Probabilités, Aussois: “Structures de régularité et mécaniquestatistique.

• 26.7.2016. ICME 13, Hamburg: “Images des Mathématiques”, a website dedicatedto current research topics for the general public.

• 27.5.2015. Journées de Probabilités, Toulouse: Structures de régularité et renor-malisation d’EDPS de FitzHugh–Nagumo.

• 27.5.2014. Journées de Probabilités, CIRM, Marseille: Théorie des valeurs extrêmeset problème de sortie stochastique.

• 9.6.2009. Journées de Probabilités, Poitiers: Métastabilité dans des EDPS du typeGinzburg–Landau.

• 4.9.2008. Journées de Probabilités, Lille: Métastabilité et loi de Kramers pour lesdiffusions dans des potentiels à selles non-quadratiques.

• 4.6.2007. CCT07, Marseille: Metastability in interacting nonlinear stochastic differ-ential equations.

• 20.9.2006. Journées de Probabilités, CIRM, Marseille: Synchronisation dans les dif-fusions couplées.

• 5.9.2005. Journées de Probabilités, Nancy: Distribution des temps de résidencepour la résonance stochastique.

• 13.9.2004. QMath9, Giens: On the stochastic exit problem — irreversible case.• 8.9.2004. Journées de Probabilités, CIRM, Marseille: Le problème de sortie d’une

diffusion d’un domaine borné par une orbite périodique instable: Au-delà des grandesdéviations.

• 6.7.2002. Let’s face chaos through nonlinear dynamics, Maribor: Stochastic reso-nance: Some new results.

• 5.6.2000. Second Nonlinear Control Network (NCN) Workshop, Paris: Effect ofnoise and open loop control on dynamic bifurcations.

• 2.8.1999. Equadiff’99, Berlin: Bifurcations, scaling laws and hysteresis in singularlyperturbed systems.

18 January 22, 2019

• 30.6.1999. Let’s face chaos through nonlinear dynamics, Maribor: Dynamic bifur-cations: hysteresis, scaling laws, and feedback control .

• 15.3.1999. Nonlinear Control Network (NCN) Workshop “Stability and Stabiliza-tion”, Ghent: Effect of noise and open loop control on dynamic bifurcations.

Other participation in conferences

• 21–23.2.2018. 10es rencontres du GDR DYNQUA, Lille.• 23–24.1.2018. Inhomogeneous Random Systems, Institut Henri Poincaré, Paris.• 3–7.4.2017. CIRM, Marseille, Dynamiques stochastiques hors d’équilibre.• 22–24.2.2017. 9es rencontres du GDR DYNQUA, Toulon.• 20–24.6.2016. Conférence finale du projet région MADACA, Chalès.• 6–10.6.2016. SMF 2016, Tours.• 26–27.1.2016. Inhomogeneous Random Systems, Institut Henri Poincaré, Paris.• 3–5.6.2015. Journées en l’honneur de Marc Yor, Paris.• 2–6.2.2015. 7ème Rencontre du GDR Dynamique Quantique, Nantes.• 27–28.1.2015. Inhomogeneous Random Systems, Institut Henri Poincaré, Paris.• 5–7.2.2014. 6ème Rencontre du GDR Dynamique Quantique, Roscoff.• 15–17.7.2013. Stochastics and Real World Models, IGK, Bielefeld.• 22–23.1.2013. Inhomogeneous Random Systems, Institut Henri Poincaré, Paris.• 18–22.6.2012. Journées de Probabilités, Roscoff.• 8–10.2.2012. 4ème Rencontre du GDR Dynamique Quantique, IMT Toulouse.• 24–25.1.2012. Inhomogeneous Random Systems, Institut Henri Poincaré, Paris.• 3–6.8.2011. Limit theorems in Probability, Statistics and Number Theory, Bielefeld.• 20–24.6.2011. Journées de Probabilités, Nancy.• 25–27.11.2010. Quantum dynamics, CIRM, Marseille.• 14–16.10.2010. Workshop on Probabilistic Techniques in Statistical Mechanics, Ber-

lin.• 24–26.3.2010. Second meeting of the GDR “Quantum Dynamics”, Dijon.• 26–27.1.2010. Inhomogeneous Random Systems, Institut Henri Poincaré, Paris.• 1–8.6.2008. Hyperbolic dynamical systems, Erwin Schödinger Insitute, Wien.• 22–23.1.2008. Inhomogeneous Random Systems, Institut Henri Poincaré, Paris.• 5–9.11.2007. Entropy, turbulence and transport, Institut Henri Poincaré, Paris.• 9–13.7.2007. ICIAM 07, Zürich.• 23–24.1.2007. Inhomogeneous Random Systems, Institut Henri Poincaré, Paris.• 15–19.1.2007. Vth Meeting of the GDRE Mathematics and Quantum Physics, CIRM,

Marseille.• 4–29.7.2005. Mathematical Statistical Physics, Les Houches.• 16–19.3.2005. Workshop random spatial models from physics and biology, Berlin.• 18–23.4.2004. Equilibrium and Dynamics of Spin Glasses, Ascona.• 3–28.3.2003. Statistical Mechanics and Probability Theory, CIRM, Marseille.• 27–31.5.2002. Aspects Mathématiques des Systèmes Aléatoires et de la Mécanique

Statistique, CIRM, Marseille.• 9–11.7.2001. Workshop on stochastic climate models, Chorin.• 2–7.7.2001. Stochastic analysis, Berlin.• 11–17.3.2001. Stochastics in the sciences, Oberwolfach.• 5–9.7.1999. ICIAM 99, Edinburgh.

Curriculum Vitæ – Nils Berglund 19

Outreach talks

• 1.3.2016. Mardis de la Science, Hôtel Dupanloup, Orléans: Modèles aléatoires enbiologie.

• 5.10.2014. Fête de la Science, Orléans: Mathématiques du Quotidien.• 20.6.2014, 27.6.2014, 19.6.2015, 26.6.2015, 24.6.2016, 29.6.2016, 19.6.2017,26.6.2017. Centre Galois, Orléans: Mathématiques et Biologie.

• 22.6.2011, 29.6.2011, 28.6.2013. Centre Galois, Orléans: Probabilités et PhysiqueStatistique.

Description of Research Activities

Past Research Activities

Hamiltonian Systems

With Hervé Kunz, as well as Alex Hansen, Eivind Hauge and Jarek Piasecki, I have anal-ysed dynamical systems of the billiard type. These systems are described by symplecticmaps of the plane, which can display a great variety of behaviours, from integrable tochaotic.

In particular, we have used methods from perturbation theory (Kolmogorov–Arnold–Moser theory, Nekhoroshev theory) to describe the dynamics of billiards in magneticfields [BK96] and in electromagnetic fields [BHHP96, Ber00b].

With Turgay Uzer, I have studied the dynamics of atoms in electromagnetic fields,using methods of Celestial Mechanics (Delaunay variables, averaging) [BU01].

Singular perturbation theory

With Hervé Kunz, I have studied slow–fast ordinary differential equations, and systemswith slowly time-dependent parameters. These are described by singularly perturbedequation of the form

εx = f(x, t) , x ∈ R n

where ε is a small parameter.

Using methods from analytic [Was87] and geometric singular perturbation theory[Fen79], we have analysed in particular the following aspects:

• The dynamics in a neighbourhood of equilibrium branches t 7→ x?(t), f(x?(t), t) = 0.Fenichel’s geometrical theory shows the existence of invariant manifolds of the formx = x(t, ε), x(t, ε) = x?(t) +O(ε). We have shown, in particular, that these manifoldscan be approximated by asymptotic expansion with exponential accuracy.

• The assumptions for the existence of invariant manifolds break down in the vicin-ity of bifurcation points, that is in points (x?(t0), t0) in which the Jacobian matrix∂xf(x?(t0), t0) admits eigenvalues with vanishing real part. One speaks in this caseof a dynamic bifurcation. We have developed a method allowing to determine thescaling behaviour of solutions in a neighbourhood of these points, in a very generalsetting, using the bifurcation point’s Newton polygon [BK99, Ber01, Ber98, Ber00d,

20 January 22, 2019

Ber00a]. This method also allows to describe the scaling behaviour of hysteresiscycles [Ber01].

• In a mechanical system, we have proved the existence of chaotic hysteresis, whichcan be described by geometrical methods [BK97].

With Klaus Schneider, I have applied these methods to problems of feedback controlof dynamic bifurcations [Ber00c, BS99].

Slow–fast stochastic differential equations

With Barbara Gentz, I have studied the pathwise behaviour of solutions of stochasticdifferential equations with two time scales, of the form

dxt =1

εf(xt, yt, ε)dt+

σ√εF (xt, yt, ε)dWt , x ∈ R n ,

dyt = g(xt, yt, ε)dt+ σ′G(xt, yt, ε)dWt , y ∈ Rm ,

where ε, σ and σ′ are small parameters. Such equations describe systems with fast andslow variables, perturbed by random noise. They play an important rôle in applicationsin Physics (e.g. hysteresis in ferromagnets, Josephson junctions), in Climatology (mod-els of the thermohaline circulation, Ice Ages), and biology (neural dynamics, genericregulatory networks).

The monograph [BG06] describes a new, constructive method for the quantitative de-scription of the sample-path behaviour of such equations. This approach combines meth-ods from singular perturbation theory (Fenichel’s geometric theory [Fen79], asymptoticexpansions) with methods from stochastic analysis (large deviations [FW98], the exitproblem, properties of martingales). A large part of the book is dedicated to applica-tions of this approach to concrete problems from Physics, Climatology and Biology.

The main steps of our approach are the following:

• A slow manifold of the systems is a set of the form {(x?(y), y) ∈ R n+m : f(x?(y), y) =

0, y ∈ D0}. It is stable if all eigenvalues of the Jacobian matrix ∂xf(x?(y), y) have neg-ative real parts, bounded away from zero, for all y ∈ D0. In this case one constructsa neighbourhood B(h) of the manifold, where h measures the size of the neighbour-hood, such that an estimate of the form

C−(t, ε) e−κ−h2/2σ2

6 Px?(y0),y0

{τB(h) < t

}6 C+(t, ε) e−κ+h

2/2σ2

holds for the first-exit time τB(h) of paths from B(h). This implies that paths are likelyto spend exponentially long time spans in B(h), as long as h is chosen somewhatlarger than σ.

• In case the slow manifold in unstable, one can show that sample paths typically leavea vicinity of the manifold in a time of order ε|log σ|.

• The slow manifold admits bifurcation points whenever eigenvalues of the Jacobianmatrix ∂xf(x?(y), y) have a vanishing real part at some y ∈ D0. In such cases, theslow manifold can fold back on itself, or split into several manifolds. The analysisof such cases proceeds in two steps. First, one reduces the problem to a lower-dimensional one by projection on the centre manifold. Next one carries out a localanalysis of the reduced dynamics. Using informations on the deterministic dynamics,partitions of the time interval, and the strong Markov property, one can describe the

Curriculum Vitæ – Nils Berglund 21

behaviour of typical paths. Depending on the situations, paths choose to follow oneof the new slow manifolds, our jump to a remote manifold.

In addition to the general theory [BG03], we have described in particular the follow-ing phenomena and applications:

• Dynamic bifurcations with noise: Pitchfork bifurcation [BG02d], saddle–node [BG02b]and Hopf bifurcation [BG06, Chapter 5]. A remarkable fact is that the noise can fa-cilitate transitions between manifolds, so that these can happen earlier as in thedeterministic case.

• Stochastic resonance: [BG02e, BG04, BG05, BG14]. This phenomenon appears whena deterministic periodic perturbation is combined with the noise, yielding almost pe-riodic transitions between stable manifolds, which would be impossible in the ab-sence of noise. The analysis of the distribution of waiting times between transitionsrequired an extension of the classical Wentzell–Freidlin theory [FW98] to systemswith periodic orbits.

• Hysteresis: Effect of noise on scaling laws of the area of hysteresis loops [BG02b].• Models from Physics: In particular from Solid State Physics [BG02a].• Climate models: Models of Ice Ages and the Gulf Stream [BG02c].• Application in Biology: Models of neurons, such as the Hodgkin–Huxley equations,

in which noise is responsible for the phenomenon of excitability [BG06, Chapter 6].• Quantum dynamics: The effect of classical noise on certain quantum systems has

been studied in the PhD thesis of Jean-Philippe Aguilar [AB08].

Effect of noise on spatially extended systems

With Barbara Gentz and Bastien Fernandez I have examined spatially extended systemswith stochastic perturbations, in the framework of the research project “Modélisationstochastique de phénomènes hors équilibre” (supported by the French Ministry of Re-search by a contract of 70’000 Euros). Such systems model in particular the influenceof different heat reservoirs, which influence transport properties through physical sys-tems [EPRB99].

In [BFG07a, BFG07b], we examine the dynamics of a chain of bistable coupled units,described by a diffusion on R Z /NZ of the form

dxσi (t) = f(xσi (t))dt+γ

2

[xσi+1(t)− 2xσi (t) + xσi−1(t)

]dt+ σdWi(t) .

Here bistability is created by the form of f , e.g. the choice f(x) = x − x3 causes thesystem to hesitate between values +1 and −1. On the other hand, the coupling term withnearest neighbours compels the units to cooperate, yielding a tendency of local systemsto synchronise. The system has two fundamental states, given by I+ = (1, 1, . . . , 1) andI− = −I+. The noise triggers transitions between these fundamental states, and possiblyother existing metastable states.

With the help of Wentzell–Freidlin theory, we were able to prove the following:

• At weak coupling γ, the system has 2N local (metastable) equilibrium states. Tran-sitions between these states are similar to those of an Ising model with Glauberdynamics, indeed they occur through the growth of a droplet of one phase within thephase with opposite sign [dH04].

22 January 22, 2019

• At strong coupling (of the order N2), by contrast, the system synchronises: Onlythe two metastable equilibrium states I± are left. During transitions between thesetwo metastable states, the elements of the chain keep the same position in theirrespective local potential with high probability.

• The most interesting apect is the transition between these two regimes, which in-volves a sequence of symmetry-breaking bifurcations. The description of these bi-furcations involves the so-called equivariant bifurcation theory, which takes the sys-tem’s symmetries into account. In particular in the limit of large chain length N ,we were able to determine the bifurcation diagram with the help of the theory ofsymplectic maps, allowing for a precise determination of the time scales and thegeometry of transition paths.

In all these regimes, Wentzell–Freidlin theory yields the expected transition time be-tween metastable states on the level of large deviations. Results by Bovier and cowork-ers [BEGK04, BGK05] allow to go beyond Wentzell–Freidlin exponential asymptotics, andto determine prefactors of metastable transition times (by proving the so-called Kramersformula, see for instance [Ber13]).

Current and planned research activities

Metastability

We continue our work on metastability in systems of coupled stochastic differential equa-tions. As the particular system described above depends on parameters, it undergoesbifurcations whenever the determinant of the Hessian of the potential vanishes. Theclassical Kramers formula fails in these cases, since it would predict vanishing or di-verging transition times. We have extended the Kramers formula to situations with bi-furcations [BG10, BG09a], by taking into account the effect of higher-order terms of thepotential at critical points.

Another extension of Kramers’ formula is to the infinite-dimensional case of stochas-tic partial differential equations. In [BG13], we have obtained sharp estimates on ex-pected transition times for a class of one-dimensional parabolic equations of the form

dut(x) =[∆ut(x)− U ′(ut(x))

]dt+

√2ε dW (t, x) .

This result uses spectral Galerkin approximations of the system, and required a controlof capacities with error bounds uniform in the dimension. In the work [BDGW17] withGiacomo Di Gesù (Vienna) and Hendrik Weber (Warwick), we have obtained an analogousresult for the two-dimensional Allen–Cahn equation, when the transition state is theidentically zero solution. This equation needs to be renormalised to be well-posed, whichresults in the Fredholm determinant in the Eyring–Kramers prefactor to be replaced bya Carleman–Fredholm determinant.

Another pecularity of the above models is that they are invariant under a group ofsymmetries, so that the classical Kramers formula for expected transition times does notapply. The PhD thesis of Sébastien Dutercq addresses the description of these systems,in particular by deriving a corrected Kramers formula taking the symmetries into ac-count [BD16a]. These results have been applied in particular to a variant of the systemstudied in [BFG07a, BFG07b], in which the sum of coordinates is constrained to remain

Curriculum Vitæ – Nils Berglund 23

equal to zero. For weak coupling, one then obtains a Kawasaki-type dynamics, with anexplicit expression for the spectral gap [BD16b].

Neuroscience

Several models for action-potential generation in neurons, such as the Hodgkin–Huxley,FitzHugh–Nagumo and Morris–Lecar equations involve systems of slow–fast differentialequations. For appropriate parameter values, these systems display the phenomenon ofexcitability: They admit a stable equilibrium point, which, however, is such that small de-terministic or random perturbations cause the system to make a big excursion in phasespace, corresponding to a spike. An important question is to determine the statistics ofinterspike intervals. In certain, effectively one-dimensional cases, the interspike distri-bution is close to an exponential one [BG09b]. In multidimensional cases, however, onenumerically observes different distributions, involving for instance clusters of spikes[MVE08]. A major difficulty in the mathematical analysis of these equations stems fromthe fact that they are far from being reversible.

Building on methods in [BG06], we have started developing a mathematical descrip-tion of the effect of noise on excitable systems. This work is part of the ANR projectMANDy, Mathematical Analysis of Neuronal Dynamics (principal investigator: MichèleThieullen, University Paris 6). The PhD thesis of Damien Landon addresses the problemof characterising the interspike distribution for the FitzHugh–Nagumo model [Lan12].Using properties of substochastic Markov chains and quasistationary distributions, wehave been able to describe this distribution in the regime where the excitable stationarypoint is a focus. In particular, we have proved that the distribution is asymptoticallygeometric [BL12].

An interesting feature of three-dimensional models is that they can produce mixed-mode oscillations, which are patterns alternating large- and small-amplitude oscillations(see [DGK+12] for a review). In collaboration with Barbara Gentz and Christian Kuehn(Vienna), we have started a systematic study of the effect of noise on mixed-mode oscil-lations in these systems. First results in [BGK12] quantify the effect of noise on maskingsmall-amplitude oscillations, and on decreasing the number of small oscillations betweenspikes. This description has been extended to the global dynamics, using an analysis ofPoincaré sections for the stochastic system [BGK15].

The thesis of Manon Baudel is concerned with a formalisation of the theory of randomPoincaré maps, and in particular with the spectral theory of these processes. The resultsin [BB17] provide expressions for eigenvalues exponentially close to 1 of the randomPoincaré map and the corresponding left and right eigenfunctions in terms of committorfunctions between neighbourhoods of periodic orbits.

Regularity structures

With Christian Kuehn (Munich), I have recently started applying Martin Hairer’s theoryof regularity structures [Hai14] to coupled SPDE–ODE systems of the form

∂tu = ∆u+ f(u, v) + ξ ,

∂tv = g(u, v) ,

24 January 22, 2019

where u and v are functions of time t > 0 and x ∈ Td, the torus in dimension d ∈ {2, 3},and ξ denotes space-time white noise. For a cubic nonlinearity f and a linear g, wewere able to show [BK16] local existence of solutions for this highly singular system, byadapting the theory in [Hai14]. This includes the case of the FitzHugh–Nagumo equationdescribing a large population of diffusively coupled neurons. It is of course desirable toobtain more quantitative results, for instance on the appearance of spiral waves in thiskind of system.

In [BK17], we consider space-fractional SPDEs of the form

∂tu = ∆ρ/2u+ f(u) + ξ ,

where ∆ρ/2 denotes the fractional Laplacian of parameter ρ ∈ (0, 2]. We examine how thesize of the model space of a regularity structure describing this equation diverges as ρapproaches a critical value from above, which depends on the space dimension and thedegree of the nonlinearity.

Bibliography

[AB08] Jean-Philippe Aguilar and Nils Berglund, The effect of classical noise on a quantumtwo-level system, Journal of Mathematical Physics 49 (2008), 102102 (23 pages).

[BB17] Manon Baudel and Nils Berglund, Spectral Theory for Random Poincaré Maps, SIAMJ. Math. Anal. 49 (2017), no. 6, 4319–4375. MR 3719020

[BD16a] Nils Berglund and Sébastien Dutercq, The Eyring-Kramers law for Markovian jumpprocesses with symmetries, J. Theoret. Probab. 29 (2016), no. 4, 1240–1279. MR3571245

[BD16b] , Interface dynamics of a metastable mass-conserving spatially extended diffu-sion, Journal of Statistical Physics 162 (2016), 334–370.

[BDGW17] Nils Berglund, Giacomo Di Gesù, and Hendrik Weber, An Eyring–Kramers law forthe stochastic Allen–Cahn equation in dimension two, Electron. J. Probab. 22 (2017),1–27.

[BEGK04] Anton Bovier, Michael Eckhoff, Véronique Gayrard, and Markus Klein, Metastabilityin reversible diffusion processes. I. Sharp asymptotics for capacities and exit times,J. Eur. Math. Soc. (JEMS) 6 (2004), no. 4, 399–424.

[Ber98] Nils Berglund, On the reduction of adiabatic dynamical systems near equilibriumcurves, Preprint mp-arc/98-574. Proceedings of the international workshop CelestialMechanics, Separatrix Splitting, Diffusion, Aussois, France, 1998.

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[Ber13] Nils Berglund, Kramers’ law: Validity, derivations and generalisations, Markov Pro-cess. Related Fields 19 (2013), no. 3, 459–490.

[BFG07a] Nils Berglund, Bastien Fernandez, and Barbara Gentz, Metastability in interactingnonlinear stochastic differential equations: I. From weak coupling to synchroniza-tion, Nonlinearity 20 (2007), no. 11, 2551–2581.

[BFG07b] , Metastability in interacting nonlinear stochastic differential equations II:Large-N behaviour, Nonlinearity 20 (2007), no. 11, 2583–2614.

25

26 BIBLIOGRAPHY

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[BGK12] Nils Berglund, Barbara Gentz, and Christian Kuehn, Hunting French ducks in a noisyenvironment, J. Differential Equations 252 (2012), no. 9, 4786–4841.

[BGK15] , From Random Poincaré Maps to Stochastic Mixed-Mode-Oscillation Patterns,J. Dynam. Differential Equations 27 (2015), no. 1, 83–136. MR 3317393

[BHHP96] Nils Berglund, Alex Hansen, Eivind H. Hauge, and Jaroslaw Piasecki, Can a localrepulsive potential trap an electron?, Phys. Rev. Letters 77 (1996), 2149–2153.

[BK96] Nils Berglund and Hervé Kunz, Integrability and ergodicity of classical billiards in amagnetic field, J. Statist. Phys. 83 (1996), no. 1-2, 81–126.

[BK97] , Chaotic hysteresis in an adiabatically oscillating double well, Phys. Rev. Let-ters 78 (1997), 1691–1694.

[BK99] , Memory effects and scaling laws in slowly driven systems, J. Phys. A 32(1999), no. 1, 15–39.

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[BK17] , Model spaces of regularity structures for space-fractional SPDEs,arXiv:1701.03066, 2017.

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[BU01] Nils Berglund and Turgay Uzer, The averaged dynamics of the hydrogen atom incrossed electric and magnetic fields as a perturbed Kepler problem, Found. Phys. 31(2001), no. 2, 283–326, Invited papers dedicated to Martin C. Gutzwiller, Part III.

[DGK+12] M. Desroches, J. Guckenheimer, C. Kuehn, B. Krauskopf, H. Osinga, and M. Wechsel-berger, Mixed-mode oscillations with multiple time scales, SIAM Review 54 (2012),no. 2, 211–288.

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