## Nicolas Lanchier

## Biography

Most mathematical models introduced in the life and social sciences literature use equations (called differential equations) that only involve time and ignore the spatial structure of our environment. The spatial component, however, has been identified as an important factor in how communities are shaped, and spatial models can result in predictions that differ from their "time-only" counterparts. The aim of Nicolas Lanchier's research is to understand the role of space in biological and social communities through the mathematical analysis of a class of stochastic processes known as interacting particle systems. Popular examples of such models are the contact process and the voter model.

## Education

Ph.D. University of Rouen, France 2005

## Research Interests

Most mathematical models introduced in the life and social sciences literature that describe inherently spatial phenomena of interacting populations consist of systems of ordinary differential equations, thus leaving out any spatial structure. The spatial component, however, is identified as an important factor in how communities are shaped, and spatial models can result in predictions that differ from their nonspatial counterparts. The aim of my research is to understand the role of space in ecology, epidemiology, population genetics, opinion dynamics, cultural dynamics and evolutionary game theory through the mathematical analysis of a class of stochastic processes known as interacting particle systems. These processes are ideally suited to investigate the consequences of the inclusion of a spatial structure in the form of stochastic and local interactions. This includes generalizations of the contact process and the voter model in spatially heterogeneous environments but also on inhomogeneous graphs, hypergraphs, and dynamic graphs.

## Publications

- Nicolas Lanchier. Evolutionary games on the lattice: payoffs affecting birth and death rates. Ann. Appl. Probab (2015).
- Nicolas Lanchier and Nicole Taylor. Galam's bottom-up hierarchical system and public debate model revisited. Adv. Appl. Probab (2015).
- Nicolas Lanchier. The naming game in language dynamics revisited. J. Appl. Probab (2014).
- Nicolas Lanchier, Stylianos Scarlatos. Clustering and coexistence in the one-dimensional vectorial Deffuant model. ALEA Lat. Am J. Probab. Math. Stat (2014).
- Stephen Evilsizor, Nicolas Lanchier. Evolutionary games on the lattice: best-response dynamics. Electron. J. Probab (2014).
- Nicolas Lanchier. Stochastic spatial model of producer-consumer systems on the lattice. Adv. Appl. Probab (2013).
- Nicolas Lanchier. The role of dispersal in interacting patches subject to an Allee effect. Adv Appl. Probab (2013).
- Nicolas Lanchier, Jared Neufer. Stochastic dynamics on hypergraphs and the spatial majority rule model. J. Stat. Phys (2013).
- Nicolas Lanchier, Stylianos Scarlatos. Fixation in the one-dimensional Axelrod model. Ann. Appl. Probab (2013).
- Nicolas Lanchier. The Axelrod model for the dissemination of culture revisited. Ann. Appl. Probab (2012).
- Nicolas Lanchier. The critical value of the Deffuant model is equal to one half. ALEA Lat. Am. J. Probab. Math. Stat (2012).
- Nicolas Lanchier, Jason Schweinsberg. Consensus in the two-state Axelrod model. Stochastic Process. Appl (2012).
- Yun Kang, Nicolas Lanchier. The role of space in the exploitation of resources. Bull. Math. Biol (2012).
- Daniela Bertacchi, Nicolas Lanchier, Fabio Zucca. Contact and voter processes on the infinite percolation cluster as models of host-symbiont interactions. Ann. Appl. Probab (2011).
- Nicolas Lanchier. Contact process with destruction of cubes and hyperplanes: forest fires versus tornadoes. Adv. Appl. Probab (2011).
- Nicolas Lanchier. Two-scale multitype contact process: coexistence in spatially explicit metapopulations. Markov Process. Related Fields (2011).
- Yun Kang, Nicolas Lanchier. Expansion or extinction: deterministic and stochastic two-patch models with Allee effects. J. Math. Biol (2011).
- Nicolas Lanchier. Opinion dynamics with confidence threshold: an alternative to the Axelrod model. ALEA Lat. Am. J. Probab. Math. Stat (2010).
- Nicolas Lanchier, Claudia Neuhauser. Stochastic spatial models of host-pathogen and host-mutualist interactions II. Stoch. Models (2010).
- Ben Chan, Rick Durrett, Nicolas Lanchier. Coexistence for a multitype contact process with seasons. Ann. Appl. Probab (2009).
- Nicolas Lanchier, Claudia Neuhauser. Spatially explicit non-Mendelian model. Ann. Appl. Probab (2009).
- Lamia Belhadji, Nicolas Lanchier. Two-scale contact process and effects of habitat fragmentation on metapopulations. Markov Process. Related Fields (2008).
- Rick Durrett, Nicolas Lanchier. Coexistence in host-pathogen systems. Stochastic Process. Appl (2008).
- Nicolas Lanchier, Claudia Neuhauser. Voter model and biased voter model in heterogeneous environments. J. Appl. Probab (2007).
- Lamia Belhadji, Nicolas Lanchier. Individual versus cluster recoveries within a spatially structured population. Ann. Appl. Probab (2006).
- Nicolas Lanchier, Claudia Neuhauser. A spatially explicit model for competition among specialists and generalists in a heterogeneous environment. Ann. Appl. Probab (2006).
- Nicolas Lanchier, Claudia Neuhauser. Stochastic spatial models of host-pathogen and host-mutualist interactions I. Ann. Appl. Probab (2006).
- Nicolas Lanchier. Multitype contact process with frozen sites: a spatial model of allelopathy. J. Appl. Probab (2005).
- Nicolas Lanchier. Phase transitions and duality properties of a successional model. Adv. Appl. Probab (2005).

## Research Activity

- Lanchier,Nicolas*. Stochastic spatial models of social dynamics. NSA(3/24/2015 - 3/23/2016).
- Lanchier,Nicolas*. Stochastic processes on hypergraphs and dynamic graphs. NSF-MPS(8/15/2010 - 7/31/2014).

## Teaching Website

## Courses

Fall 2021 | |
---|---|

Course Number | Course Title |

APM 541 | Stochastic Modeling in Biology |

MAT 595 | Continuing Registration |

APM 792 | Research |

MAT 792 | Research |

APM 799 | Dissertation |

Summer 2021 | |
---|---|

Course Number | Course Title |

MAT 595 | Continuing Registration |

MAT 792 | Research |

APM 792 | Research |

Spring 2021 | |
---|---|

Course Number | Course Title |

STP 421 | Probability |

MAT 493 | Honors Thesis |

STP 499 | Individualized Instruction |

APM 504 | App. Prob. and Stochastic Proc |

MAT 590 | Reading and Conference |

APM 792 | Research |

MAT 792 | Research |

APM 795 | Continuing Registration |

APM 799 | Dissertation |

MAT 799 | Dissertation |

Fall 2020 | |
---|---|

Course Number | Course Title |

APM 541 | Stochastic Modeling in Biology |

MAT 595 | Continuing Registration |

APM 792 | Research |

MAT 792 | Research |

APM 799 | Dissertation |

Summer 2020 | |
---|---|

Course Number | Course Title |

MAT 595 | Continuing Registration |

MAT 792 | Research |

APM 792 | Research |

Spring 2020 | |
---|---|

Course Number | Course Title |

MAT 493 | Honors Thesis |

STP 499 | Individualized Instruction |

APM 504 | App. Prob. and Stochastic Proc |

MAT 590 | Reading and Conference |

MAT 792 | Research |

APM 792 | Research |

APM 795 | Continuing Registration |

APM 799 | Dissertation |

Fall 2019 | |
---|---|

Course Number | Course Title |

STP 421 | Probability |

APM 541 | Stochastic Modeling in Biology |

MAT 792 | Research |

APM 792 | Research |

APM 799 | Dissertation |

Summer 2019 | |
---|---|

Course Number | Course Title |

APM 792 | Research |

Spring 2019 | |
---|---|

Course Number | Course Title |

STP 492 | Honors Directed Study |

MAT 493 | Honors Thesis |

STP 499 | Individualized Instruction |

APM 504 | App. Prob. and Stochastic Proc |

MAT 590 | Reading and Conference |

APM 792 | Research |

APM 799 | Dissertation |

Fall 2018 | |
---|---|

Course Number | Course Title |

STP 425 | Stochastic Processes |

STP 493 | Honors Thesis |

MAT 792 | Research |

APM 792 | Research |

APM 799 | Dissertation |

Summer 2018 | |
---|---|

Course Number | Course Title |

APM 792 | Research |

Spring 2018 | |
---|---|

Course Number | Course Title |

STP 492 | Honors Directed Study |

MAT 493 | Honors Thesis |

STP 499 | Individualized Instruction |

APM 504 | App. Prob. and Stochastic Proc |

APM 792 | Research |

APM 799 | Dissertation |

Fall 2017 | |
---|---|

Course Number | Course Title |

STP 421 | Probability |

STP 493 | Honors Thesis |

APM 541 | Stochastic Modeling in Biology |

MAT 792 | Research |

APM 792 | Research |

Summer 2017 | |
---|---|

Course Number | Course Title |

APM 792 | Research |

Spring 2017 | |
---|---|

Course Number | Course Title |

STP 492 | Honors Directed Study |

MAT 493 | Honors Thesis |

APM 504 | App. Prob. and Stochastic Proc |

MAT 590 | Reading and Conference |

APM 792 | Research |

APM 799 | Dissertation |

## Presentations

- Nicolas Lanchier. Fluctuation versus fixation in the Axelrod model. Colloquium of the Mathematical and Theoretical Biology Institute (Jul 2014).
- Nicolas Lanchier. Fluctuation versus fixation in the constrained voter model. Institute of Mathematical Statistics Annual Meeting 2014, Sydney, Australia (Jul 2014).
- Nicolas Lanchier. Fluctuation versus fixation in the constrained voter model. 37th conference on Stochastic Processes and Their Applications, Buenos Aires, Argentina (Jul 2014).
- Nicolas Lanchier. Fluctuation versus fixation in the constrained voter model. Eight International Conference on Recent Advances in Applied Dynamical systems, Guilin, China (Jun 2014).
- Nicolas Lanchier. Fluctuation versus fixation in the Axelrod model. Mathematics Seminar of the College of Mathematics and Information Science, Wenzhou University, China (Jun 2014).
- Nicolas Lanchier. Fluctuation versus fixation in the Axelrod model. Mathematics Seminar at Zhejiang University of Science and Technology, China (Jun 2014).
- Nicolas Lanchier. Overview of the standard and constrained voter models. Advanced lecture of the Mathematical and Theoretical Biology Institute (Jun 2014).
- Nicolas Lanchier. Fluctuation versus fixation in the constrained voter model. Seminar of the School of Letters and Sciences, Arizona State University (Feb 2014).
- Nicolas Lanchier. Fluctuation versus fixation in the constrained voter model. Mathematical Biology seminar at Arizona State University, USA (Oct 2013).
- Nicolas Lanchier. Mathematics: numbers and shapes. Talk for the class of Kindergarten at the ASU Preparatory Academy (Sep 2013).
- Nicolas Lanchier. Poisson point processes and the exponential random variable. Advanced lecture of the Mathematical and Theoretical Biology Institute (Jun 2013).
- Nicolas Lanchier. Evolutionary games on the lattice. Advanced lecture of the Mathematical and Theoretical Biology Institute (Jun 2013).
- Nicolas Lanchier. Evolutionary games on the lattice. Seminar of the Computational Science Training for Undergraduates in the Mathematical Sciences (Feb 2013).
- Nicolas Lanchier. Fluctuation and fixation in the one-dimensional Axelrod model. Applied Mathematics Colloquium and Mathematical Seminar at the University of Arizona (Jan 2013).
- Nicolas Lanchier. Fluctuation and fixation in the one-dimensional Axelrod model. Workshop in Kinetic Theory for the Emergence of Complex Behavior in Social and Economic Systems (Jan 2013).
- Nicolas Lanchier. Stochastic spatial model of producer-consumer systems on the lattice. AMS meeting at the University of Arizona, USA (Oct 2012).
- Nicolas Lanchier. Flux and fixation in the one-dimensional Axelrod model. Mathematical Biology seminar at Arizona State University, USA (Oct 2012).
- Nicolas Lanchier. Overview of the voter model. Seminar of the Mathematical and Theoretical Biology Institute at Arizona State University, USA (Jul 2012).
- Nicolas Lanchier. Flux and fixation in the Axelrod model. Seminar of the Mathematical and Theoretical Biology Institute at Arizona State University, USA (Jul 2012).
- Nicolas Lanchier. Overview of the voter model & Flux and fixation in the Axelrod model (2 x 3 hours). Summer Graduate Workshop on Stochastics Applied to Biological Systems at MBI, Ohio State, USA (Jun 2012).
- Nicolas Lanchier. Two-strategy games on the lattice. Workshop in Spatial Models of Micro and Macro Systems at the MBI, Ohio State, USA (Apr 2012).
- Nicolas Lanchier. Spatial evolutionary games. Probability seminar at Arizona State University, USA (Feb 2012).
- Lanchier, Nicolas. Two-strategy games on the lattice. Colloquium of the School of Geographical Sciences and Urban Planning at Arizona State University (Nov 2011).
- Lanchier, Nicolas. Two-strategy games on the lattice. Iowa State University Mathematics Colloquium, USA (Sep 2011).
- Lanchier, Nicolas. Two-strategy games on the lattice. Mathematical biology seminar, Arizona State University (Aug 2011).
- Lanchier, Nicolas. The Axelrod model for the dissemination of culture revisited. Seminar of the Mathematical and Theoretical Biology Institute at Arizona State University (Jul 2011).
- Lanchier, Nicolas. Stochastic dynamics on hypergraphs and the majority rule. Seminar of the Mathematical and Theoretical Biology Institute at Arizona State University (Jul 2011).
- Lanchier, Nicolas. The Axelrod model for the dissemination of culture revisited. Workshop in Probability at the Institute for Mathematical Sciences, Singapore (May 2011).
- Lanchier, Nicolas. Stochastic dynamics on hypergraphs and the majority rule. Seminar of the Institute for Mathematical Sciences, Singapore (May 2011).
- Lanchier, Nicolas. The Axelrod model for the dissemination of culture revisited. Iowa State University Mathematics Colloquium, USA (Apr 2011).
- Lanchier, Nicolas. The Axelrod model for the dissemination of culture revisited. Workshop of the Statistical and Applied Mathematical Sciences Institure, USA (Mar 2011).
- Lanchier, Nicolas. Geometric properties of the spatial majority rule model. AMS meeting in UCLA (Oct 2010).
- Lanchier, Nicolas. Stochastic dynamics on hypergraphs and the majority rule. Probability seminar, Arizona State University (Oct 2010).
- Lanchier, Nicolas. Geometric properties of the spatial majority rule model. 38th Annual Meeting of the Statistical Society of Canada, Quebec City, Canada (May 2010).
- Lanchier, Nicolas. Coexistence in spatially explicit metapopulations. XI Congreso Latinoamericano de Probabilidad y Estadistica Matematica, Caracas (Nov 2009).
- Lanchier, Nicolas. Coexistence in spatially explicit metapopulations. Mathematical biology seminar, Arizona State University (Sep 2009).
- Lanchier, Nicolas. Theoretical framework to model interacting population. Workshop, Palo Alto (May 2009).
- Lanchier, Nicolas. Coexistence in spatially explicit metapopulations. 33rd conference on Stochastic Processes and Their Applications, Berlin (May 2009).
- Lanchier, Nicolas. Coexistence in spatially explicit metapopulations. Probability seminar, University of San Diego (Mar 2009).
- Lanchier, Nicolas. Survival and coexistence in spatially explicit metapopulations. Second Congress Canada France (Jun 2008).
- Lanchier, Nicolas. Survival (and coexistence) in spatially explicit metapopulations. Seminar in mathematics at Arizona State University (Sep 2007).
- Lanchier, Nicolas. Individual versus cluster recoveries on social networks. Workshop on the mathematics of global public health (Mar 2007).
- Lanchier, Nicolas. Host-symbiont interactions in static and dynamic environments. Seminar of the University of Minnesota (Nov 2006).
- Lanchier, Nicolas. Stochastic spatial models of host-symbiont interactions: Static and dynamic environments. Seminar of the University of Orleans (Jun 2006).
- Lanchier, Nicolas. Stochastic spatial models of host-symbiont interactions: Static and dynamic environments. Seminar in mathematics at Cornell University (Jan 2006).
- Lanchier, Nicolas. Competition among specialists and generalists in a heterogeneous environment. Seminar of the University of Rouen (Sep 2005).
- Lanchier, Nicolas. Individual versus cluster recoveries on a lattice of social clusters. Probability summer school of Cornell University (Jul 2005).
- Lanchier, Nicolas. Stochastic spatial models of host-pathogen and host-mutualist interactions. Workshop on probability of the University of Rouen (Jun 2005).
- Lanchier, Nicolas. Continuity result for multicolor particle systems. Seminar of the University of Minnesota (Apr 2005).
- Lanchier, Nicolas. Continuity result for multicolor particle systems. Seminar of the University of Rouen (Mar 2005).
- Lanchier, Nicolas. Stochastic spatial models of host-pathogen and host-mutualist interactions. Seminar of the University of Marseille (Mar 2005).
- Lanchier, Nicolas. Interacting particle systems and spatial structures. Seminar of the University of Rouen (Jun 2004).
- Lanchier, Nicolas. Phase transitions for the multitype contact processwith frozen sites. Seminar of the University of Rouen (Dec 2003).
- Lanchier, Nicolas. Phase transitions for an ecological succession model. Probability summer school of the University of Prague (Jul 2003).
- Lanchier, Nicolas. Phase transitions for an ecological succession model. Workshop on probability of the University of Rouen (Jun 2003).
- Lanchier, Nicolas. Phase transitions for an ecological succession model. Seminar of the University of Rouen (May 2003).

## Service

- Personnel and Budget Committee, Member (2015 - 2016)
- Research Assistant Professor Hiring Committee, Member (2015 - 2015)
- Actuarial Lecturer Hiring Committee, Member (2015 - 2015)
- Mathematics Colloquium Committee, Member (2013 - 2013)
- Organizer of the probability seminar, Organizer (2013 - 2013)
- Research Assistant Professor Hiring Committee, Member (2013 - 2013)
- SoMSS Advisory Committee on Statistics, Member (2013 - 2013)
- Probability and Statistics Hiring Committee, member (2009 - 2010)
- STP 421 qualifying exam committee, member (2009 - 2009)
- STP 421 qualifying exam committee, member (2008 - 2008)
- Probability Hirring Committee, member (2008 - 2008)
- STP 421 qualifying exam committee, member (2008 - 2008)
- Awards Committee, member (2007 - 2008)
- STP 421 qualifying exam committee, member (2007 - 2007)