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.
Ph.D. University of Rouen, France 2005
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.
Summer 2022 | |
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Course Number | Course Title |
MAT 595 | Continuing Registration |
APM 792 | Research |
MAT 792 | Research |
MAT 795 | Continuing Registration |
Spring 2022 | |
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Course Number | Course Title |
STP 421 | Probability |
MAT 493 | Honors Thesis |
MAT 499 | Individualized Instruction |
APM 504 | App. Prob. and Stochastic Proc |
MAT 584 | Internship |
MAT 590 | Reading and Conference |
APM 792 | Research |
MAT 792 | Research |
APM 795 | Continuing Registration |
MAT 799 | Dissertation |
APM 799 | Dissertation |
Fall 2021 | |
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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 | |
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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 | |
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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 | |
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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 | |
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Course Number | Course Title |
APM 792 | Research |
Spring 2019 | |
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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 | |
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Course Number | Course Title |
STP 425 | Stochastic Processes |
STP 493 | Honors Thesis |
MAT 792 | Research |
APM 792 | Research |
APM 799 | Dissertation |
Summer 2018 | |
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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 | |
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Course Number | Course Title |
STP 421 | Probability |
STP 493 | Honors Thesis |
APM 541 | Stochastic Modeling in Biology |
MAT 792 | Research |
APM 792 | Research |