A Mathematical Perspective on Resilience and Sustainability in Climate and Biodiversity
Michel de Lara (ENPC, CERMICS)
In this talk, I gather previous works related to mathematical methods for the management of natural resources, and present how they can contribute to tackle questions in resilience and sustainability.
For this purpose, I will outline the following items.
- Scan through the vocabulary of sustainability and resilience in the IPCC (climate) and IPBES (biodiversity) international bodies reports:
goals, indicators, vulnerability, adaptive capacity, robustness, risk, scenarios, models.
- Address theoretical questions such as how can we formalize sustainability and resilience with tools from control theory (optimal control, viability) and decision under uncertainty (multistage stochastic optimization, risk). For instance, when goals to achieve are formulated as constraints to satisfy — like minimal spawning stock biomass every year in fishery management, or maximal number of infected in epidemics control — we present the notion of viability kernel, and its stochastic and robust variants.
- Present solution methods: how can we tackle the solving of problems, once mathematically formalized? We sketch stochastic and robust dynamic programming in small state dimension.
- Outline examples: biodiversity (fisheries, epidemiology), energy and climate.
- Raise open questions and challenges: numerical methods for large-scale multistage stochastic optimization problems; value of information; insurance value of natural capital; risk measures for random processes; axiomatics for acceptable processes.