School on Mathematical Modeling and Governance

October 30 – November 3, 2023

São Paulo, Brazil



We understand governance as management at the highest level of countries and the world. Governance implies decision-making in a context of high risk and high uncertainty where stakeholders have conflicting interests.

The context of governance challenges science. Mathematical modeling can be part of the solution, but it can be a part of the problem as well. The school aims to develop an awareness of the challenges involved and will provide “food for thought” to develop comprehension of what is involved, a consciousness of the capabilities, limitations of mathematical modeling in decision-making, and self-awareness.

We will address the question: Why and how science for governance is “science with consciousness” (also called complex thinking) and must be different from “everyday science” ( technically speaking: normal science).

The course will address how a complex systems approach modifies our mathematical modeling. We will critically examine stochastic models and their relations to deterministic ones emphasizing the trade-off between mathematical accessibility and truth value.

The second part of the course will address, in mathematical form, decision theory and its relation to game theory. We will discuss decision making under uncertainties, game equivalence, game strategies, evolutionary games and more.

The activity will consist of lectures, debate forums, and practices on specific problems. The lecture classes (L) will address the different topics in different forms: Matters of logic and epistemology will take the form of discussion and debate forums (D). Specific problems (P) will fill the proposed daily activities putting into practice the subjects already discussed. Active participation of students will be encouraged at all times.

There is no registration fee and limited funds are available for travel and local expenses.


  • Hernan G. Solari (IFIBA-CONICET and FCEN-UBA, Argentina)
  • Christian E. Schaerer (FP-UNA, Paraguay)
  • Claudia Pio Ferreira (IBB – Unesp, Brazil)
  • Marcelo Kuperman (CNEA-CONICET and Instituto Balseiro, Argentina)

List of participants: Updated on November 14, 2023.

Survey: Here 

Lecturers and Speakers


  • Mathematical modeling in the context of governance by CF, MK, CS and HS
  • Basic epistemology: Why and how Science for governance differs from normal (everyday) science by HS
  • Stochastic processes: Introduction and the determinist limit by HS
  • Introduction to Planning Decision Making by MK
  • Decision Making and game theory by MK


  • CF: Claudia Pio Ferreira (IBB – Unesp, Brazil)
  • MK: Marcelo Kuperman (CNEA-CONICET and Instituto Balseiro, Argentina)
  • CS: Christian E. Schaerer (FP-UNA, Paraguay)
  • HS: Hernan G Solari (FCEN-UBA & IFIBA-CONICET, Argentina)

Specific Problems:

  • P1: Is the phenomenological moment part of science or not? (by HS)
  • P3: Aedes aegypti populations. Fisheries. Check rules for correct modelling (by CF & HS)
  • P4: Exploration and conservation of natural resources (by MK)
  • P5: The rational use of resources to achieve sustainability (by CS)

Debate sessions:

  • D1: Philosophy and politics of modeling.

Invited talks: Silvio Funtowicz (University of Bergen, Norway) and Andrea Saltelli (University of Bergen, Norway) [Philosophy]

  • D2: Field interventions using genetically modified Aedes aegypti mosquitoes in Brazil.

Invited Talks: Luísa Reis-Castro (USC, USA) [Anthropology] 

  • D3: Controlling insects

Invited talk: Ary Hoffmann (U. Melbourne, Australia)[Ecology] 

  • D4: Management of complex ecosystems

Invited talk: Adrian Monjeau (U. Patagonia & F. Bariloche, Argentina) [Ecology] and Pedro Laterra (U. Buenos Aires, Argentina) [Biology]

  • D5: The rational use of resources to achieve sustainability.

Invited talk: Antonieta Rojas de Arias (CEDIC, U. Asunción, Paraguay) [Biology]


Reading Materials: Here



Online application is closed


Download de program: PDF 


Basic epistemology: Truth, belief and doubt. Experience and cognition. The place of models and theories in science. Cognition: imagination or abstraction? Consequences for modeling. Scientific inference. Difference between observed and fact. Is epistemology partially determined by our goals? Abductive/retroductive, deductive and predictive moments in the construction of models. The constructive spiral. Interdependence of the constructive moments. The phenomenological links with the observable. Logical principles of modeling: reality, no arbitrariness, continuity of reason, cognitive surpass, mediation, the logical collapse of a theory (refutation), dialectical openings.

Stochastic process: Introduction: Populations and events. Evolution of populations through events. Intrinsic stochasticity. Distribution of times between events. Heavy-tailed distributions versus Exponential distribution. Individuals in stages or stages of the individual? A-priori or a-posteriori statistics? Models based on individuals, populations, and meta-populations. Deterministic limit Kurtz’ theorems. The deterministic limit as a large number and short time approximation. Stochastic fluctuations around the limit. Validity of the approximation.

Planning decision making: Basis concepts of decision theory: alternatives; constraints; objectives. Choices under certainty: preferences and utility; choice. Choices under ignorance: contingent results, maxmin, minmax and mixed rules. Choices under uncertainty. Von Neuman-Morgestern Expected utility. Basic concepts of non-cooperative game theoretic situations. Game representation: Normal form, extensive form and backward induction. Strategies: pure/mixed, dominant/dominated, conservative, best response, rationalizability. Nash equilibrium: unicity, multiplicity, absence of equilibria in pure strategies, efficiency. Repeating a game. Evolutionary game: Replicator dynamics, stability. Representation of cooperative games Imputations. Stable allocations: the “core” of a cooperative game. The “Shapley” value.

L are lectures, P are problem solving sessions and D for talks and discussion sessions.

Videos and Files

2023-10-30 2023-10-31
  • 09:00 - Hernan G Solari (FCEN-UBA & IFIBA-CONICET, Argentina): TBA Class 3 0f 4
  • 11:00 - Hernan G Solari (FCEN-UBA & IFIBA-CONICET, Argentina): TBA - Class 4 of 4
2023-11-01 2023-11-02 2023-11-03




School on Mathematical Modeling and Governance

Additional Information

BOARDING PASS: All participants, whose travel has been provided or will be reimbursed by ICTP-SAIFR, should bring the boarding pass  upon registration. The return boarding pass (PDF, if online check-in, scan or picture, if physical) should be sent to by e-mail.

COVID-19: Brazilians and foreigners no longer have to present proof of vaccination before entering the country. 

Visa information: Nationals from several countries in Latin America and Europe are exempt from tourist visa. Nationals from Australia, Canada and USA are exempt from tourist visa until January 10, 2024. Please check here which nationals need a tourist visa to enter Brazil.

Accommodation: Participants, whose accommodation will be provided by the institute, will stay at The Universe Flat. Hotel recommendations are available here.

How to reach the Institute: The school will be held at ICTP South American Institute, located at IFT-UNESP, which is across the street from a major bus and subway terminal (Terminal Barra Funda). The address which is closer to the entrance of the IFT-UNESP building is R. Jornalista Aloysio Biondi, 120 – Barra Funda, São Paulo. The easiest way to reach us is by subway or bus, please find instructions here.