Join us at the inauguration event! - POSTPONED

Our three main speakers

Dylan Possamai - When incentives meet stochastic calculus:  designing contracts in hidden‑action worlds

How can you reward effort you never see? From the wage packet of a single employee to the tariff offered to a million electricity consumers, the central puzzle of contract theory is to align pay‑offs with actions that are private, noisy, or both. My research shows that this economic puzzle has a natural home in modern probability: the right language is that of stochastic control and backward stochastic differential equations (BSDEs). Once the problem is rewritten in this language, many familiar dead‑ends in incentive design suddenly open up.
The story begins with the classical one‑agent "moral‑hazard'' model. By coding the agent's promised utility as the solution of a second‑order BSDE, we proved that the principal's seemingly intractable optimisation collapses to a single Hamilton–Jacobi–Bellman equation; every admissible contract can therefore be reached by standard dynamic‑programming tools  .
Real organisations, however, are run by teams. Extending the framework to agents who jostle for relative status, we characterised the Nash equilibrium of their effort game with a system of BSDEs and showed that the optimal pay scheme, though still linear, tilts risky projects towards the least rivalry‑averse workers—a mathematical explanation of why diverse teams outperform homogeneous ones .
Scaling further, we let the "team'' become a continuum. In electricity markets, for instance, a producer cannot observe how each household lowers its peak demand. A mean‑field version of the model delivers an explicit two‑tier tariff that rewards consumers for cutting both their average use and its volatility, outperforming classical rebates in numerical experiments  .
Two recent twists push the probabilistic narrative even deeper. First, when agents are time‑inconsistent but sophisticated—they know they will procrastinate—the principal's problem becomes a Volterra control with infinitely many constraints; yet the BSDE machinery still yields qualitative and sometimes closed‑form solutions. Second, allowing agents to randomise their effort compactifies the control set, restoring existence theorems without delicate PDE regularity .
Across these settings—single worker, competing team, vast population, self‑control issues, and randomised actions—the same take‑home message emerges: by translating incentives into stochastic calculus, we gain both rigorous mathematics and contracts that regulators, employers, and energy providers can actually implement.

David Loeffler - Can computers help mathematicians to prove theorems?

I will give a short introduction to 'proof assistants' (such as Lean, Isabelle, and Rocq), which are software packages which can follow the logic of mathematical arguments and check their correctness; and how these are playing a role in contemporary mathematical research – firstly by guaranteeing that proofs found by human brain-power are free of gaps or mistakes, and more ambitiously, as a step towards computers discovering new proofs for themselves.

Sarah Zerbes - Introduction on Fermat's Last Theorem

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