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## A minimaxmax problem for improving the torsional stability of rectangular plates Gazzola, Filippo | CIRM H

Multi angle

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Research talks

We introduce a new function which measures the torsional instability of a partially hinged rectangular plate. By exploiting it, we compare the torsional performances of different plates reinforced with stiffening trusses. This naturally leads to a shape optimization problem which can be set up through a minimaxmax procedure.

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| CIRM H

Multi angle

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Research talks

We will analyze consequences of various types of Prikry forcing on combinatorial properties at singular cardinals and their successors, focusing on weak square and simultaneous stationary reflection. The motivation is how much compactness type properties can be obtained at successors of singulars, and especially the combinatorics at $\aleph_{\omega+1}$.

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## Reconstruction by optimal transport: applications in cosmology and finance Loeper, Grégoire | CIRM H

Multi angle

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Research talks

Following the seminal work by Benamou and Brenier on the time continuous formulation of the optimal transport problem, we show how optimal transport techniques can be used in various areas, ranging from "the reconstruction problem" cosmology to a problem of volatility calibration in finance.

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## Viability and arbitrage under Knightian uncertainty Burzoni, Matteo | CIRM H

Multi angle

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Research talks

We provide a general framework to study viability and arbitrage in models for financial markets. Viability is intended as the existence of a preference relation with the following properties: It is consistent with a set of preferences representing all the plausible agents trading in the market; An agent with such a preference is in equilibrium, namely, he or she prefers to stay at the initial endowment respect to trade. We extend the original framework of Kreps ('79) and Harrison-Kreps ('79) to accommodate for Knightian Uncertainty: preferences of plausible agents are not necessarily determined by a single probability measure. The relations between arbitrage, viability, and existence of (non-)linear pricing rules are investigated.
This is a joint work with Frank Riedel and Mete Soner.
We provide a general framework to study viability and arbitrage in models for financial markets. Viability is intended as the existence of a preference relation with the following properties: It is consistent with a set of preferences representing all the plausible agents trading in the market; An agent with such a preference is in equilibrium, namely, he or she prefers to stay at the initial endowment respect to trade. We extend the original ...

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## Quantum spin systems and phase transitions. Part 4 Ueltschi, Daniel | CIRM H

Multi angle

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Research talks

These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that allows to prove the existence of phase transitions. Finally, we will discuss certain probabilistic representations and their consequences. These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that ...

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## Market delay and $G$-expectations Dolinsky, Yan | CIRM H

Multi angle

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Research talks

We study duality and asymptotic of super-replication with market delay. Our main result is the link between scaling limits of delayed markets and the $G$-expectation of Peng.