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This thesis studies coevolutionary games on adaptive networks in which agents are equipped with bounded memory and the ability to rewire. We examine the emergence of cooperation, the evolution of network topology, and the reward disparities that arise across the different experimental scenarios. We depart from the classical well-mixed and memoryless populations used in Classical Game Theory by considering finite populations of heterogeneous agents whose behavior depends on their randomly assigned strategy type. The model is implemented as an agent-based simulation on three representative network topologies: Watts–Strogatz, Barabási–Albert, and Erdős–Rényi. Across all scenarios, the results consistently show that network adaptivity and rewiring promote cooperation and increase the rewards of cooperative agents relative to those who tend to defect, primarily by facilitating the formation of cooperative clusters. The findings highlight the joint importance of memory and adaptive network structure in sustaining cooperation and suggest extensions for future research, including heterogeneous memory capacities and endogenous strategy change.

In this talk I will present a purely variational approach to the regularity theory of optimal transportation introduced by Goldman and Otto. The approach closely follows De Giorgi's strategy for the regularity theory of minimal surfaces: at its core lies a Campanato iteration, which allows one to transfer the scaling law of the local transport energy to small scales. In regularity theory, this typically leads to Schauder estimates; but the same idea can also be used to study the local energy scaling of minimizers of non-convex variational problems related to branching phenomena in strongly uniaxial ferromagnets and type-I superconductors in the intermediate state. I will highlight this connection and give a brief overview of further recent developments and point out some other interesting applications. ______________________________ Invited by Prof. Phan Thành Nam

TBA

Quantum Geometry Speaker: Murad Alim (TUM) Abstract: Quantum theory has not only reshaped our understanding of the physical world; it has also become a powerful source of ideas for modern mathematics. In this talk, I will introduce aspects of the emerging field of quantum geometry, where insights from quantum field theory and string theory interact with symplectic, complex, and algebraic geometry. I will explain how dualities in physical theories often reveal that seemingly different mathematical structures share common underlying principles, leading to deep new results and unexpected bridges between diverse areas. A central example is mirror symmetry, a duality relating symplectic and complex geometry with far-reaching consequences for enumerative geometry, representation theory and number theory.