17.12.2025 16:30 Tobias Ried (Georgia Tech): From optimal transport to branched microstructures: a journey through elliptic regularity theory
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.
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Invited by Prof. Phan Thành Nam
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22.12.2025 16:30 Chiara Sabina Bariletto: TBA
TBA
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07.01.2026 14:30 Antrittsvorlesungen: Violetta Weger (TUM) und Murad Alim (TUM): Fakultätskolloquium
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.
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