15.12.2025 15:00 Néstor Jara: Dichotomies respect to growth rates and their spectra
Since the works of M. Pinto [2], it has been studied that nonautonomous dynamics
can present different behaviors other than exponential, as polynomial, superexponential,
among others. More recently, C. Silva [4] presented a formalism to expand some classic
results [3] regarding the spectral structure that an equation can present when studied
under the lenses of a given growth rate.
In this talk, based on [1], we investigate the properties of the dichotomy spectrum of
nonautonomous linear systems under general growth behaviors. By introducing compar-
ison criteria we clarify how generalized dichotomies and bounded growth interact. We
also study the evolution of the dichotomy spectrum under these comparisons, revealing
that faster growth rates compress the spectrum, while slower growth rates expand it.
Joint work with:
Claudio A. Gallegos
References
[1] Gallegos, C. A.; Jara, N. The interplay of μ-dichotomy, bounded growth, and spectral
properties via growth rate comparisons (2025). arXiv:2507.21940.
[2] Naulin, R.; Pinto, M. Dichotomies and asymptotic solutions of nonlinear differential systems.
Nonlinear Anal. Theory Methods Appl. 23 (1994), No. 7, 871–882.
[3] Siegmund, S. Dichotomy spectrum for nonautonomous differential equations. J. Dynam. Dif-
ferential Equations 14 (2002), 243–258.
[4] Silva, C. M. Nonuniform μ-dichotomy spectrum and kinematic similarity. J. Differential Equa-
tions, 375, 618-652 (2023).
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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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