Tullio Ceccherini-Silberstein (Università di Beneveto)
A Garden of Eden Theorem for Smale Spaces abstract
Abstract:
Smale spaces were introduced in the late 1970s by David Ruelle in his influential monograph on thermodynamic formalism.These dynamical systems include: Anosov diffeomorphisms, non-wandering sets of Smale\'s Axiom A diffeomorphisms, various types of solenoids and attractors, as well as (in a symbolic dynamical setting) subshifts of finite type.In a recent joint work with Michel Coornaert, we proved, among other things, a Garden of Eden type theorem (GOET) for irreducible Smale spaces. This generalizes previous results by Fiorenzi (GOET for irreducible subshisfts of finite type) and ours (GOET for Anosov diffeomorphisms on tori).
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Luan Jahija (Université de Genève)
Impacts of thermal pressurization during earthquakes based on a numerical analysis abstract
Abstract:
Earthquakes are among the most powerful and destructive natural phenomena, driven by complex interactions along Earth’s tectonic faults.We investigate the physical mechanisms that govern earthquake dynamics, with a particular focus on the role of thermal pressurization in fault zones. When two tectonic plates slide against each other, the extreme conditions of friction and temperature alter the pressure of fluids trapped within the rock, directly influencing fault stability and rupture propagation.Using numerical modelling, we developed and analysed equations describing these complex processes. We began with simplified friction models based on Amonton–Coulomb’s law and then introduced more realistic rate-and-state friction laws. The models were progressively extended to incorporate the effects of thermal diffusion, pore fluid pressure, and chemical reactions within rocks.The simulations highlight how different physical parameters such as thermal diffusivity or fluid generation affect the transition between stable (creeping) and unstable (seismic rupture) behaviour. This work contributes to a better understanding of the conditions that favour earthquake initiation and amplification, bridging the gap between simple theoretical models and observed geophysical processes.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Prof. Dr. Yannick Sire (Johns Hopkins University)
Regularity vs singularity formation for harmonic map heat flows with free boundaries abstract
Abstract:
I will report on recent results on geometric flows associated to harmonic mappings with free boundary.Those maps are instrumental in several geometric problems, such as extremal metrics for the Steklov spectrum for instance and one can formulate several possible parabolic equations whose stationnary solutions are such maps.I will describe these formulations, each of which offering interesting applications and analytic problems. In various cases, one can derive partial regularity results for weak solutions and describe the structure of the singular set. I will try to give an overview of such results. However, a formulation, related to the Plateau flow, poses more challenging issues and I will formulate some conjectures about its singularity formation. The construction of solutions blowing up in finite or infinite time uses a new gluing technique, which has been successfully used recently to investigate singularity formations in other flows, such as Fast Diffusion equations or Yang-Mills heat flow.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Andre Laestadius
Smoothing the Landscape: Moreau-Yosida Regularization in Modern Density-Functional Theory abstract
Abstract:
In the standard convex‑analytic formulation of density‑functional theory the universal functional is non‑smooth, complicating the connection to a practical scheme. We apply Moreau–Yosida regularisation that adds a quadratic penalty term to obtain smooth approximants of the functional whose derivatives are Lipschitz‑continuous and converge to the exact functional as the regularisation parameter goes to zero. This regularity enables a framework for inversion to obtain the Kohn‑Sham "effective" potential utilizing the proximal map that is a crucial ingredient of Moreau–Yosida regularisation. This can also be done in practice using a plane‑wave basis.References:Herbst, M.F., Bakkestuen, V.H. and Laestadius, A., 2025. Kohn-Sham inversion with mathematical guarantees. Physical Review B, 111(20), p.205143. Penz, M. and Laestadius, A., 2026. Adaptation of Moreau–Yosida regularization to the modulus of convexity. Journal of Mathematical Analysis and Applications, 554(2), p.129956
16:15 • EPF Lausanne, CM 1 517
Ibrahim Trifa (ETH)
What is... the Lagrangian Hofer norm? abstract
Abstract:
<p><span style="color: black; font-size: 12pt; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif;" data-olk-copy-source="MessageBody">Given a Lagrangian inside a symplectic manifold, one can define a metric, called the Hofer distance, on the space of Hamiltonian isotopies of this Lagrangian. It is known to be bounded in the case of a circle inside the plane, while it is unbounded for a diameter inside the disc (Khanevsky, 2009), or the standard Lagrangian inside the Euclidean ball of even dimension (Seyfaddini, 2013). The question remains open in most cases, such as the equator inside the sphere or a circle inside the disc. In this talk, I will show the unboundedness of this distance for a disjoint union of circles inside the disc. This result relies on a theorem of Morabito, together with a standard argument of Khanevsky.</span></p>
16:30 • UZH Zentrum, Building KO2, Room F 150