Sylvain Crovisier (Université Paris-Saclay)
Ergodic theory of surface diffeomorphisms
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Gianluca Somma (Università di Padova)
Abstract:
Abstract Transport equations describe the evolution of quantities conserved along a velocity field and play a central role in Analysis and Mathematical Physics. In the Euclidean setting, DiPerna-Lions (1989) proved existence and uniqueness of solutions for velocity fields with Sobolev regularity. In this talk, I will discuss the extension of this theory to the non-Euclidean setting of Heisenberg groups, where the natural assumption is horizontal Sobolev regularity. In particular, I will present a recent result on existence and uniqueness of solutions to transport equations associated with the class of contact velocity fields. This is joint work with L. Ambrosio, S. Verzellesi and D. Vittone.
12:15 • Universität Basel, Seminarraum 05.001, Spiegelgasse 5
Beomjun Sohn (Universität Aachen)
Hofer-Zehnder capacity of disk tangent bundles of triaxial ellipsoids, I abstract
Abstract:
Symplectic capacities are invariants in symplectic geometry that provide a notion of size and are monotone under symplectic embeddings. One important example is the Hofer–Zehnder capacity, defined in terms of Hamiltonians compactly supported on the given symplectic manifold. In the first talk, we discuss methods for proving the finiteness of this capacity and some of its applications to Hamiltonian dynamics. In particular, we focus on cotangent bundles, where the almost existence theorem is still open in general, but is implied by the finiteness of the Hofer–Zehnder capacity.
12:30 • Université de Neuchâtel, Rue Emile-Argand 11, Room B217
Anne Moreau
Double Poisson vertex algebras from jet algebras and quivers abstract
Abstract:
Double Poisson vertex algebras can be viewed as vertex-algebraic analogues of double Poisson algebras. In this talk, I will explain how to construct such structures using the jet algebra construction. This construction naturally leads to Poisson vertex algebras on representation spaces of double Poisson (vertex) algebras. Using related procedures such as Poisson reductions and Hamiltonian reductions, we obtain a variety of interesting examples of double Poisson vertex algebras, in particular those arising from double quivers. I will also discuss motivations coming from vertex algebras. This is based on joint works with Tristan Bozec and Maxime Fairon.
14:15 • EPF Lausanne, CM 1 517
Lukas Lewark (ETH Zürich)
Concordance, Rasmussen invariants, Satellites and Twisting abstract
Abstract:
A knot in the 3-sphere is slice if it bounds a smooth disk in the 4-ball. Knots modulo slice knots form an abelian group called the concordance group. We will explore what can be said about this group by mixing the following three ingredients: Rasmussen invariants (which come from Khovanov homology); satellite knots (which are the result of knotting a solid torus that itself contains a knot); and twisting (which means to put a full twist into a bunch of strands of a knot). This talk will feature joint work with Claudius Zibrowius, and joint work in progress with Chiara Donatone, Marc Kegel, and Paula Truöl.
14:15 • Université de Genève, Conseil Général 7-9, 1-15
Björn Bornkamp (Novartis)
A Structured Workflow to Assess Treatment Effect Heterogeneity in Drug Development abstract
Abstract:
Understanding whether a treatment works differently across patient subgroups is a central question in drug development. However, answering it reliably is notoriously difficult. Clinical trials are typically powered for overall treatment effects, leaving subgroup analyses underpowered and vulnerable to both false positives and false negatives, as illustrated by multiple real cases where subgroup findings couldn\'t be confirmed in follow-up trials. Despite these severe limitations however questions around treatment effect heterogeneity are of great interest to sponsors, regulators, and clinicians alike and need to be addressed in drug development.In this talk, I will present WATCH (Workflow to Assess Treatment EffeCt Heterogeneity) for exploratory assessment of TEH in randomized clinical trials. The challenges resulting from insufficient data-based information on the question of interest (TEH) are approached via (i) providing a structured and pre-planned analysis approach for this exploratory question, providing more standardization and reducing analyst degrees of freedom, (ii) documenting a-priori, external evidence on potential effect modifiers upfront and as part of the workflow and (iii) utilizing flexible, multivariate analysis methods based on statistical learning methods. I will present the workflow steps, and discuss current analysis methods used to implement the workflow, as well as open methodological questions.
16:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Prof. Dr. Georgios Moschidis (EPFL)
Naked singularities with finite blue-shift for the Einstein--massless Vlasov system abstract
Abstract:
<div class="elementToProof"> <p class="elementToProof">In his celebrated proof of the weak cosmic censorship conjecture for the spherically symmetric Einstein-scalar field system, Christodoulou exploited the following property of that specific matter model: Naked singularities, when they arise, exhibit infinite blue-shift along the null geodesics terminating at the singularity. This behaviour is consistent with self-similarity: Even for more general spherically symmetric matter models, it can be shown that self-similar naked singularities must exhibit infinite blue-shift. Whether, for these more general models, all naked singularities have the infinite blue shift property (and hence are potentially subject to an instability mechanism analogous to that introduced by Christodoulou) still remains an open question.</p> </div> <div class="elementToProof"> <p class="elementToProof"> </p> </div> <div class="elementToProof"> <p class="elementToProof">In this talk, we will present the construction of a spherically symmetric solution to the Einstein-massless Vlasov system which contains a locally naked singularity with finite total blue-shift along its past null cone. The initial data giving rise to this solution have limited differentiability, but belong to a regularity class above the scale invariant threshold.</p> </div>
16:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 35/36
Prof. Dr. Christoph Czichowsky (LSE)
No-Arbitrage, Superreplication and Utility Maximisation in Propagator Price Impact Models abstract
Abstract:
We develop a comprehensive mathematical finance framework for propagator models with transient linear price impact. These models lead to infinite-dimensional, non-Markovian control problems and fall outside the scope of classical arbitrage and duality theory. We establish a fundamental theorem of asset pricing, a superreplication theorem with liquidity-adjusted risk measures, and a full convex-duality approach to utility maximisation. Despite the non-linearity of preferences and the path-dependent impact structure, we show that optimal strategies can be obtained from an equivalent frictionless optimisation problem under a suitably constructed shadow price.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43