Eugenia Malinnikova (Stanford University)
Carleman estimates, unique continuation, and Landis conjecture
13:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Vladimir Dotsenko (University of Strasbourg)
Higher-dimensional Givental symmetries abstract
Abstract:
Some 20 years ago, Chen, Gibney and Krashen introduced beautiful algebraic varieties parametrizing "pointed trees of projective spaces"; these varieties generalize the celebrated Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points. In the latter case, the homology operad encodes the tree level part of a cohomological field theory. It follows from the work of Givental and many others that the space of all such structures on a given graded vector space has a very rich symmetry group; this fact has been used in many different research areas. In this talk, I shall prove that the homology of the operad made of Chen-Gibney-Krashen spaces possesses many interesting properties, and in particular, there are higher-dimensional Givental symmetries that emerge in this story. Curiously enough, this leads to new results on classical Givental symmetries as well. This is joint work with Eduardo Hoefel, Sergey Shadrin and Grigory Solomadin.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Bruno Vallette (Université Sorbonne Paris Nord)
Operadic Calculus for Higher Colour-Kinematics Duality abstract
Abstract:
This talk aims at providing gauge field theory, in particular colour–kinematics duality and the double copy construction, with the required higher algebraic structures. From the algebro-homotopical perspective, a classical field theory is encoded by a cyclic homotopy Lie algebra whose Maurer–Cartan functional defines the action. For many gauge theories of interest, including Chern–Simons and Yang–Mills, this algebra splits as a tensor product of a cyclic Lie algebra, the colour Lie algebra, and a cyclic homotopy-commutative algebra, the kinematic algebra.The duality between colour and kinematics, first observed by Bern–Carrasco–Johansson in the study of Yang–Mills amplitudes, suggests that the kinematic algebra carries a Lie-type structure. For theories with at most cubic interactions, this structure is captured by coexact Batalin-Vilkovisky (BV) algebras, algebraic objects dual to the exact BV algebras arising in Poisson geometry. To incorporate higher-order interactions, following ideas of M. Reiterer, a homotopy refinement of this notion becomes necessary.The purpose of this talk is to provide a conceptual definition of homotopy coexact BV algebras, expressed in relation to homotopy commutative and BV algebras, together with a concrete operadic model. Our framework gives explicit presentations in terms of generating operations and relations and enables the systematic application of homotopical methods—including homotopy transfer, rectification, infinity-morphisms, and deformation theory—to the resulting algebras. The quartic-level structures recently identified in Yang–Mills theory fits naturally into this framework. This is a joint work with Anibal Medina-Mardones.
14:45 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Prof. Dr. Maria Colombo (EPFL)
Abstract:
In the last 20 years, there have been remarkable progress in understanding non-uniqueness of solutions to the fundamental partial differential equations of incompressible fluid dynamics, namely, the Euler and Navier-Stokes equations. They stem from different viewpoints: just to mention a few, they include convex integration, instability in self-similar variables, numerical evidences. The talk will provide an overview of these developments, focussing on results about the 2 dimensional Euler equations. It will also highlight new results showing that solutions obtained in the vanishing viscosity limit from the (well-posed) Navier-Stokes equations can be nonunique.
17:15 • Universität Bern, Sidlerstrasse 5, 3012 Bern, Room B6