Weekly Bulletin

The FIM provides a Newsletter called FIM Weekly Bulletin, which is a selection of the mathematics seminars and lectures taking place at ETH Zurich and at the University of Zurich. It is sent by e-mail every Tuesday during the semester, or can be accessed here on this website at any time.

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FIM Weekly Bulletin

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Monday, 25 March
Time Speaker Title Location
13:15 - 14:15 Vladimir Dotsenko
Université de Strasbourg
Abstract
I shall recall the definition of a wheeled operad (introduced by Merkulov about 15 years ago) and explain how homotopy invariants of wheeled operads appear naturally when computing stable homology of Lie algebras of derivations of free algebras. This a common generalization of the Loday-Quillen-Tsygan theorem on additive K-theory of an associative algebra, and the Fuchs' stability theorem for homology of the Lie algebra of vector fields.
Talks in Mathematical Physics
Lie algebra homology and wheeled operads
HG G 43
15:15 - 16:30 Jean-Philippe Chassé
ETH Zürich
Abstract
There are many natural metrics that one can put on the collection of all exact (closed connected) Lagrangians of a given Liouville manifold: Lagrangian Hofer metric, spectral metric, shadow metric, etc. However, in most instances, the known properties of the ensuing metric space are quite limited, as these spaces tend to be quite unruly. For this reason, I have previously studied the subspace of Lagrangians respecting an appropriate notion of "geometric boundedness"—a much more manageable space as it turns out. In this talk, I will present some new results on the metric properties in this smaller space of geometrically bounded Lagrangians, where all these metrics behave essentially the same. As applications, we will get some yet-unknown topological properties of the space of all exact Lagrangians of a Liouville manifold.
Symplectic Geometry Seminar
The metric geometry of geometrically bounded Lagrangians
HG G 43
Tuesday, 26 March
Time Speaker Title Location
15:15 - 16:15 Prof. Dr. Anuj Kumar
UC Berkeley
Abstract
We construct nonunique solutions of the transport equation in the class $L^\infty$ in time and $L^r$ in space for divergence free Sobolev vector fields $W^{1, p}$. We achieve this by introducing two novel ideas: (1) In the construction, we interweave the scaled copies of the vector field itself. (2) Asynchronous translation of cubes, which makes the construction heterogeneous in space. These new ideas allow us to prove nonuniqueness in the range of exponents beyond what is available using the method of convex integration and sharply matchwith the range of uniqueness of solutions from Bruè, Colombo, De Lellis ’21.
Analysis Seminar
Nonunique solutions of the transport equation for Sobolev vector fields
HG G 43
16:30 - 18:15 Isabelle Gallagher

Abstract
Abstract: The evolution of a gas can be described by different models depending on the scale of observation. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. On the one hand Lanford showed in 1974 that the Boltzmann equation appears as a law of large numbers in the low density limit of a gas of hard spheres, at least for very short times. On the other hand, fluid mechanics equations such as the Navier-Stokes equations can be derived from the Boltzmann equation in the limit of when the mean free path tends to zero. Reconciling both approaches in order to derive fluid mechanics equations from Newton's laws for the system of particles is to this day an open question. In this talk we shall explain these different limiting procedures, their difficulties and some recent advances in Hilbert's program.
Zurich Colloquium in Mathematics
On the dynamics of dilute gases
KO2 F 150
Wednesday, 27 March
Time Speaker Title Location
13:30 - 14:30 Pedram Safaee
Universität Zürich
Abstract
We will introduce the concept of twisted Birkhoff sum and the twisted Cocycle. We give some motivations for studying this Cocycle and discuss the positivity of the top Lyapunov exponent. This is based on joint work with Hesam Rajabzadeh.
Ergodic theory and dynamical systems seminar
Nondegeneracy of the spectrum of the twisted Cocycle for interval exchange transformations
HG G 19.1
Thursday, 28 March
Time Speaker Title Location
10:15 - 12:00 Umut Çetin
London School of Economics
Abstract
Nachdiplomvorlesung
Mathematics of Market Microstructure
HG G 43
16:15 - 18:00 Prof. Dr. Marcin Napiórkowski
University of Warsaw
Abstract
According to the Bogoliubov theory, the low energy behaviour of the Bose gas at zero temperature can be described by non-interacting bosonic quasiparticles called phonons. In my talk I will explain how the damping rate of phonons at low momenta, the so-called Beliaev damping, can be computed with simple arguments involving an effective Friedrichs model for phonons.
PDE and Mathematical Physics
Beliaev damping in Bose gas
Y27 H 46
Friday, 29 March
— no events scheduled today —
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