Francisco Arana-Herrera (Rice University)
Title T.B.A.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Marc Magaña (Universitat Autònoma de Barcelona)
Abstract:
In this talk, we explore the continuity properties of the solution map, in Hölder and Zygmund spaces, to a class of nonlinear transport equations in R^n. The velocity field in these equations is given by the convolution of the density with a kernel that is homogeneous of degree -(n-1) and smooth away from the origin. This setting encompasses significant models, including the 2D Euler equations and the 3D surface quasi-geostrophic (SQG) equations.
14:15 • Universität Basel, Spiegelgasse 5, Seminarraum 05.002
Kathryn Hess Bellwald (EPFL)
Hochschild homology: the universal shadow abstract
Abstract:
Hochschild homology has proved to be an important invariant in algebra and homotopy theory, in particular due to its relevance in algebraic K-theory and fixed point theory, leading to the development of numerous variants of the original construction. Ponto\'s theory of shadows provides a bicategorical axiomatization of Hochschild homology-type invariants, which captures the essential common properties of all known variants of Hochschild homology, such as Morita invariance. In recent work, Nima Rasekh and I clarified the relationship between shadows and Hochschild homology. After extending the notion of Hochschild homology to bicategories in a natural manner, we proved the existence of a universal shadow on any bicategory B, taking values in the Hochschild homology of B, through which all other shadows on B factor. Shadows are thus co-represented by a bicategorical version of Hochschild homology. Using the universal shadow on the free adjunction bicategory, we established a universal Morita invariance theorem, of which all known cases are immediate corollaries. In this talk I will give an overview of my work with Rasekh and provide relevant examples of shadows, including the free loop space construction, then discuss potential generalization and extensions of our results.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Dr. Markus Tempelmayr (EPFL)
Abstract:
Reaction-diffusion equations are ubiquitous in mathematical descriptions of physical phenomena. In this talk, we show how long-range correlated noise in a microscopic model leads to a universal macroscopic behaviour. The macroscopic limit is reminiscent of the dynamical $\\Phi^4$ model, a singular stochastic PDE which is in need of renormalization. We shall see how details of the microscopic reaction term have a non-trivial effect on the coupling constant of the macroscopic limit, and how renormalization of the macroscopic equation has a harmless interpretation on the microscopic counterpart. Time permitting we give an idea of the proof, which is based on a term-by-term expansion (i.e. regularity structures) tailored to the law of the noise.
16:15 • Universität Bern, Hörsaal B78, ExWi, Sidlerstrasse 5, 3012 Bern
Prof. Dr. Luis Vega González (Basque Center for Appl. Math., Spain)
The dynamics of viscous vortex filaments and the Binormal Curvature Flow abstract
Abstract:
I’ll present some recent work about the connection of vortex filaments/tubes that move according to Navier Stokes Equation and the binormal curvature flow of curves in 3d. This is a joint work with Marco A. Fontelos and Mikel Ispizua.
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Dr. Benjamin Bonnefont (Université de Genève)
Fourier dimension of imaginary Gaussian multiplicative chaos abstract
Abstract:
Recent works have established sharp Fourier decay for subcritical real Gaussian multiplicative chaos (GMC) on the circle, and in this talk I will discuss the corresponding harmonic picture for imaginary GMC. Gaussian multiplicative chaos is obtained by exponentiating log-correlated Gaussian fields; on the unit circle, one may take the trace of the two-dimensional Gaussian free field with covariance $\\log 1/|e^{i\\theta}-e^{i\\theta\'}|$. For purely imaginary parameters $\\gamma=i\\beta$ with $\\beta\\in(0,1)$, the resulting object $M_{i\\beta}$ exists as a complex-valued random distribution and enjoys strong integrability properties.The Fourier dimension captures the decay of the Fourier coefficients $c_n$ of a distribution. It is defined as the supremum of $s\\in(0,1)$ such that $|c_n|^2 = O(|n|^{-s})$. We prove that the Fourier dimension of $M_{i\\beta}$ is almost surely $1-\\beta^2$ and establish a joint CLT for the rescaled coefficients.The proof uses the method of moments specific to the imaginary regime. The moments of $c_n$ (and mixed moments of nearby modes) are rewritten as Coulomb-gas integrals on the circle, and then analysed via the Selberg inner product and Jack polynomial expansions, which convert the moment integrals into positive partition sums amenable to sharp asymptotic analysis.Joint work with Hermanni Rajamäki and Vincent Vargas.
17:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H12