Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
In this talk, we consider partial differential equations of parabolic $p$-Laplace type in noncylindrical domains $U = \bigcup_{t \in [0,T]} \{t\} \times \Omega_t$, where the underlying spatial set $\Omega_t \subset \mathbb{R}^n$ may change in time. Our goal is to characterize time-dependent boundary values that yield the existence of a solution, focusing on domains $U$ that satisfy a Lipschitz condition with respect to a parabolic metric. In particular, we discuss the extension to $U$ of certain functions that are only defined on the parabolic boundary of $U$, and conversely the trace space for functions defined on $U$ and contained in a suitable parabolic function space. The talk is based on joint work with Daniel Campbell and Sebastian Schwarzacher.
The goal of this talk is to present the construction of new families of complete Calabi-Yau metrics with maximal volume growth on the small resolutions of the ordinary double point singularity in dimension 3. These metrics have tangent cone $\mathbb{C} ×(\mathbb{C}^2/\mathbb{Z}_2)$ at infinity and are parametrised by their Kähler class. As the Kähler class degenerates, the metrics converge in the pointed Gromov-Hausdorff sense to a singular Calabi-Yau metric with an isolated conical singularity modelled on the Stenzel metric at the ordinary double point, thereby providing a new metric realisation of the Atiyah flop. As we will explain, this construction is meant to provide a local adiabatic model for certain degenerations of compact Calabi-Yau manifolds.
Baxter's classical theorem for orthogonal polynomials on the unit circle establishes that the linear Fourier coefficients of a measure are in $\ell^1$ if and only if the nonlinear coefficients, i.e., the so-called Verblunsky coefficients, are in $\ell^1$. We prove an analog of Baxter's theorem for the SU(2)-valued nonlinear Fourier transform. The proof of Baxter's theorem is qualitative in nature. We explore possible formulations of such quantitative theorems with norm and Lipschitz estimates. In particular, we construct a counterexample for certain such estimates
