Seminários, para a disseminação informal de resultados de investigação, trabalho exploratório de equipas de investigação, actividades de difusão, etc., constituem a forma mais simples de encontros num centro de investigação de matemática.
O CAMGSD regista e publica o calendário dos seus seminários há bastante tempo, servindo páginas como esta não só como um método de anúncio dessas actividades mas também como um registo histórico.
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
