More Than One Step to Financial Stability

Visiting Scholar Garry Schinasi examines the European proposals for the creation of both a European Systemic Risk Board (ESRB) to oversee macroprudential regulation and a European System of Financial Supervision (ESFS) to strengthen microprudential supervision. He argues that structural vulnerabilities of this regulatory framework need to be addressed to ensure that the early-warning systems will be adequate to avoid future crises. Specifically, Schinasi points to the fact that the ESRB lacks binding powers to enforce regulation as well as the lack of a legislative framework to resolve the insolvency of systemically important financial institutions (SIFIs).

GIT semistability of Hilbert points of Milnor algebras

Our first result is that a homogeneous form $F$ in $n$ variables is GIT semistable with respect to the natural $SL(n)$-action if and only if the first non-trivial Hilbert point of the associated Milnor algebra is semistable. We also prove that the induced morphism on the GIT quotients is finite, and injective on the locus of stable forms. Our second result is that the associated form of $F$, also known as the Macaulay inverse system of the Milnor algebra of $F$, and which is apolar to the last non-trivial Hilbert point of the Milnor algebra, is GIT semistable whenever $F$ is a smooth form. These two results answer questions of Alper and Isaev from arXiv:1407.6838.Comment: 19 pages, to appear in Math. An

Stability for Borell-Brascamp-Lieb inequalities

We study stability issues for the so-called Borell-Brascamp-Lieb inequalities, proving that when near equality is realized, the involved functions must be $L^1$-close to be $p$-concave and to coincide up to homotheties of their graphs.Comment: to appear in GAFA Seminar Note