Twistor spinors with zero on Lorentzian 5-space

We present in this paper a $C^1$-metric on an open neighbourhood of the origin in \RR^{5}. The metric is of Lorentzian signature $(1,4)$ and admits a solution to the twistor equation for spinors with a unique isolated zero at the origin. The metric is not conformally flat in any neighbourhood of the origin. The construction is based on the Eguchi-Hanson metric with parallel spinors on Riemannian 4-space.Comment: 17 page

An algebraic approach to minimal models in CFTs

CFTs are naturally defined on Riemann surfaces. The rational ones can be solved using methods from algebraic geometry. One particular feature is the covariance of the partition function under the mapping class group. In genus $g=1$, this yields modular forms, which can be linked to ordinary differential equations of hypergeometric type with algebraic solutions.Comment: 30 pages. Revised and extended version. (The paper was originally part of arXiv:1305.0469, which had been split into the present paper and arXiv:1705.07627.

About Twistor Spinors with Zero in Lorentzian Geometry

We describe the local conformal geometry of a Lorentzian spin manifold $(M,g)$ admitting a twistor spinor $\phi$ with zero. Moreover, we describe the shape of the zero set of $\phi$. If $\phi$ has isolated zeros then the metric $g$ is locally conformally equivalent to a static monopole. In the other case the zero set consists of null geodesic(s) and $g$ is locally conformally equivalent to a Brinkmann metric. Our arguments utilise tractor calculus in an essential way. The Dirac current of $\phi$, which is a conformal Killing vector field, plays an important role for our discussion as well

Using collateral to secure loans

In “Using Collateral to Secure Loans,” Yaron Leitner asks: Why is collateral used to secure some loans, but not others? And why does collateral potentially involve more risk? He considers these questions, looking at some of the explanations for using collateral, focusing on its benefits and drawbacks.Loans

Liquidity and exchanges, or contracting with the producers

Yaron Leitner discusses liquidity, a desirable feature of a well-functioning market. In "Liquidity and Exchanges, or Contracting with the Producers," Leitner explains how exchanges can provide liquidity. He also discusses his recent research, which explains some contractual problems that may arise in very liquid markets, as well as the potential role of an exchange in overcoming these problems.Liquidity (Economics)