Events

The D-equivalence conjecture of Bondal and Orlov predicts that birational Calabi-Yau varieties have equivalent derived categories of coherent sheaves.  I will explain how to prove this conjecture for hyperkahler varieties of K3^[n] type (i.e. those that are deformation equivalent to Hilbert schemes of K3 surfaces).  This is joint work with Junliang Shen, Qizheng Yin, and Ruxuan Zhang.

If the leading principle is that reducing carbon emissions today is more valuable than reducing emissions tomorrow, how should financial carbon discounting work? Starting from carbon budgets that limit global warming to under a specified level with a given probability, a carbon discount bond system is developed that depends on the stochastic carbon emissions and an associated emissions abatement plan. We show that the sooner and more capital is invested to reduce carbon emissions, the better. The proposed financial design and pricing approach also considers the notion of a carbon budget debt and its financial treatment in a tiered carbon discounting system. Hedge portfolios and carbon budget derivatives emerge that mitigate financial losses if emissions exceed a planned/mandated carbon budget. Initial observations point to a multicurve term structure underlying the constructed carbon discount bond system that is linked to the carbon budgets and emissions abatement urgency.

Weil–Petersson volumes are fascinating objects. They are defined as volumes of moduli spaces of oriented hyperbolic surfaces, and they satisfy the so-called Mirzakhani's recursion. The goal of this talk is to discuss a non-orientable analogue of Weil–Petersson volumes as well as their recursive structure. I will show how volumes are defined, compute the volume of hyperbolic Klein bottles, and most importantly, explore a possible relation to other objects in mathematics such as the Virasoro algebra and topological recursion. This talk is based on a joint work with Elba Garcia-Failde and Paolo Gregori.