L1

We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropical geometry).

Abstract: The valuation of a finite resource, be it acopper mine, timber forest or gas field, has received surprisingly littleattention from the academic literature. The fact that a robust, defensible andaccurate valuation methodology has not been derived is due to a mixture ofdifficulty in modelling the numerous stochastic uncertainties involved and thecomplications with capturing real day-to-day mining operations. The goal ofproducing such valuations is not just for accounting reasons, but also so thatoptimal extraction regimes and procedures can be devised in advance for use atthe coal-face. This paper shows how one can begin to bring all these aspectstogether using contingent claims financial analysis, geology, engineering,computer science and applied mathematics.

The viability of a market impact model is usually considered to be equivalent to the absence of price manipulation strategies in the sense of Huberman & Stanzl (2004). By analyzing a model with linear instantaneous, transient, and permanent impact components, we discover a new class of irregularities, which we call transaction-triggered price manipulation strategies. Transaction-triggered price manipulation is closely related to the non-existence of measure-valued solutions to a Fredholm integral equation of the first kind. We prove that price impact must decay as a convex decreasing function of time to exclude these market irregularities along with standard price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest. Joint work with Aurélien Alfonsi, Jim Gatheral, and Alla Slynko.

I'll define the category of B-branes in a LG model, and show that for affine models the Hochschild homology of this category is equal to the physically-predicted closed state space. I'll also explain why this is a step towards proving that LG B-models define TCFTs.