### Fall 2018 Samuel Eilenberg Lectures

*Geometric aspects of p-adic Hodge theory*

**ABSTRACT**

“Building up in a leisurely fashion, we will describe some recent advances in our understanding of the cohomology of algebraic varieties over p-adic fields, especially the integral cohomology. The main goal of the course is to define prismatic cohomology and explain how it unifies the various cohomology theories of interest in p-adic geometry. “

*Samuel Eilenberg Lecture Flyer*

### Fall 2018 Minerva Lectures

Come join us on **Mondays at 1:10 pm in RM 507.** Starting **Monday,** **September 10, 2018** Professor **Walter Schachermayer** (University of Vienna), will be giving a special lecture about **Asymptotic Theory of Transaction Costs**.

**Professor Walter Schachermayer **(University of Vienna)

**TITLE**

**Asymptotic Theory of Transaction Costs**

“One of the great features of traditional asset pricing theory is the assumption that there are no market frictions. In particular, one assumes that there is no bid-ask spread, so that no transaction costs have to be considered. This bold simplification of the real world situation was crucial to clarify the picture.

In a second step, however, it becomes important to carefully analyze the impact of transaction costs on the optimal behaviour of economic agents. Special emphasis will be given to asymptotic results, i.e., the limiting behaiviour when transaction costs tend to zero.

In the first half of the series of lectures we shall develop the basics of this theory and subsequently apply these results to a study of the classical Black-Scholes model.

In the second half we shall focus on applications which lead beyond the usual semi-martingale framework. A typical example will be a price process driven by fractional Brownian motion. This setting does not fit into the usual no arbitrage framework as these processes fail to be semi-martingales. The consideration of (small) proportional transaction costs allows us to find shadow price processes attached to these models, which allows to apply the well developed martingale theory also to these models.”

**Time & Location**

**Mondays** at **1:10 pm – 2:25 pm**

Mathematics Hall, Room **507**