### Fall 2018 Joseph Fels Ritt Lectures

The Fall 2018 Ritt Lectures, by **Professor Eugenia Malinnikova**, will take place on **Wednesday, November 14, 2018**** between 4:30 – 5:30pm in Rm 520 and Thursday, November 15, 2018 between 5:30 – 6:30pm in Rm 417**. Professor **Eugenia Malinnikova** (Norwegian University of Science and Technology), will deliver a two talk series titled:

*An improvement of Liouville’s theorem for discrete harmonic functions*

**ABSTRACT**

“The classical Liouville theorem says that if a harmonic function on the plane is bounded then it is a constant. At the same time for any angle on the plane, there exist non-constant harmonic functions that are bounded everywhere outside the angle. The situation is different for discrete harmonic functions on the standard square lattices. The following strong version of the Liouville theorem holds on the two-dimensional lattice. If a discrete harmonic function is bounded on 99% of the lattice then it is constant. Simple counter-example shows that in higher dimensions such improvement is no longer true.

We will present some discrete methods, compare the behavior of continuous and discrete harmonic functions and discuss some related questions and motivation.

The lectures are based on a joint work with L. Buhovsky, A. Logunov and M. Sodin.”

Tea will be served at 4 pm in 508 Mathematics.

*Joseph Fels Ritt Lecture Flyer*

### 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**