# Mathematics

## Diffusion Models for Systemic Risk 2

We will present inter-bank borrowing and lending models based on systems of coupled diffusions. First-passage models will be reviewed and applied to mean-field type models in order to illustrate systemic events and compute their probability via large deviation theory. Then, a game feature will be introduced and Nash equilibria will be derived or approximated using the Mean Field Game approach.

## Khovanov homology

Lecture notes on Khovanov homology.

## Contingent Capital and Financial Networks 1

These lectures will cover two topics. The first is contingent capital in the form of debt that converts to equity when a bank

nears financial distress. These instruments offer a potential solution to the problem of banks that are too big to fail by

providing a credible alternative to a government bail-out. Their properties are, however, complex. I will discuss models for the analysis of contingent capital with particular emphasis on their incentive effects and the design of the conversion trigger. The second topic in these lectures is the problem of quantifying contagion and amplification in financial networks. In particular, I will focus on bounding the potential impact of network effects under the realistic condition that detailed information on the structure of the network is unavailable

## Diffusion Models for Systemic Risk 1

We will present inter-bank borrowing and lending models based on systems of coupled diffusions. First-passage models will

be reviewed and applied to mean-field type models in order to illustrate systemic events and compute their probability via

large deviation theory. Then, a game feature will be introduced and Nash equilibria will be derived or approximated using the

Mean Field Game approach.

## Over the Counter Markets

This lecture is part of a series on "*Risk Sharing in Over-the-Counter Markets"*

## Financial System Architecture

These lecture notes are part of a series on "*Risk Sharing in Over-the-Counter Markets"*

## 2014 West Coast Algebraic Topology Summer School

## PIMS-SFU Undergraduate Summer School on Multiple Zeta Values

Featured lecturer: Mike Hoffman

## Duality Notes

These are notes for the Duality talk presented as part of the West Coast Algebraic Toplogy Summer School.

## Verlinde Algebra

Lecture Notes on Verlinde Algebra