## Colloquium - Will Rushworth, Erin Caulfield, Weijie Pang - Postdoc Threads

- Calendar
- Mathematics & Statistics

- Date
- 01.10.2020 3:30 pm - 4:30 pm

### Description

Title: Postdoc Threads

**Speaker 1: Will Rushworth (McMaster University)**

Title: Concordance of links in 3-manifolds

Abstract: A knot is an embedding of a circle in the 3-sphere. Abstractly, this circle the boundary of a disc. A natural question is therefore: can the embedding of the circle be extended to an embedding of a disc?

In 3 dimensions the answer is 'no'. However, if one allows an extra dimension of freedom a rich and fascinating theory develops: the theory of link concordance. We shall sketch some aspects of this theory, especially those that appear when one looks at links in 3-dimensional spaces other than the 3-sphere.

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**Speaker 2: Erin Caulfield (McMaster University)**

Title: Classifying expansions of the real ﬁeld by complex subgroups

Abstract: We are interested in classifying expansions of the real ﬁeld by ﬁnitely generated multiplicative subgroups of the complex numbers. In particular, we would like to classify these expansions by the structure of their deﬁnable sets. In this talk, we will discuss our progress towards obtaining such a classiﬁcation.

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**Speaker 3: Weijie Pang (McMaster University)**

Title: Derivatives Valuation under Market Illiquidity

Abstract: Before the 2008 financial crisis, most research in financial mathematics focused on pricing derivatives without considering the effects of counter parties' default, illiquidity problems, and the role of the repurchase agreement (Repo) market. In this article, we include a possible crisis by using an alternating renewal process to describe the switching between a normal financial regime and a financial crisis. We develop a framework for pricing a European claim in this state-dependent framework. The price is characterized as a solution to a backward stochastic differential equation (BSDE), and we prove the existence and uniqueness of this solution. In a numerical study based on a deep learning algorithm for BSDEs, we compare the effect of different parameters on the valuation of it.

Coffee and Cookies will be served in the lounge (Hamilton Hall 216) at 3:00 pm. Everyone is welcome.