Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.
This will be a whistle-stop tour of a few topics on infectious disease modelling, mainly influenza. Topics to include:
- challenges in capturing dynamics of pathogens with multiple co-circulating strains
- untangling the 2009 influenza pandemic from medical insurance claims data from the US
- bioinformatic methods to detect viral packaging signals
- and a big science project (top secret until the talk!)
Julia will be visiting the Mathematical Institute on sabbatical this term, and hopes this talk will help us find areas of overlapping interests.
- Mathematical Biology and Ecology Seminar
In this talk, we will discuss about some recent results of optimal investment problems and related backward stochastic differential equations (BSDE).
In the first part, we will solve utility maximization with (unbounded) random endowments by using the tools from quadratic BSDE with unbounded terminal data. This will in turn solve a long-term outstanding problem about utility indifference valuation of unbounded payoffs (e.g. call options). Joint work with Ying Hu and Shanjian Tang.
In the second part, we will present a new class of dynamic utilities, called forward performance criteria, firstly introduced by Musiela and Zariphopoulou. We will show how they can be constructed by using ergodic BSDE and infinite horizon BSDE. As an application, we will study the large maturity behavior of (forward) entropic risk measures. Joint work with Alfred Chong, Ying Hu and Thaleia Zariphopoulou.
- Stochastic Analysis Seminar
The cyclic surgery theorem of Culler, Gordon, Luecke, and Shalen implies that any knot in S^3 other than a torus knot has at most two nontrivial cyclic surgeries. In this talk, we investigate the weaker notion of SU(2)-cyclic surgeries on a knot, meaning surgeries whose fundamental groups only admit SU(2) representations with cyclic image. By studying the image of the SU(2) character variety of a knot in the “pillowcase”, we will show that if it has infinitely many SU(2)-cyclic surgeries, then the corresponding slopes (viewed as a subset of RP^1) have a unique limit point, which is a finite, rational number, and that this limit is a boundary slope for the knot. As a corollary, it follows that for any nontrivial knot, the set of SU(2)-cyclic surgery slopes is bounded. This is joint work with Raphael Zentner.
- Topology Seminar
Take a one-dimensional random walk with zero mean increments, and consider the sizes of its overshoots over the zero level. It turns out that this sequence, which forms a Markov chain, always has a stationary distribution of a simple explicit form. The questions of uniqueness of this stationary distribution and convergence towards it are surprisingly hard. We were able to prove only the total variation convergence, which holds for lattice random walks and for the ones whose distribution, essentially, has density. We also obtained the rate of this convergence under additional mild assumptions. We will also discuss connections to related topics: local times of random walks, ergodic theory and renewal theory. This is joint work with Vlad Vysotsky.
- Stochastic Analysis Seminar