IASBS Mathematics Colloquium

Spring 1397

1397-02-04
Speaker: Soodeh Moallemian (University of Tehran, Neuroscience imaging analysis group)
Title: An introduction of image processing, application to fMRI data
Abstract: In this talk, first we will give a brief introduction of image processing as one of the interesting problems of today’s scientific world. Then bringing forward a background about MRI/fMRI data acquisition and its techniques, we will describe one of the problems that has been engaging the scientists’ minds: “how to make the results of MR images more accurate?!” and describe the statistical significant brain activation through a complex determining method and compare the brain activation detected using this method with the magnitude-only approach.

1397-02-25
Speaker: Saeed Karami (IASBS)
Title: Stagnation of GMRES and polynomial numerical hulls of matrices
Abstract: The GMRES algorithm was designed to compute the solution of linear systems. We study complete stagnation of GMRES, for which there is no progress until the last iteration. Our tools for analysis are the well known sets: numerical range and polynomial numerical hulls. We characterize polynomial numerical hulls for some special matrices. Moreover, we obtain equivalent conditions for the problem of complete stagnation of the GMRES, when the coefficient matrix is direct sum of two Jordan blocks.

1397-03-01
Speaker: Ali Foroush Bastani (IASBS)
Title: Computational option pricing: Challenges and opportunities
Abstract: In the first part of this talk, I will present a brief overview of different numerical techniques currently employed to price a variety of financial option contracts, specially those of American type. An American option is a contract, giving its holder the right, but not the obligation to buy (sell) an underlying asset (e.g. 100 shares of a specific company) on or before a predetermined expiration date for a known strike price. These financial contracts are popular tools in most of the world exchanges and their accurate pricing is an important topic in mathematical finance. Among the available techniques, those which are based on partial differential equations and also integral equations have gained much popularity in recent years and an increasing number of research activities have been devoted to solve the corresponding problems. In the second part of this talk, I will present some of these challenges and will point out to some interesting research directions in this area.

1397-03-08
Speaker: M. Farrokhi D. G. (IASBS)
Title: A search for (positive) identities in groups
Abstract: Almost all parts of mathematics are engaged with solving some kind of equations. Indeed, this is how mathematics evolved. In the world of groups, as an algebraic system, relations among generators plays the role of ID cards, thats is, every group can be recognized with the equations to which its generators satisfy. The aim of this talk is to review some well-known equations and identities in groups as well as presenting some current progresses.

1397-04-05
Speaker: Bahareh Akhtari (IASBS)
Title: Introduction to Counterparty Risk
Abstract: The financial disasters (such as the crisis 2007-2009) made the risk analysts infer some significant points. In some texts, which review the financial crises, applying the right measure has been brought up as a key point to manage the credit risk. It has been discussed that some measures, such as Value at Risk (VAR), are not necessarily efficient in all market situations and it may lead to an insufficient management. However, the reviewing and managing the risks in isolation manner is another major point dealt with less than the first one. This matter has been presented by concept “counterparty risk” as the most complex financial risk and seriously highlighted over the last two decades. Also, the transactions on the Over-the-Counter (OTC) markets, which possess a customized structure and include no central organization clearing and settling the contracts, reveal the important role of the counterparty risk. In this talk, I intend to introduce this topic and address some aspects of that.