IASBS Mathematics Colloquium

Autumn 1397

1397-07-17
Speaker: Caucher Birkar (University of Cambridge)
Title: Classification of algebraic varieties
Abstract: ---

1397-08-01
Speaker: Masoud Hasani (Ph.D. Student of University of Zanjan and Laboratoire de Mathémathiques d'Avignon)
Title: Cohomogeneity one actions on Einstein's three-dimensional world
Abstract: In a recent research, the cohomogeneity one conformal actions on the three-dimensional Einstein universe are studied and the acting groups are classified up to conjugacy. The action of a Lie group $G$ on a smooth manifold $M$ is called cohomogeneity one if $G$ admits a codimension $1$ orbit in $M$. The Einstein universe $\mathbb{E}in^{1,n}$ is the Lorentzian analogue of the round sphere $\mathbb{S}_{n+1}$. It is a compact Lorentzian manifold which contains the Lorentzian model spaces of constant curvature (the Minkowski space, the de-Sitter space, and the Anti de-Sitter space) as open dense subsets. It is shown that, up to conjugacy, $PSL(2,\mathbb{R})$ is the only Lie group which acts on $\mathbb{E}in^{1,2}$ irreducibly, conformally, and with cohomogeneity one. Moreover, it is proved that every cohomogeneity one reducible conformal action on $\mathbb{E}in^{1,2}$ fixes a point in the $4$-dimensional projective space $\mathbb{R}\mathbb{P}^4$.

1397-08-22
Speaker: Fazlollah Soleymani (IASBS)
Title: Pricing the financial Heston–Hull–White model with arbitrary correlation factors via an adaptive FDM
Abstract: This talk is concerned with the pricing procedure of one the most challenging models known as the Heston–Hull–White partial differential equation (PDE) in option pricing, at which the model is a time-dependent 3D linear PDE including three mixed derivative terms. The model comes from the fact that the price, the volatility and the interest rate are assumed to be stochastic processes. To contribute and avoid huge discretized systems, an adaptive distribution of the nodes (viz, nonuniform nodes) is taken into account with emphasis on the hot area of the solution curve. New adaptive finite difference (FD) formulas of higher orders are constructed on these meshes. Then, a set of semi-discretized equations is attained which is tackled by a time-stepping method.

1397-08-30
Speaker: Mehdi Aaghabali (University of Tehran)
Title: Leavitt path algebras and their graded structure
Abstract: Despite being introduced only 10 years ago, Leavitt path algebras have arisen in a variety of different contexts as diverse as analysis, symbolic dynamics, noncommutative geometry, and representation theory. In fact, Leavitt path algebras are algebraic counterpart to graph C*-algebras, a theory which has become an area of intensive research globally. There are strikingly parallel similarities between these two theories. Even more surprisingly, one cannot (yet) obtain the results in one theory as a consequence of the other; the statements look the same, however, the techniques to prove them are quite different. These all suggest that there might be a bridge between Algebra and Analysis yet to be uncovered.

In this talk, we introduce Leavitt path algebras and try to classify them by means of (graded) Grothendieck groups.

1397-09-06
Speaker: Alireza Tasdighi (IASBS)
Title: Quasi-cyclic low density parity check (QC-LDPC) codes: Introduction, constructing methods and their applications
Abstract: Low-density parity-check (LDPC) codes have attracted much attention over the past two decades since they can asymptotically approach the Shannon capacity in a variety of data transmission and storage scenarios. As a type of promising structured LDPC codes, the QC-LDPC codes not only inherit the advantage of conventional LDPC codes, i.e., excellent error performance, but also possess simple representations to realize fast encoding and efficient decoding. In this talk we provide a brief introduction to such type of channel codes, first. Secondly, we propose to point some pioneering construction methods along with our new approach. Finally a survey on the state-of-the-art in QC-LDPC code applications for different channel conditions, including the additive white Gaussian noise (AWGN) channels and Rayleigh fading channels is given.