5 MAR 2020
8:30 - 12:00

In this mini-course, we will illustrate some functional analytic approaches to the study of the statistical properties of dynamical systems.

We will present Lasota-Yorke technique for existence of absolutely continuous invariant measures for some classes of dynamical systems. We will then study the spectral properties of Frobenius-Perron operator in order to obtain more information about such invariant measures. If time permits, we will continue to talk about the speed of convergence of the iterates of the transfer operator and the central limit theorems.

References.
A. Boyarsky, P. Gora, Laws of chaos. Invariant measures and dynamical systems in one dimension. Probability and its Applications. Birkhuser Boston, Inc., Boston, MA, 1997.
C. Liverani, Invariant Measures and their Properties. A functional Analytic point of view (available online)

5 MAR 2020
12:30 - 14:00

The main goal of this short course is to present a proof of Calabi_Yau theorem. It was first conjectured by Calabi that any volume form on a compact Kahler manifold can be realized as the volume form associated to a Kahler metric. In a seminal work, Yau proved Calabi's conjecture. A very important consequence of Calabi-Yau theorem is the existence of Kahler-Ricci flat metrics on compact Kahler manifolds with trivial canonical bundle.

Outline of the course:
1) background material on complex manifolds, Hermitian and Kahler metrics, Ricci form
2) Some background on elliptic PDE such as Schauder estimates
3) Yau's original proof on apriori $C^0$ estimate
4) Some advance approach to Calabi-Yau theorem
5) an overview on complex Monge-Ampere via Pluripotential theory (if time permitted)

27 FEB 2020
8:30 - 12:00

In this mini-course, we will illustrate some functional analytic approaches to the study of the statistical properties of dynamical systems.

We will present Lasota-Yorke technique for existence of absolutely continuous invariant measures for some classes of dynamical systems. We will then study the spectral properties of Frobenius-Perron operator in order to obtain more information about such invariant measures. If time permits, we will continue to talk about the speed of convergence of the iterates of the transfer operator and the central limit theorems.

References.
A. Boyarsky, P. Gora, Laws of chaos. Invariant measures and dynamical systems in one dimension. Probability and its Applications. Birkhuser Boston, Inc., Boston, MA, 1997.
C. Liverani, Invariant Measures and their Properties. A functional Analytic point of view (available online)

27 FEB 2020
12:30 - 14:00

The main goal of this short course is to present a proof of Calabi_Yau theorem. It was first conjectured by Calabi that any volume form on a compact Kahler manifold can be realized as the volume form associated to a Kahler metric. In a seminal work, Yau proved Calabi's conjecture. A very important consequence of Calabi-Yau theorem is the existence of Kahler-Ricci flat metrics on compact Kahler manifolds with trivial canonical bundle.

Outline of the course:
1) background material on complex manifolds, Hermitian and Kahler metrics, Ricci form
2) Some background on elliptic PDE such as Schauder estimates
3) Yau's original proof on apriori $C^0$ estimate
4) Some advance approach to Calabi-Yau theorem
5) an overview on complex Monge-Ampere via Pluripotential theory (if time permitted)

21 FEB 2020
08:00 - 18:30

Linux for Winter School (Cognitive Science)

20 FEB 2020
8:30 - 12:00

Our aim in this course is to review some results and techniques in ergodic theory of action of Lie groups and their discrete subgroups and then to sketch the proof of a profound theorem of G. A. Margulis known as "superrigidity".

Margulis' superrigidity theorem says that under some conditions on Lie groups and their discrete subgroups, any isomorphism between discrete subgroups extends to isomorphism of the ambient groups, and roughly speaking these discrete subgroups determines the Lie groups completely.
To this end, we need to talk about some backgrounds from the structure theory of semisimple Lie groups and Algebraic groups together with some tools from Homogeneous dynamics, for instance Moore's theorem on ergodicity of action of certain closed subgroups of Lie groups on their quotients by lattices.
Finally, we shall briefly discuss some applications of superrigidity in Riemannian geometry and also in characterization of lattices in higher rank simple Lie groups.

The main reference for the course will be the following book:
Zimmer, Robert J. Ergodic theory and semisimple groups. Monographs in Mathematics, 81. Birkh�user Verlag, Basel, 1984.

20 FEB 2020
12:30 - 14:00

The main goal of this short course is to present a proof of Calabi_Yau theorem. It was first conjectured by Calabi that any volume form on a compact Kahler manifold can be realized as the volume form associated to a Kahler metric. In a seminal work, Yau proved Calabi's conjecture. A very important consequence of Calabi-Yau theorem is the existence of Kahler-Ricci flat metrics on compact Kahler manifolds with trivial canonical bundle.

Outline of the course:
1) background material on complex manifolds, Hermitian and Kahler metrics, Ricci form
2) Some background on elliptic PDE such as Schauder estimates
3) Yau's original proof on apriori $C^0$ estimate
4) Some advance approach to Calabi-Yau theorem
5) an overview on complex Monge-Ampere via Pluripotential theory (if time permitted)

20 FEB 2020
08:00 - 18:30

Linux for Winter School (Cognitive Science)

19 FEB 2020
-

Farmanieh Conference Hall

19 FEB 2020
15:00 - 16:00

Abstract: In this work, some evidences for existing an asymmetry in the density of left- and right-handed cosmic electrons (δL and δR respectively) in universe motivated us to calculate the dominated contribution of this asymmetry in the generation of the B-mode power spectrum. In the standard cosmological scenario, Compton scattering in the presence of scalar matter perturbation cannot generate magnetic-like pattern in linear polarization C_lB^((S))= 0, while in the case of polarized Compton scattering C_lB^((S))∝δ_L^2. By adding up the power spectrum of the B-mode generated by the polarized Compton scattering to power spectra
produced by weak lensing effects and Compton scattering in the presence of tensor perturbations, we show that there is a significant amplification in ClB in large scale l < 500 for δL > 10−6, which can be observed in future experiments. Finally, we have shown that C_lB^((S)) generated by polarized Compton scattering can suppress the tensor-to-scalar ratio (r-parameter) so that this contamination can be comparable to a primordial tensor-to-scalar
ratio spatially for δL > 10−5.


Larak Seminar Room

19 FEB 2020
15:30 - 17:30

Given a category without a certain structure, we would like to construct a new category having that structure, in a universal manner . For a category C , the quotients of span category Span(C) provide us a good setting to construct new categories having the given structure of C. For a topos T , we construct new toposes that enjoy extra structures like booleanness, internal axiom of choice and etc. To do this, we study a kind of relations on span category Span(T) that we call them logical relations. Their quotient construction produce toposes with good properties. This is based on a joint project with M. Golshani.

19 FEB 2020
13:30 - 15:00

New generations of observations provide a huge amount of data, posing the big data problem, which makes scientists consider data science as an increasingly important player in almost all data-based projects. Anomaly/outlier detection is one challenging area in most of the observations as well as machine learning, especially for big data in high dimensions. An example of application is provided in astronomy by the LSST and SKA, the next-generation optical and radio telescopes which are expected to observe completely new types of celestial objects lurking in the torrent of data in the 100PB-10EB range.
We have explored a general anomaly detection framework based on dimensionality reduction and unsupervised clustering (DRAMA). This approach identifies the primary prototypes in the data with anomalies detected by their large distances from the prototypes, either in the latent space or in the original, high-dimensional space.
In this talk, I will present several recent applications of AI in astrophysics and cosmology as well as some of my researches. Then, we will know more about anomaly detection techniques and compare them to DRAMA in a wide variety of challenges.
The talk is mostly base on https://arxiv.org/abs/1909.04060

18 FEB 2020
13:00 - 14:30

Venue:
School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM),
Opposite the ARAJ, Artesh Highway, Tehran, Iran

If you like to join, please send me an email at ali.yousefi@ipm.ir

Poster

17 FEB 2020
11:00 - 12:00

Based on: A master thesis.


Abstract: Relativistic collisions of heavy ions lead to the formation of a new phase of matter called Quark-Gluon Plasma. In addition, strong magnetic field generates in these collisions and affects the dynamics of particles in the quark-gluon plasma and causes the appearance of the Landau levels in the particle’s energy spectrum. We investigate the impact of the magnetic field on dilepton production and synchrotron radiation. Due to this, we calculate the scattering probability of quark and anti-quark annihilation and dilepton creation by taking all Landau Levels into account. Then, by assuming that the magnetic field is very strong, we find an expression for scattering cross section in the lowest Landau level and show that by increasing the magnetic field intensity, the scattering cross section increases too. To study the synchrotron radiation, we obtain a relation for its spectral distribution, and by plotting it we observe how much and how it depends on the magnetic field. In these two processes, we also examine the effect of other factors such as the type of primary fermions."


Larak Seminar Room