**Course Title:**Advanced Algebraic Topology

**Resource Person:**Barbu Berceanu

**Duration:**October 30- November 23, 2017

**Course description:**

**Schedule:**The course will comprise on 12 lectures (each of 2 hours duration). There will be three lectures per week on Monday (14:00-16:00), Wednesday(14:00-16:00) and Thursday (15:00-17:00). The course will be starting from October 30, 2017.

**Who can attend:**There is no registration fee for this course but we are restricted to limited number of participants. Undergraduate students and graduate students are encouraged to attend this course. For registration, contact imrananwar@sms.edu.pk.

**Short Course**

**Introduction to basic principles of fluid mechanics**

by

*Constantin Fetecau & Dumitru Vieru*

**October 02 – November 29, 2017**

__Schedule:__ The course will consist of 18 lectures (each of 2 hours duration). The lectures will be on Monday (15:00-17:00) and Wednesday (15:00-17:00).

__Course objectives:__ Provide a fundamental understanding of the principles of fluid mechanics with heat transfer due to convection, conduction and radiation.

__Prerequisites____:__ Basic knowledge of vector analysis and partial differential equations.

__Topics which will be covered:__ Classical fluid mechanics is a branch of the continuum mechanics and it is based on the assumption that a fluid has a continuous structure. The fundamental property of fluids is that cannot be in equilibrium in a state of stress, therefore, the mutual action between two adjacent parts is not collinear to the normal at the common surface. The equations of motion of a general continuous medium lead to a system of differential equations which has to be satisfied by the velocity, density, pressure, etc. of an arbitrary fluid. In this course we shall consider the governing differential equations of the fluid flow, their derivation from fundamental axioms, and the various forms which they take under the assumptions concerning the fluid or the type of motion. Using the principles of classical fluid mechanics we shall present the basic equations of the fluid motion in a correct mathematical way and a concise form. The basic equations of fluid motion will be determined based on the following fundamental principles: (i) the continuum hypothesis; (ii) the conservation of mass; (iii) balance of momentum (Newton second law of motion);(iv) balance (conservation) of energy. Theoretical/practical aspects of fluid dynamics, the importance and utility of the governing equations (the Navier-Stokes equations) will be studied.

There is no registration fee for this course but we are restricted to limited number of participants. Undergraduate students and graduate students are encouraged to attend this course. For registration, please contact:events@sms.edu.pk.

**Short Course**

**Tensor and exterior products of vector spaces**

by

* Johann Davidov*

November 10 – December 15, 2017

__Schedule:__ The course will consist of 10 lectures (each of 2 hours duration). The lectures will be on Tuesday (15:30-17:30) and Friday (14:30-16:30). The course will be starting from November 10, 2017.

__Course objectives:__ The purpose of the course is to fill in the gap left in the university courses.

__Prerequisites____:__ Standard facts about vector spaces and linear maps.

__Topics which will be covered:__ Tensor and exterior products of vector spaces (and more generally, of modules) have wide application in many branches of mathematics, even in array programming languages. They should be part of the mathematical culture of every professional mathematician. Unfortunately, this topic is usually not included in the standard university programs.

There is no registration fee for this course but we are restricted to limited number of participants. Undergraduate students and graduate students are encouraged to attend this course. For registration, please contact:events@sms.edu.pk.

**SMS Special Seminar Series**

Monday at 11:00 am in the SMS Seminar Room

Speakers: Umar Shahzad

Title: Understanding Equivariant Cohomology

Abstract: Equivariant cohomology is a cohomology theory from algebraic topology which applies to topological spaces with a *group action*. It can be viewed as a common generalization of group cohomology and an ordinary cohomology theory. This is a series of talks on understanding equivariant cohomology and equivariantintegration. The aim of these seminars is to explain Fiber bundles, Maps between fiber bundles, Principal G-bundles, Hopf bundles, Pullback of a fiber bundle.

**SMS Special Seminar Series**

Wednesday and Friday at 11:00 am in the SMS Seminar Room

Speakers: Imran Anwar

Title: Graded Free Resolutions and Hilbert Functions

Abstract: The aim of these seminars is to explain the graded algebraic structures, free resolutions of graded rings and modules, Betti numbers, Hilbert Function and Hilbert series from the book of Irena Peeva with illustrating examples. It will provide a glimpse on some exciting directions in which commutative algebraists are working.

**Short Course**

*Differential Geometry of Curves*

by

Johann Davidov

March 20 – April 19, 2017

**Schedule:** The course will consist of 10 lectures (each of 2 hours duration). The lectures will be on Monday (14:00-16:00) and Wednesday (14:00-16:00).

**Topics which will be covered:** Curves in Euclidean spaces, Frenet frames, Plane curves, Space curves, Relations between the curvature and the torsion, Frenet equations, Fundamental theorem of the local theory of curves, Curves in the Minkowski space Frenet equations in the Minkowski space , Global theory of curves, Global theory of curves–continuation.

There is no registration fee for this course but we are restricted to limited number of participants. Undergraduate students and graduate students are encouraged to attend this course. For registration, please contact: imrananwar@sms.edu.pk.

**ASSMS INTENSIVE COURSE**

on

**Algebraic Topology**

**January 30 – February 23, 2017**

**Resource Persons:** Prof. Barbu Berceanu

**Schedule:** The course will comprise on 12 lectures (each of 2 hours duration). There will be three lectures per week on Monday (14:00-16:00), Wednesday (14:00-16:00) and Thursday (11:00-13:00). The course will be starting from January 30, 2017.

**Contents of the Course:** Homotopy equivalences, Fundamental Groups, Van-Kampan Theorem, Free product of groups, Cell complexes, Covering spaces, Homotopy invariance, Mayer-Vietoris sequences, simplicial and singular homologies.

**Who can attend:** There is no registration fee for this course but we are restricted to limited number of participants. Undergraduate students and graduate students are encouraged to attend this course. For registration, contact imrananwar@sms.edu.pk.

**ASSMS INTENSIVE COURSE**

on

**Advanced General Topology**

**October 31- November 25, 2016**

**Resource Persons:** Prof. Barbu Berceanu

**Schedule:** Monday, Wednesday and Thursday from 11:00-13:00.

**Organizers:** Dr. Imran Anwar, Dr. Abdul Rauf Nizami, Yameen Khan

Click here for detail or download form in (.doc, .pdf) and send it to email mentioned in course detail-document.

**ASSMS intensive Course**

on

**An Introduction to Differential Forms**

**October 26 – December 05, 2016**

**Resource Persons: **Prof. Johann Davidov

**Schedule:** Monday and Wednesday from 14:00-16:00.

**Organizers:** Dr. Imran Anwar, Absar Ul Haq, Bilal Masood

Click here for detail or download form in (.doc, .pdf) and send it to email mentioned in course detail-document.

**ASSMS INTENSIVE COURSE**

on

**Recent and interesting results in Fluid Mechanics**

**October 12 – November 14, 2016**

**Resource Persons:**Prof. Constantin Fetecau, Prof. Dumitru Vieru, Azhar Ali Zafar

**Schedule:** Monday and Wednesday from 11:00 – 13:00.

**Organizers:** Dr. Azhar Ali Zafar, Dr. Imran Anwar

Click here for detail or download form in (.doc, .pdf) and send it to email mentioned in course detail-document.