**Postdoctoral Fellowship – 2018**

The Abdus Salam School of Mathematical Sciences (ASSMS) invites applications for the post of Postdoctoral Fellowships.

**SMS Weekly Talk**

Tuesday, September 26 at 14:30 in the SMS Seminar Room

**Speaker**: Shamsa Kanwal (ASSMS, Lahore)

**Title**: On r-Standard Bases

**Abstract:** In this talk, we will discuss r-standard basis, which mainly involve restricted division introduced by V. Gerdt. Moreover, we will discuss standard bases for special subspaces. We use modular methods to solve problems to compute these bases and discuss various algorithms.

**SMS Weekly Talk**

Thursday, September 28 at 14:30 in the SMS Seminar Room

**Speaker**: Yasir Mahsud (ASSMS, Lahore)

**Title**: Elliptic Curves

**Abstract:** Elliptic curves are especially important in number theory, and constitute a major area of current research; for example, they were used in the proof, by Andrew Wiles, of Fermat’s Last Theorem. They also find applications in elliptic curve cryptography (ECC) and integer factorization. During this talk, I will discuss elliptic curves over R and C along with their brief introduction over finite fields. I will also discuss their geometry over R and C. Furthermore, I will discuss what are they algebraically.

**SMS Special Seminar Series**

Monday at 11:00 am in the SMS Seminar Room

**Speaker**: 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

**Speaker**: 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.

For more details about the talks please contact:

Dr. Imran Anwar

Email: imrananwar@sms.edu.pk

Tel: +92-42-99231859 Ext-104