### March 2017

**SMS Weekly Talk**

Thursday, March 30 at 2:30 pm in the SMS Seminar Room

**Speaker: **Asma Khalid (AS-SMS)

**Title:** Completeness and Morphisms of Algebras

**Abstract:** A completion is any of several related functors on rings and modules that result in complete topological rings and modules. It is among the most basic tools in analyzing commutative rings. The completion of a ring is useful in commutative algebra because it sometimes allows us to bring methods of analysis to bear on problems in algebra. One of the main aim of this talk is to explain smooth morphisms of rings which are one of the main ingredients in Desingularization. Moreover, we will also discuss number of morphism and regular morphisms of Noetherian rings and some of their interesting properties.

**SMS Weekly Talk**

**Speaker:**Numan Amin (AS-SMS)

**Title:**Introduction to Tropical Geometry

**Abstract:**Tropical geometry is a fascinating area of mathematics that is relatively new with connection to various other fields including physics and geometry. It has been studied quite vigorously in the last few years. I will

discuss the basics of tropical geometry by explaining the arithmetic in tropical. I will define tropical polynomial, its hypersurface and explain the connection between the newton polygon and the hypersurface of tropical polynomial. We will also see the relation between the tropical variety with variety in classical geometry.

**SMS Weekly Talk**

**Speaker:**Azeem Khadam (AS-SMS)

**Title:**Grothendieck’s Local Cohomology — II

**Abstract:**I will continue my discussion of local cohomology which was introduced by Grothendieck in the early sixties. Local cohomology modules can be used to measure the depth of a module on an ideal, and as a way to test the Cohen-Macaulay properties. Moreover, the cohomology of coherent sheaves on projective varieties can be recovered from graded components of local cohomology modules, providing useful insights into theorems about projective varieties that were originally proved in other ways.

**SMS Weekly Talk**

**Speaker:**Shamsa Kanwal (AS-SMS)

**Title:**Introduction to Border Bases

**Abstract:**Gröbner bases has become an essential tool in algebra in the last few decades. Theory of Border bases is an extension of the theory of Gröbner bases in the case of zero-dimensional ideals. I will give a brief introduction to Border bases, its importance and some of its applications. Moreover, I will discuss the algorithm for the calculation of Border bases using some examples.

**SMS Weekly Talk**

Speaker: Seyedeh Zahra Rezaei Lalami (University of Leicester)

Abstract: This talk aims at discussing the actuarial science as an emerging academic discipline. Actuarial science couples mathematics with other fields of science to consider real world scenarios. Part of the talk will be aimed at advertising the university of Leicester actual sciences program. I will discuss actuarial qualifications a student enrolled in the program can get. I will also discuss its wider scope in industry since university of Leicester has many top employers on its panel for student placement.

**SMS Weekly Talk**

Thursday, March 07 at 2:30 pm in the SMS Seminar Room

Speaker: Itrat Abbas (AS-SMS)

Title: Introduction to Fractional Order Viscoelasticity

Abstract: The fractional calculus and fractional differential equations are used quiet often to describe many physical phenomena. I will explain, using some examples, the use of fractional calculus to model some materials which lie between Hook’s solid and Newtonian fluids.

**SMS Weekly Talk**

Thursday, March 02 at 2:30 pm in the SMS Seminar Room

**Speaker**: Laila Naqvi

**Title**: Mesh-free Methods in Numerical Analysis

### February 2017

**SMS Weekly Talk**

Tuesday, February 28 at 2:30 pm in the SMS Seminar Room

**Speaker**: Azeem Khadam

**Title**: Grothendieck’s Local Cohomology

**Abstract**: Local cohomology was introduced by Grothendieck in the early sixties, in part to answer a conjecture of Pierre Samuel about when certain types of commutative rings are unique factorization domains. Local cohomology modules can be used to measure the depth of a module on an ideal, and as a way to test the Cohen-Macaulay properties. Moreover, the cohomology of coherent sheaves on projective varieties can be recovered from graded components of local cohomology modules, providing useful insights into theorems about projective varieties that were originally proved in other ways.

**SMS Weekly Talk**

February 23 at 2:30 pm in the SMS Seminar Room

**Speaker**: Azeem Khadam

**Title**: Grothendieck’s Local Cohomology

**Abstract**: Local cohomology was introduced by Grothendieck in the early 1960’s, in part to answer a conjecture of Pierre Samuel about when certain types of commutative rings are unique factorization domains. According to Wikipedia, he introduced it in a series of lectures in Harvard, later written up by Hartshorne, see [1]. Local cohomology modules can be used to measure the depth of a module on an ideal, and as a way to test the Cohen-Macaulay properties. Moreover, the cohomology of coherent sheaves on projective varieties can be recovered from graded components of local cohomology modules, providing useful insights into theorems aboutprojective varieties that were originally proved in other ways.

**SMS Weekly Talk**

February 21 at 2:30 pm in the SMS Seminar Room

**Speaker**: Umar Shahzad

**Title**: Topological Vertex Formalism

**Abstract**: Gopakumar and Vafa introduced new topological invariants associated to a Calabi-Yau threefold _. These invariants are associated with a curve class_________ _ Later on, Vafa and others introduced a combinatorial algorithm to calculate these invariants associated to the toric Calabi-Yau threefold _. Having the trivalent graph associated to _, they associated a topological vertex ___(a rational function) to each vertex of the graph. _; _ and _ are the partitions assign to each edge of the vertex. In this talk, I will try to explain the algorithm for calculating the Gopakumar-Vafa invariants which I discussed above. We will also try to discuss some examples as well.

**SMS Weekly Talk**

February 16 at 2:30 pm in the SMS Seminar Room

**Speaker**: Umar Shahzad

**Title**: Introduction To Toric Geometry

**Abstract**: Toric varieties become very famous among the algebraic geometric community after its first formal introduction by Demazure. One can think toric variety as __ fibration over some certain special region in __. The simplest example that one can think is a sphere as circles fibred over an interval in _. In this talk, I will discuss the basics of toric geometry, and how we can construct toric varieties using the strongly convex rational polyhedral cones. I will demonstrate a certain class of toric varieties known as toric Calabi Yau threefolds.

**SMS Weekly Talk**

February 14 at 2:30 pm in the SMS Seminar Room

**Speaker**: Abdual Rauf Nizami

**Title**: Khovanov Homology ofBraid Links

**Abstract**: Although computing the Khovanov homology of links is common in literature, no general formulas have been given for all families of knots and links. We give general formulas of the Khovanov homology of some families of 2- and 3-strand braid links.

**SMS Weekly Talk**

February 09 at 2:30 pm in the SMS Seminar Room

**Speaker**: Shamas Bilal

**Title**: _-Dissipative differential inclusions

**Abstract**: In this talk we will discuss about well known Filippov-Pliss lemma for evolution inclusions given by multivalued perturbation of _ −dissipative differential inclusions in Banach spaces with uniformly convex dual.

### January 2017

**Speaker:**Amer Iqbal (LUMS & AS-SMS), Jamil Aslam (QAU), Babar Qureshi (LUMS), Rizwan Khalid (NUST)

**Title:**Understanding Salam

**Abstract:**In this two day activity, dedicated to celebrate Prof. Abdus Salam’s lasting contributions to theoretical physics, four big ideas of contemporary physics to which Salam contributed heavily will be explained starting from beginning. The school should be of interest to graduate students and other physicists (scientists) interested in learning about Salam’s theories and their phenomenal impact on physics.