### September 2017

**SMS Weekly Talk**

Tuesday, September 19 at 14:30 in the SMS Seminar Room

**Speaker**: Anam Rani (ASSMS, Lahore)

**Title**: Perinormal Rings and Domains

**Abstract:** Recently, Epstein and Shapiro introduced and studied the perinormal domains: those domains A whose overrings satisfying going down over A are flat A-modules. These domains fall strictly between the Krull domains and the seminormal domains. In this talk, I will discuss the concept of P-domain introduced by Mott and Zafrullah. I will show that every P-domain is perinormal and has no proper lying over overring (an overring B of a ring A such that A is contained in B satisfies lying over property). At the end, I will give basic properties of this class and discuss some illuminating examples.

**SMS Weekly Talk**

Thursday, September 21 at 14:30 in the SMS Seminar Room

**Speaker**: Nadia Shoukat (ASSMS, Lahore)

**Title**: Hibi Rings and Rank Bounded Hibi Subrings

**Abstract:** Hibi rings and their dening ideals are attached in a natural way to nite distributive lattices. They were first introduced by Hibi in 1987. In the last decades, many authors have investigated various properties and invariants of Hibi rings. In this presentation, we will discuss certain characteristics of Hibi rings and Grobner Basis of the Hibi ideal. Moreover, we will discuss rank bounded Hibi subrings. Moreover, we will discuss rank bounded Hibi subrings. They were introduced by Aramova, Herzog and Hibi in 2000.

**PhD Thesis Defense**

Friday, September 22 at 11:30 in the SMS Seminar Room

**Speaker**: Anam Rani (AS-SMS)

**SMS Weekly Talk**

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

**Speaker**: Ali Owais (ASSMS, Lahore)

**Title**: Total Edge Irregular Strength of Complete Graphs

**Abstract:** IA total edge irregular k-labelling λ of a graph G=(V,E) is a labelling of vertices V and edges E with labels from the set {1, 2, . . ., k} in such a way that for any two different edges ‘e’ and ‘f’ the weights are different i.e. wt(e)≠ wt(f). Here the weight of an edge e=uv ; v, u є V and wt(e)= λ(u)+λ(e)+λ(v) i.e. sum of labels of vertices u, v and of the edge e. The minimum k for which the graph G has an edge irregular total k-labelling is called the total edge irregularity strength of G i.e. tes(G). In this talk, we will discuss various techniques used to determine the exact value of the total edge irregular strength for complete graph.

**SMS Weekly Talk**

Tuesday, September 12 at 14:30 in the SMS Seminar Room

**Speaker**: Shamas Bilal (ASSMS, Lahore)

**Title**: Nonlocal Problems for m-dissipative Evolution Inclusions

**Abstract:** In systems and control theory, dissipative systems are dynamical systems with states x(t) , inputs u(t) and outputs y(t), which satisfy the so-called “dissipation inequality”. In this talk, we will discuss the proof of the existence of solutions for one-sided Lipschitz perturbations of general m-dissipative evolution inclusions with nonlocal initial conditions in Banach spaces with uniformly convex duals. Moreover, we will discuss examples to illustrate the applicability of our result.

**SMS Special Seminar**

Monday, September 11 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 equivariant integration. The aim of this talk is to explain Fiber bundles, Maps between fiber bundles, Principal G-bundles, Hopf bundles, Pullback of a fiber bundle.

**SMS Weekly Talk**

Friday, September 8 at 11:00AM in the SMS Seminar Room

**Speaker**: Ali Raza (ASSMS, Lahore)

**Title**: Interpolation Spaces and General Holmstedt’s formulae

### August 2017

**PhD Thesis Defense**

**Candidate:**Mr. Itrat Abbas.

**SMS Special Seminar**

Thursday, August 24 at 11:00 am in the SMS Seminar Room

**Speaker**: Malik Tusif Ahmed and Azeem Khadam

**Title**: Questions on (generalized) Local Cohomology – II (continued)

**Abstract**: This is a continuation of the series of talks based on some work AK carried out with Peter Schenzel. We will discuss some aspects of Grothendieck’s local cohomology and its variations. We will begin with explanation of the direct limit in the category of modules with some examples including Cech complex. The idea of an inverse limit in the category of modules will be illustrated by using the example of p-adic numbers. We will also try to explain how the various local cohomology theories are connected with each other.

**SMS Special Seminar**

Monday, August 21 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 equivariant integration. The aim of this talk is to explain Fiber bundles, Maps between fiber bundles, Principal G-bundles, Hopf bundles, Pullback of a fiber bundle.

Workshop on Contemporary Topics in Analysis, Algebra and Geometry (August 15-19, 2017)

**SMS Special Seminar**

Thursday, August 03 at 11:00am in the SMS Seminar Room

**Speaker**: Hassan Azad (KFUPM)

**Title**: Real Algebraic Groups and Applications to Embedding Algorithms

**Abstract**: A problem of algorithmic interest is how to embed given Lie algebras of prescribed types into maximal ones of the same type. These algorithms are given in a recent preprint (arxiv:1603.08167). One needs these algorithms to give invariant solutions of differential equations. I will discuss briefly the main tools used in devising such algorithms.

**PhD Thesis Defense**

Tuesday, August 01, 2017 at 12:00(noon) in the SMS Seminar Room

**Candidate:**Mr. Muhammad Azeem Khadam (AS-SMS)

**Title:**Local Bezout Inequalities and Homological Methods.

### July 2017

**PhD Thesis Defense**

**Candidate:**Niat Nigar (AS-SMS)

**Title:**Free Convection Flows of a Viscous Fluid and Various Motions of Rate Type Fluids.

### May 2017

**Candidate:**Maria Naseem (AS-SMS)

**Title:**Total and Entire Labeling of Graphs

**Speaker:**Haniya Azam (LUMS, Lahore)

**Title:**What is Schubert calculus?

**Abstract**

**:**Nearly 150 years ago Schubert published his book on ‘Calculus of Enumerative Geometry’. As the name suggests, his work was about finding number of points, lines, planes etc., and was the first systematic study of what is now called Intersection Theory. Highly intuitive to begin with, this work became rigorous later on by the introduction of Schubert Varieties.One beautiful aspect of this subject is that geometric information about these varieties lies in the combinatorics of partitions.In this talk we will introduce Schubert varieties inside a Grassmanian (more generally, a Flag) manifold. This will be followed by Schubert Calculus- an application of intersection theory to problems in enumerative geometry. Lastly, we will be demonstrating what generates the cohomology of this manifold. Hopefully, we will have enough time to give concrete examples.

**Candidate:**Shehraz Akhtar (AS-SMS)

**Title:**Natural Convection Flows of Viscous Fluids and Different Motions of Couple Stress Fluids

**Speaker:**Muhammad Imran Qureshi (LUMS, Lahore)

**Title:**Algebraic Varieties via unprojections: Tom & Jerry

**Abstract**

**:**Many interesting classes of algebraic varieties can be studied in terms of their corresponding graded rings. In many interesting cases the corresponding ring is a Gorenstein ring. One can construct algebraic varieties in codimension less than and equal to 3 by using the structure theorems of the corresponding Gorenstein rings. In codimension greater than 3, one method of constructing algebraic varieties is the technique of unprojection. The aim of this talk is to explain the idea of unprojection by explicit examples. In particular, I will focus on two matrix formats, Tom and Jerry which gives the construction of algebraic varieties in codimension 4 via unprojection of 3 dimensional algebraic varieties.

**Speaker:**Sohail Zafar (UMT, Lahore)

**Title:**Binomial edge ideals of k-deficient graphs

**Abstract**

**:**In this talk, we will study binomial edge ideals, some of its combinatorial and algebraic properties.The class of k-deficient graphs came into existence, when the sequentially Cohen-Macaulay property of binomial edge ideals was discussed. If we remove k edges (with one fixed vertex) from the complete graph, such a connected graph is called k-deficient graph.

We will study primary decomposition, krull dimension, depth, Hilbert series and Castelnuovo-Mumford regularity of binomial edge ideal of k-deficient graphs.

There is not so much work done so far in the direction of the minimal free resolution of binomial edge ideals. The ideal consists of binomials so the problem to find minimal free resolution looks hard. The minimal free resolution of the binomial edge ideal of simplest classes like complete graph, line graph, complete bipartite graph and cycle graph is known. We will discuss brand new idea of computing the minimal free resolution of k-deficient graphs by using the concept of initial ideals (by converting binomial edge ideal to monomial edge ideal).

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

**Title:**Thermodynamics formalism in Ergodic theory

**Abstract**

**:**The Introduction of Thermodynamics formalism within mathematical field is due to Yakov Sinai, David Ruelle (1935- ) and Rufus Bowen (1947-1978) in early ’70. The aim of this talk is to provide a brief introduction of elements of Thermodynamics formalism in Ergodic theory. Throughout the talk our dynamical system will remain Symbolic dynamical systems. The main idea is to introduced the concept of pressure function, equilibrium state, potential and phase transition etc in the language of invariant probability measure.

**Speaker:**Waqas Ali Azhar (AS-SMS)

**Title:**Introduction to One Dimensional Dynamics

**Abstract**

**:**The goal of this talk is to introduce many of the basic techniques from the theory of dynamical systems in a setting as simple as possible. For this reason, all the dynamics will be considered one dimensional i.e. on the real line or unit circle in the plane. We introduce topics such as hyperbolicity, topological conjugacy and structural stability. The main idea is to understand in the light of examples what it means for a dynamical system to be chaotic.

**Speaker:**Samina Mazhar (Queen Mary College, Lahore)

**Title:**Fuzzy Lattice and Statistical Metric

**Abstract**

**:**In this talk, I will discuss some concepts from lattice theory aiming to introduce [0,1] as a complete bounded lattice possessing an involution but unfortunately failing to follow some desirable laws. Then, I will relate the above stated lattice as range of the mapping known as “Fuzzy Set”. Afterwards, I will introduce some mappings from Statistical Metric Spaces to enrich our theory on fuzzy sets. Lastly, I will attempt to show some marvelous applications of this area.

### April 2017

**SMS Weekly Talk**

**Speaker:**Mumtaz Hussain (La Trobe University, Australia)

**Title:**Diophantine approximation on manifolds: theory and applications

**Abstract**

**:**The well-known theorems of Khintchine and Jarnik in Diophantine approximation provide a comprehensive description of the measure theoretic properties of real numbers approximable by rational numbers with a given error. Various generalizations of these fundamental results have been obtained for other settings, in particular, for curves and more generally manifolds. In this talk, I will explain my recent Jarnik type results for a parabola in homogeneous settings. This result is the first of its kind.

**Thesis Defense**

**PhD Thesis Defense:**Imran Abbas Baloch (AS-SMS)

**Title of the thesis:**Harmonically (s,m)-Convex Functions and Related Inequalities

**Advanced Topics in Theoretical Physic**

**Speaker:**Amer Iqbal (AS-SMS & LUMS)

**Title:**Topological Strings-I (Spinors in various Dimensions)

**Abstract:**Spanning over a few lectures, Amer Iqbal will introduce the world of topological strings which are some extremely useful and fascinating objects in a theoretical physicist’s inventory.

In our quest to understand topological strings, their properties and applications we will begin with a review of spinors in various dimensions.We will discuss the spin groups, their relation with orthogonal groups and irreducible spin representations. We will pay special attention to spinors in two dimensions.

**SMS Weekly Talk**

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

**Title:**On Standard Basis of an Ideal

**Abstract:**A standard basis of an ideal is nothing but a special set of generators, which allows the computation of many invariants of the ideal just from its leading monomials. In this talk I will give a brief introduction about the importance and inception of the concept of standard basis in commutative algebra. I will discuss different algorithms to compute standard basis.

**SMS Weekly Talk**

**Speaker:**Ambreen Ahmed (AS-SMS)

**Title:**Riemann Surfaces and its Triangulation

**Abstract:**A Riemann surface is a one dimensional complex manifold. It arises naturally in the study of complex functions. The study of maps from Riemann surfaces to other spaces is a rich and very active field. In this talk we will discuss examples of Riemann surfaces and holomorphic maps on them. We will also discuss the triangulation of Riemann surfaces, Hurwitz formula, the construction of Riemann surface associated with $\sqrt{z}$ and the one with genus one

### 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.