st 21 Ramanujan Symposium : Book Post National Conference on Algebra and its Applications NCAA 2018

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Dr. A. Tamilselvi Convener Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chennai – 600 005. Ramanujan Institute Advancedfor Ramanujan Institute Advancedfor Ramanujan Institute Advancedfor 21 21 21 Study Study Mathematicsin (RIASM) Study Study Mathematicsin (RIASM) Study Study Mathematicsin (RIASM) University Madras,of Chennai. University Madras,of Chennai. University Madras,of Chennai. Algebra Algebra Algebra st st st National Conference National National Conference National National Conference National Feb Feb Feb Ramanujan Symposium Ramanujan Ramanujan Symposium Ramanujan Ramanujan Symposium Ramanujan Web: riasm.unom.ac.in Web: riasm.unom.ac.in Web: riasm.unom.ac.in . 28 . 28 . 28 NCAA 2018 NCAA NCAA 2018 NCAA NCAA 2018 NCAA and and and – – – Mar Mar Mar its its its Applications Applications Applications . 02, 2018 02, . . 02, 2018 02, . . 02, 2018 02, . on on on nttt hs en eevn gat from Our grants receiving UGC (RIASM). been has Mathematics Institute in were Advanced for Study Institute two Ramanujan the as these named and Mathematics in Study for Advanced Centre 1967 UGC the form to amalgamated In two Madras. as the functioning under bodies independent were Mathematics of Institute Ramanujan the and Mathematics 1957 During Ramanujan. Srinivasa to memorial a as 1950 in Chettiar Alagappa Rm. Prof. by started in research activity its started Madras, of University nttt hs en eevn gat from Our grants receiving UGC (RIASM). been has Mathematics Institute in were Advanced for Study Institute two Ramanujan the as these named and Mathematics in Study for Advanced Centre 1967 UGC the form to amalgamated In two Madras. as the functioning under bodies independent were Mathematics of Institute Ramanujan the and Mathematics 1957 During Ramanujan. Srinivasa to memorial a as 1950 in Chettiar Alagappa Rm. Prof. by started in research activity its started Madras, of University nttt hs en eevn gat from Our grants receiving UGC (RIASM). been has Mathematics Institute in were Advanced for Study Institute two Ramanujan the as these named and Mathematics in Study for Advanced Centre 1967 UGC the form to amalgamated In two Madras. as the functioning under bodies independent were Mathematics of Institute Ramanujan the and Mathematics 1957 During Ramanujan. Srinivasa to memorial a as 1950 in Chettiar Alagappa Rm. Prof. by started in research activity its started Madras, of University bod n hs tpc. h proposed The ideas. exchange of topics. and these confer India on and in abroad both universities societies different professional by applications organized its been have conferences/workshops and of number algebra of areas different in working those to place one at intended bring is conference This years. many for past its applications algebra in and activity bod n hs tpc. h proposed The ideas. exchange of topics. and these confer India on and in abroad both universities societies different professional by applications organized its been have conferences/workshops and of number algebra of areas different in working those to place one at intended bring is conference This years. many for past its applications algebra in and activity bod n hs tpc. h proposed The ideas. exchange of topics. and these confer India on and in abroad both universities societies different professional by applications organized its been have conferences/workshops and of number algebra of areas different in working those to place one at intended bring is conference This years. many for past its applications algebra in and activity - - - h Dprmn o Mathematics, of Department The h Dprmn o Mathematics, of Department The h Dprmn o Mathematics, of Department The hr hs en go da o research of deal good a been has There hr hs en go da o research of deal good a been has There hr hs en go da o research of deal good a been has There SAP, DST, S SAP, SAP, DST, S SAP, SAP, DST, S SAP, ence ence ence 97 Rmnjn nttt was Institute Ramanujan 1927. 97 Rmnjn nttt was Institute Ramanujan 1927. 97 Rmnjn nttt was Institute Ramanujan 1927. About Department About About Department About About Department About il rvd a ltom for platform a provide will il rvd a ltom for platform a provide will il rvd a ltom for platform a provide will About Conference About About Conference About About Conference About - - - 6 te eatet of Department the 66, 6 te eatet of Department the 66, 6 te eatet of Department the 66, ERB and NBHM. and ERB ERB and NBHM. and ERB ERB and NBHM. and ERB nvriy of University nvriy of University nvriy of University A . A . A . SPEAKERS INCLUDE Supported by

Prof. K.N.Raghavan, IMSc, Chennai. University Grants CALL FOR PAPERS Commission, Prof. Parameswaran Sankaran, IMSc, New Delhi, India. Unpublished, original papers are Chennai. invited for presentation in the conference. Selected refereed papers will be published in Prof. Amritanshu Prasad, IMSc, Chennai. We are also seeking funds from the proceedings. The papers for the conference should preferably be typed in LaTeX format NBHM, Prof. Jaya. N. Iyer, IMSc, Chennai. with standard Math Style. The abstract of the India. papers may be sent to the following Email: Prof. S. Viswanath, IMSc, Chennai. [email protected]. For details visit our website riasm.unom.ac.in. Prof. Clare D’Cruz, CMI, Chennai. DST-SERB, India. Abstract Submission : 29.12.2017 Prof. R.P.Sharma, H.P. University, Shimla. REGISTRATION Paper Submission : 12.01.2018 Prof. L.R. Vermani, Kurukshetra University. The Registration fee has to be paid by Acceptance : 25.01.2018 Demand Draft in favour of “Director and Prof. Sudesh Kaur Khanduja, IISER, Mohali. Head, RIASM”, payable at Chennai. Full paper should be submitted by 5 P.M., Registration is to be done online 31.01.2018. Prof. Mohammad Ashraf, Aligarh Muslim (riasm.unom.ac.in). A copy of the University. registration form along with DD may kindly CONTACT be sent to the Convener on or before Prof. Asma Ali, Aligarh Muslim University. Dr. A. Tamilselvi 16.02.2018. There may be spot registration Convener Prof. Siddhartha Bhattacharya, TIFR, available on 28.02.2018 at 9:00 am. Ramanujan Institute for Advanced Study in Mumbai. Mathematics Registration fee (before 16.02.2018): University of Madras, Chennai – 600 005. Prof. Mrinal Kanti Das, ISI Kolkatta. Rs. 1500. E.Mail: [email protected] Spot Registration fee: Dr. Pooja Singla, IISc Bangalore. Rs. 2000.

Prof. C. Selvaraj, Periyar University, Salem. The participants are requested to make their own arrangements for their accommodation Dr. K. Kannan, Jaffna University, Srilanka. and travel expenses. ✞ ☎ Abstracts of Speakers ✝ ✆

Koszul duality and modules for the alternating Schur algebra

Amritanshu Prasad

The Institute of Mathematical Sciences, Chennai, India.

In Schur-Weyl duality, the Schur algebra is the commutant of the action of the symmetric group on tensor-space. If the action of the symmetric group is restricted to the alternating group, then the commutant is a larger algebra which contains the Schur algebra. We call this the alternating Schur algebra. Modules for the Schur algebra can be interpreted as polynomial representations of the general linear group. Koszul duality (defined independently by Chalupnik and Touze) is an important endofunctor of this category which interchanges symmetric and alternating tensors. Under the Schur functor, it corresponds to multiplication of a symmetric group representation by the sign character. In this talk I will explain how modules for the alternating Schur algebra corre- spond to polynomial representations of general linear groups with additional struc- ture, namely a hozzmomorphism from the Koszul dual of the representation to itself satisfying a certain compatibility condition. This is based on joint work with T. Geetha and Shraddha Srivastava. Equivariant principal bundles on toric varieties

Arijit Dey

Indian Institute of Technology Madras, Chennai, India.

Following Nori, torus (T) equivariant principal G bundles over a toric variety X are precisely the functors from Gmod to the category of Tequivariant vector bundles satisfying certain conditions. Assuming the base field to be complex numbers, we will prove a Klyachko type theorem for the classification of Tequivariant principal Gbundles over X with at most factorial singularities, when G is reductive. This is based on joint work with Indranil Biswas and Mainak Poddar.

Commuting maps and their Applications

Asma Ali

Aligarh Muslim University, Aligarh, India

Let R be a an associative ring and S be a nonempty subset of R. A mapping f : R → R is said to be centralizing (resp. commuting) on S if for all x ∈ S, [f(x),x] ∈ Z(R) (resp. [f(x),x]=0). The first important result on commuting mappings is due to E. C. Posner [Proc. Amer. Math. Soc. 32, 1957] which states that the existence of a commuting derivation on a prime ring R forces R to be com- mutative. The theorem has been extremely influential that it initiated the study of commuting derivations. Since then a lot of work has been done in this direction. In this talk we discuss some results on n-centralizing (n-commuting) mappings and their applications in functional analysis that we have studied recently. This is based on joint work with Howard E. Bell and Vincenzo De Filippis. Types of Derivations on Semirings

Chandramouleeswaran

Saiva Bhanu Kshatriya College, Aruppukottai, India.

1.51.25cm The notion of the ring with derivation is quite old and plays a signif- icant role in the integration of analysis, algebraic geometry and algebra. The field theory also included derivations in its inventory of tools. The classical operation of differentiation of forms on varieties led to the notion of differentiation of singular chains on varieties, a fundamental notion of the topological and algebraic theory of homology. The most trivial example of a semiring which is not a ring is the first algebraic structure we encounter in life: the set of nonnegative integers N, with the usual addi- tion and multiplication. Similarly, the set of nonnegative real numbers R+ with the usual addition and multiplication is a semiring which is not a ring. The nontrivial examples of semirings first appear in the work of German mathematician Richard Dedekind in 1894, in connection with the algebra of ideals of a commutative ring (one can add and multiply ideals, but one cannot subtract them) and were later stud- ied independently by algebraists, especially by the American mathematician H. S. Vandiver, who worked very hard to get them accepted as a fundamental algebraic structure, being basically the best structure which includes both rings and bounded distributive lattices. He was not successful, however, and with only a few exceptions semirings had fallen into disuse and were well on their way to mathematical oblivion until they were rescued during the late 1960’s when real and significant applications were found for them. It is worth mentioning that N.H.Abel, in 1826, considered some special kind of positive semifield over real numbers. In his book on semirings and their applications, Jonathan Golan has introduced the definition of derivation on a semiring. However, it has not been dealt in detail with semirings. Infact, no standard results were studied for semirings with deriva- tion. This motivated us to study the notion of derivations and generalization of vari- ous types ofderivations on semirings in our papers that are appearing since 2010. In this talk, we discuss various generalizations of derivations on semirings.

Grobner¨ basis and its applications to Monomial Curves

Clare D’Cruz

Chennai Mathematical Institute, Chennai, India.

Grobner¨ Bases can be viewed as generalizations of Gaussian elimination or the Euclidean algorithm. We will fist define Grobner¨ Bases and show how it is useful in understanding monomial curves.

Chow theory vs topological theory

Jaya N. Iyer

The Institute of Mathematical Sciences, Chennai, India.

We will discuss comparison of the two theories, with some examples. Invariant Approximation Property of Group C∗- Algebras

K. Kannan

University of Jaffna, Thirunelveli, Jaffna, Sri Lanka.

In this talk we study analytic techniques from operator theory that encapsulate geometric properties of a group. Rapid Decay Property (Property RD) provides estimates for the operator norm of elements of the group ring (in the left-regular representation) in terms of the Sobolev norm. Roughly, property RD is the noncom- mutative analogue of the fact that smooth functions are continuous. Our work then concentrates on a particular form of an approximation property for the reduced C∗- algebra of a group: the invariant approximation property. This statement captures a particular relationship between three important operator algebras associated with a group: the reduced C∗- algebra, the von Neumann algebra, and the uniform Roe algebra.

Twisted conjugacy in Houghton groups

Parameswaran Sankaran

The Institute of Mathematical Sciences, Chennai, India.

The Houghton groups Hn,n ≥ 2, is an interesting family of groups which arise n as certain permutation groups N . For example H2 is the group S∞ of all finitary permutations of Z. We will describe the automorphism group of Hn and as an appli- cation show that Hn have the so-called R∞-property, namely, that there are infinitely many twisted conjugacy classes for any automorphism of Hn. This is based on joint work Daciberg Goncalves. On Irreducible representations of SL2(R) over complete discrete valuation rings of even characteristic

Pooja Singla

Indian Institute of Sciences, Bengaluru, India

Let R be complete discrete valuation ring such that residue field has characteristic p. In this talk we will focus on the construction of complex continuous irreducible representations of General Linear group GL2(R) and its subgroup Special Linear group SL2(R).

The construction of all irreducible representations of GL2(R) has already ap- peared in the work of Kutzko and Stasinski. Similarly, construction of all irre- ducible representations of SL2(R) for p odd has also appeared in the work of Zaikin- Japirain. However for the case p = 2, a construction of irreducible representations of SL2(R) is not yet known for general R.

For R = Z2 (the ring of 2-adic integers) a construction of the irreducible repre- sentations of SL2(R) was obtained by Nobs. In this talk we will describe a method to construct certain class of irreducible representations of SL2(R) for the case where p =2 and R has positive characteristic. As an application, we are able to show that m m the complex group algebras of SL2(Z/2 Z) and SL2(F2[t]/t ) are not isomorphic for any even m> 2. This is based on ongoing joint work with Hassain M. The KPRV theorem via paths

K.N. Raghavan

The Institute of Mathematical Sciences, Chennai, India.

Let V and V ′ be irreducible representations of a complex semisimple Lie algebra g with highest weight vectors v and v′ of weights m and m′ respectively. For w in the Weyl group, let M(m, m′,w) denote the cyclic g-submodule of V ⊗ V ′ generated by the vector v ⊗ wv′ (where wv′ denotes a non-zero vector in V ′ of weight wm′). It was conjectured by Kostant and proved by Kumar that the irreducible representa- tion V (m, m′,w) whose highest weight is the unique dominant Weyl conjugate of m+wm′ occurs with multiplicity exactly one in the decomposition of M(m, m′,w) ′ ′ into irreducibles. Since M(m, m ,w0) equals V ⊗ V , where w0 denotes the longest element of the Weyl group, it follows from this that V (m, m′,w) occurs in the de- composition of V ⊗ V ′. This corollary was conjectured earlier by Parthasarathy, Ranga Rao, and Varadarajan (PRV) and proved by Mathieu independently of Ku- mar. There’s a subsequent proof by Littelmann of the PRV conjecture using his theory of Lakshmibai-Seshadri paths. I will talk about joint work with Mrigendra Kushwaha and Sankaran Viswanath where we consider such a path approach to Kostant’s refinement of the PRV. Hopf algebra actions on semirings

V. Selvan

RKM Vivekananda College, Chennai, India.

Group actions on rings and group-graded rings are instances of a Hopf algebra(H) action on algebras. A semiring is a natural generalization of a ring. In this talk we introduce the Hopf algebra(H) action on a semiring A and give some basic results of Hopf algebra H acting on semialgbra A. We compare some ideal theoretic con- nection between a semialgebra A, its semialgebra of Hinvariants AH and the smash product semialgebra A#H. Further we prove Masches type theorem for the smash product semialgebra A#H. We conclude the talk by establishing a Morita context between the semialgebra of Hinvariants AH and the smash product semialgebra A#H.

Translational tilings of the plane

Siddharth Bhattacharya

Tata Institute of Fundamental Research, Mumbai, India.

A set A ⊂ R2 is called a translational tile if R2 can be expressed as a disjoint union of translates of A. In general it is a difficult problem to decide whether a given subset A is a translational tile. In this talk we will discuss the connection between this problem and the theory of dynamical systems, and present a solution when the underlying set A is sufficiently regular. On the Root Systems & Structure of some Indefinite , non hyperbolic classes of Kac Moody algebras

A. Uma Maheswari

Quaid-E-Millath Government College for Women (Autonomous), Chennai, India.

Kac Moody algebras are infinite dimensional analogues of finite dimensional semi simple Lie algebras. In the past three decades the theory has been develop- ing at a rapid pace mainly because of its connections and applications to different fields of Mathematics and Mathematical Physics. Among the three broad classes of Kac Moody algebras , a lot of work has already been done in the case of finite and affine cases; an indepth study on infinite dimensional Kac Moody Lie algebras remain unexplored and is still a challenging problem. Here, an insight into the subclasses of infinite dimensional non hyperbolic Kac Moody algebras namely quasi affine and quasi hyperbolic families is undertaken; Complete Classification of Dynkin diagrams associated with the specific classes are obtained; A realization as graded Lie algebras of Kac Moody type is given; Structure of the root system and the graded components are analyzed. Imaginary root system of these non hyperbolic classes are discussed. The main focus is on the latest devel- opments in the field of indefinite non hyperbolic classes of infinite dimensional Kac Moody Lie algebras. Root multiplicities of partially commutative Lie algebras and graph coloring

R. Venkatesh

Indian Institute of Sciences, Bengaluru, India.

Let G be a finite simple graph with the vertex set V (G) and the edge set E(G) and let g(G) be the partially commutative algebra associated with G. The Lie algebra g(G) is generated by the symbols {ev : v ∈ V (G)} with the relations [ev, ew]=0 if Z|V (G)| (v,w) ∈/ E(G). The Lie algebra g(G) is naturally + -graded. The dimensions of the graded spaces (called root multiplicities) of g(G) have a very close relation- ship with the generalized chromatic polynomials of G. In this talk, I will explain you this connection and tell you how to use this connection to construct a basis for g(G). As an application we will see a Lie theoretic proof Stanleys reciprocity theorem of chromatic polynomials. This is joint work with G. Arunkumar and Deniz Kus.

The Schur’s Multiplicator-II

L.R. Vermani

Kurukshetra University, Kurukshetra, India.

Let G be a group, T the additive group of rationals mod 1 regarded as a triv- ial G-module. The Schurs multiplicator M(G) of G is the second cohomology group H2(G, T ). Strictly speaking the multiplicator is the second homology group

H2(G, Z)= H2(G) of G with Z the additive group of integers regarded as a trivial 2 ∼ G- module. However H (G, T ) = Hom(H2(G),T ) which in the case of G finite 2 ∼ becomes H (G, T ) = H2(G). The structure of M(G) for finitely generated Abelian groups G was determined by R. C. Lyndon way back in 1948. For non- Abelian groups, although M(G) is a finite Abelian group, even its order is not known in general. Several authors over the years have obtained upper bounds on the order of M(G), G finite. In the present talk we review some of these results in this direction.

Weyl group orbits of regular subalgebras

S. Viswanath

The Institute of Mathematical Sciences, Chennai, India.

Kac-Moody algebras are infinite dimensional generalizations of complex semisim- ple Lie algebras. We describe some recent results on counting the number of orbits of regular subalgebras of a given Kac-Moody algebra under the action of the ambient Weyl group. In the finite dimensional case, these were computed by Dynkin sixty years ago, and systematized more recently by Oshima. In the affine case, there are typically infinitely many orbits. We consider the hyperbolic case, and show that the number of orbits is finite, and that it admits a uniform description for simply laced Lie algebras. This is joint work with L. Carbone, K.N. Raghavan, B. Ransingh and K. Roy.

Growth diagrams, local rules and beyond

Xavier Viennot

National Center for Scientific Research, France.

Robinson-Schensted-Knuth correspondence (RSK), Schtzenberger ”jeu de taquin”, Littlewood-Richarson coefficients are very classical objects in the combinatorics of Young tableaux, Schur functions and representation theory. Description has been given by Fomin in terms of ”growth diagrams” and operators satisfying the commu- tation rules of the Weyl-Heisenberg algebra. After a survey of Fomin’s approach, I will make a slight shift by introducing an equivalent description with ”local rules on edges”, and show how such point of view can be extended to some other quadratic algebras. ✞ ☎ Abstracts of Paper Presentations ✝ ✆

Morita equivalence between h−fixed semialgebra and smash product

M. Devendran

RKM Vivekananda College, Mylapore, Chennai, Tamil Nadu, India.

In this paper, we study Hopf algebra(H) action on a semialgebra A and its smash product semialgebra A#H. We study the semimodule theoretic connection between the semialgebra A and its smash product semialgebra A#H. In this paper, we prove the Masches-type theorem for the smash product A#H. Further, we establish the Morita equivalence between H-fixed semialgebra AH and the smash product semi- algebra A#H. This is joint work with V. Selvan.

On Directed graphs of Cayley functions

Lejo J. Manavalan

Cochin University of Science and Technology, Kochi, Kerala, India.

The number of elements in centralizer Cα of a permutation α in Sn is |C| =

aj Qj(j) (aj!). In this paper we prove the same using a graph theoretic approach. On Strongly Regular Semirings

P. Subbulakshmi

Department of Mathematics, Stella Maris College, Chennai, India.

Semiring is an algebraic structure which provides the most natural common gen- eralization of rings. The notion of a semiring arose from the work of (Dedekind, 1894), (Macaulay, 1916), (Krull, 1924) and others on the theory of ideals of a com- mutative ring and then explicitly by the work of (Vandiver, 1934). Semirings are also applied in diverse areas such as artificial intelligence, automata theory, cryptography, fuzzy set theory, etc. In this paper, we make a study on strongly regular semirings. This is joint work with Rosy Joseph.

2-vertex domination on S-valued graphs

S. Jeyalakshmi

Devanga Arts College, Aruppukottai, Tamilnadu, India.

The concept of domination in crisp graph was generalized to distance k-domination. Slater termed a distance k-dominating set as a k-basis. Also he has given an inter- pretation in terms of communication network. In the year 2002, Sridharan et all discussed on the distance 2-domination number of a graph. In the year 2015 we have introduced the notion of S-valued graphs where S is a semiring. Motivated by the importance of the theory of domination in graphs, we have studied in our earlier papers, various types of vertex domination in S-valued graphs. In this paper, we discuss the notion of several other types of vertex domination in S-valued graphs. In particular, we discuss in detail the notion of distance 2-domination on S-valued graphs. This is joint work with M. Chandramouleeswaran. Line graphs of S-valued graphs

T.V.G. Shriprakash

Kurinji College of Engineering and Technology, Manapparai, Tamilnadu, India.

The edge-colouring problem is to find the chromatic number χ′(G) of a given graph G. That is, the minimum number of colours needed to colour the edges of G such that no two edges receive the same colour. This concept is useful to model many Scheduling problems, Circuit board problems where the wires connecting a device have to be of different colours. Recently in the year 2015, the authors introduced the notion of semiring-valued graphs. In our earlier papers, we have introduced the notion of K−Coloring on S−valued graphs and studied the upper bounds of K−Colorable S−valued graphs. It dealt with the vertex colouring of the S−valued graph GS. Further, we have intro- duced the notion of edge-colouring of GS, where the edges of S− valued graph are coloured with different colours rather than the vertices. In this paper, we discuss the notion of line graphs of a S−valued graph and discuss some of their properties. This is joint work with M. Chandramouleeswaran.

On Automorphism groups of S-valued graphs

M. Sundar

Sree Sowdambika College Of Engineering Aruppukottai, Tamilnadu, India.

Motivated by the study of isomorphism on S−valued graphs, in this paper, we study the Automorphism groups of S−valued graphs. In particular, we define the concepts of the group of vertex Automorphism and the group of edge Automorphism on S−valued graphs. This is joint work with M. Chandramouleeswaran. Connectivity of S-valued graphs

P. Victor

Mohamed Sathak Engineering College, Kilakarai, Tamilnadu, India.

Graphs are often used to model various interconnecting networks, such as trans- port, pipe, or computer networks. In such models, one often needs or wants to get from any place to any other place, which naturally leads to the study of their connec- tivity. Various networking applications are often demanding not only that a graph is connected, but that it will stay connected even after failure of some small number of nodes (vertices) or links (edges). This can be studied in theory as graph connectivity. In the year 2015, the theory of semiring valued graphs, simply called S−valued graphs have been studied by several authors. In this paper, we study the vertex S−Connectivity and edge S−Connectivity of the S−Valued Graphs. This is joint work with M. Chandramouleeswaran.

Restrained ve- and ev- m- domination on S-valued graphs

S. Kiruthiga Deepa

Bharath Niketan Engineering College, Aundipatti, Tamilnadu, India.

The theory of domination in graphs was initiated by Berge. In 2015, Chan- dramouleeswaran et.all introduced the notion of Semiring-valued graphs (simply called S−valued graphs). Motivated by this, we discussed the notion of vertex- edge mixed domination and edge-vertex mixed domination on S−valued graphs. In our previous paper, we have introduced the notion of global ve- m-domination on S−valued graphs. In this paper we discuss the notion of restrained ve- and ev- m- domination on S−valued graphs. This is joint work with M. Chandramouleeswaran. Connected strong(weak) edge domination on S-valued graphs

S. Mangala Lavanya

Sree Sowdambika College Of Engineering, Aruppukottai, Tamilnadu, India.

In our earlier paper we have studied the notions of strong and weak edge domina- tion and connected weight dominating edge set on S−valued graphs. In this paper combining these two notions, we introduce the notion of connected strong and weak edge domination on S−valued graphs and obtain some results. This is joint work with M. Chandramouleeswaran. 160th year of Post-Centenary Diamond Jubilee of University of Madras 50th year Golden Jubilee of the Centre for Advanced Study XXI Ramanujan Symposium National Conference on Algebra and its Applications

February 28 - March 02, 2018.

PROGRAMME Wednesday, 28.02.2018

09:00 - 10:00 Registration

10:00 - 11:20 Inauguration Key Note Address : Growth diagrams, local rules and beyond Dr. Xavier Viennot National Center for Scientific Research, France.

11:20 - 11:35 Tea

Chairperson : Dr. S. Parvathi 11:35 - 12:20 Twisted conjugacy in Houghton groups Dr. Parameswaran Sankaran The Institute of Mathematical Sciences, Chennai, India.

12:25 - 13:10 The KPRV theorem via paths Dr. K. N. Raghavan The Institute of Mathematical Sciences, Chennai, India.

13:10 - 14:00 Lunch Chairperson : Dr. Asma Ali

14:00- 14:45 Gro¨bner basis and its applications to Monomial Curves Dr. Clare D’Cruz Chennai Mathematical Institute, Chennai, India.

14:50 - 15:35 Chow theory vs topological theory Dr. Jaya N. Iyer The Institute of Mathematical Sciences, Chennai, India.

15:35 - 15:50 Tea

Paper Presentations Chairperson : Dr. V. Thangaraj 15:50 - 16:05 2-vertex domination on S-valued graphs S. Jeyalakshmi Devanga Arts College, Aruppukottai, Tamilnadu, India.

16:05 - 16:20 On Directed graphs of Cayley functions Lejo J. Manavalan Cochin University of Science and Technology, Kochi, Kerala, India.

16:20 - 16:35 On Strongly Regular Semirings P. Subbulakshmi Department of Mathematics, Stella Maris College, Chennai, India.

16:35 - 16:50 Line graphs of S-valued graphs T.V.G. Shriprakash Kurinji College of Engg. and Tech., Manapparai, Tamilnadu, India. Thursday, 01.03.2018

Chairperson : Dr. A. Joseph Kennedy

09:30 - 10:15 Translational tilings of the plane Dr. Siddharth Bhattacharya Tata Institute of Fundamental Research, Mumbai, India.

10:20 - 11:05 Equivariant principal bundles on toric varieties Dr. Arijit Dey Indian Institute of Technology Madras, Chennai, India.

11:05 - 11:20 Tea

Chairperson : Dr. R. Sahadevan

11:20 - 12:05 The Schur’s Multiplicator-II Dr. L.R. Vermani Kurukshetra University, Kurukshetra, India.

12:10 - 12:55 Commuting maps and their Applications Dr. Asma Ali Aligarh Muslim University, Aligarh, India.

12:55 - 14:00 Lunch Chairperson : Dr. Premalatha Kumaresan

14:00- 14:45 Hopf algebra actions on semirings Dr. V. Selvan RKM Vivekananda College, Chennai, India.

14:50 - 15:35 On the Root Systems & Structure of some Indefinite, non hyperbolic classes of Kac Moody algebras Dr. A. Uma Maheswari Quaid-E-Millath Government College for Women, Chennai, India.

15:35 - 15:50 Tea

Paper Presentations

Chairperson : Dr. C. Srihari Nagore

15:50 - 16:05 Morita equivalence between h­ fixed semialgebra and smash product M. Devendran RKM Vivekananda College, Mylapore, Chennai, Tamil Nadu, India.

16:05 - 16:20 Connectivity of S-valued graphs P. Victor Mohamed Sathak Engineering College, Kilakarai, Tamilnadu, India. 16:20 - 16:35 Restrained ve- and ev- m- domination on S-valued graphs S. Kiruthiga Deepa Bharath Niketan Engineering College, Aundipatti, Tamilnadu, India.

16:35 - 16:50 Connected strong(weak) edge domination on S-valued graphs S. Mangala Lavanya Sree Sowdambika College Of Engineering, Aruppukottai, Tamilnadu, India.

16:50 - 17:05 On Automorphism groups of S-valued graphs M. Sundar Sree Sowdambika College Of Engineering, Aruppukottai, Tamilnadu, India. Friday, 02.03.2018

Chairperson : Dr. L. R. Vermani

09:30 - 10:15 Invariant Approximation Property of Group C∗ - Algebras Dr. K. Kannan University of Jaffna, Thirunelveli, Jaffna, Sri Lanka.

10:20 - 11:05 Types of Derivations on Semirings Dr. M. Chandramouleeswaran Saiva Bhanu Kshatriya College, Aruppukottai, India.

11:05 - 11:20 Tea

Chairperson : Dr. G. P. Youvaraj

11:20 - 12:05 Koszul duality and modules for the alternating Schur algebra Dr. Amritanshu Prasad The Institute of Mathematical Sciences, Chennai, India.

12:10 - 12:55 On Irreducible representations of SL2(R) over complete discrete valuation rings of even characteristic Dr. Pooja Singla Indian Institute of Sciences, Bengaluru, India.

12:55 - 14:00 Lunch Chairperson : Dr. E. Thandapani

14:00- 14:45 Root multiplicities of partially commutative Lie algebras and graph coloring Dr. R. Venkatesh Indian Institute of Sciences, Bengaluru, India.

14:50 - 15:35 Weyl group orbits of regular subalgebras Dr. S. Viswanath The Institute of Mathematical Sciences, Chennai, India.

15:35 Valedictory