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21 Ram Anujan Sym Posium : National About Department BookBookBook Post Post Post The Department of Mathematics, University of Madras, started its research activity in 1927. Ramanujan Institute was started by Prof. Rm. Alagappa Chettiar in st 21 Ramanujan Symposium 1950 as a memorial to Srinivasa Ramanujan. National Conference on During 1957-66, the Department of Algebra and its Applications Mathematics and the Ramanujan Institute of Mathematics were functioning as two NCAA 2018 independent bodies under the University of ApplicationsApplicationsApplications Feb. 28 – Mar. 02, 2018 Madras. In 1967 these two were its its its amalgamated to form the UGC Centre for Advanced Study in Mathematics and named andandand as the Ramanujan Institute for Advanced Study in Mathematics (RIASM). Our Institute has been receiving grants from UGC-SAP, DST, SERB and NBHM. AlgebraAlgebraAlgebra ononon About Conference There has been a good deal of research activity in algebra and its applications for past 600 005. 600 005. 600 005. many years. This conference is intended to –– – bring at one place those working in different areas of algebra and its applications. A To To To RamanujanRamanujanRamanujanSymposiumSymposium Symposium :: : number of conferences/workshops have been st st st Ramanujan Institute for Advanced organized by different universities and NationalNationalNationalConferenceConference Conference NCAANCAANCAA20182018 2018 212121 Study in Mathematics (RIASM) professional societies both in India and University of Madras, Chennai. abroad on these topics. The proposed Web: riasm.unom.ac.in conference will provide a platform for exchange of ideas. A. Tamilselvi Tamilselvi Tamilselvi A. A. A. Dr. Dr. Dr. Convener Convener Convener Mathematics Mathematics Mathematics in in in Study Study Study Advanced Advanced Advanced for for for Institute Institute Institute Ramanujan Ramanujan Ramanujan Chennai Chennai Chennai Madras, Madras, Madras, of of of University University University 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 Unpublished, original papers are Chennai.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
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