Chennai Mathematical Institute Annual Report 2011 - 2012 75 76 Chennai Mathematical Institute
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Patent Filed, Commercialized & Granted Data
Granted IPR Legends Applied IPR Total IPR filed till date 1995 S.No. Inventors Title IPA Date Grant Date 1 Prof. P K Bhattacharya (ChE) Process for the Recovery of 814/DEL/1995 03.05.1995 189310 05.05.2005 Inorganic Sodium Compounds from Kraft Black Liquor 1996 S.No. Inventors Title IPA Date Grant Date 1 Dr. Sudipta Mukherjee (ME), A Novel Attachment for Affixing to 1321/DEL/1996 12.08.1996 192495 28.10.2005 Anupam Nagory (Student, ME) Luggage Articles 2 Prof. Kunal Ghosh (AE) A Device for Extracting Power from 2673/DEL/1996 02.12.1996 212643 10.12.2007 to-and-fro Wind 1997 S.No. Inventors Title IPA Date Grant Date 1 Dr. D Manjunath, Jayesh V Shah Split-table Atm Multicast Switch 983/DEL/1997 17.04.1997 233357 29.03.2009 1998 S.No. Inventors Title IPA Date Grant Date 1999 1 Prof. K. A. Padmanabhan, Dr. Rajat Portable Computer Prinet 1521/DEL/1999 06.12.1999 212999 20.12.2007 Moona, Mr. Rohit Toshniwal, Mr. Bipul Parua 2000 S.No. Inventors Title IPA Date Grant Date 1 Prof. S. SundarManoharan (Chem), A Magnetic Polymer Composition 858/DEL/2000 22.09.2000 216744 24.03.2008 Manju Lata Rao and Process for the Preparation of the Same 2 Prof. S. Sundar Manoharan (Chem) Magnetic Cro2 – Polymer 933/DEL/2000 22.09.2000 217159 27.03.2008 Composite Blends 3 Prof. S. Sundar Manoharan (Chem) A Magneto Conductive Polymer 859/DEL/2000 22.09.2000 216743 19.03.2008 Compositon for Read and Write Head and a Process for Preparation Thereof 4 Prof. -
Dishant M Pancholi
Dishant M Pancholi Contact Chennai Mathematical Institute Phone: +91 44 67 48 09 59 Information H1 SIPCOT IT Park, Siruseri Fax: +91 44 27 47 02 25 Kelambakkam 603103 E-mail: [email protected] India Research • Contact and symplectic topology Interests Employment Assitant Professor June 2011 - Present Chennai Mathematical Institute, Kelambakkam, India Post doctoral Fellow (January 2008 - January 2010) International Centre for Theoratical physics,Trieste, Italy. Visiting Fellow, (October 2006 - December 2007) TIFR Centre, Bangalore, India. Education School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India. Ph.D, August 1999 - September 2006. Thesis title: Knots, mapping class groups and Kirby calculus. Department of Mathematics, M.S. University of Baroda, Vadodara, India. M.Sc (Mathematics), 1996 - 1998. M.S. University of Baroda, Vadodara, India B.Sc, 1993 - 1996. Awards and • Shree Ranchodlal Chotalal Shah gold medal for scoring highest marks in mathematics Scholarships at M S University of Baroda, Vadodara in M.Sc. (1998) • Research Scholarship at TIFR, Mumbai. (1999) • Best Thesis award TIFR, Mumbai (2007) Research • ( With Siddhartha Gadgil) Publications Homeomorphism and homology of non-orientable surfaces Proceedings of Indian Acad. of Sciences, 115 (2005), no. 3, 251{257. • ( With Siddhartha Gadgil) Non-orientable Thom-Pontryagin construction and Seifert surfaces. Journal of RMS 23 (2008), no. 2, 143{149. • ( With John Etnyre) On generalizing Lutz twists. Journal of the London Mathematical Society (84) 2011, Issue 3, p670{688 Preprints • (With Indranil Biswas and Mahan Mj) Homotopical height. arXiv:1302.0607v1 [math.GT] • (With Roger Casals and Francisco Presas) Almost contact 5{folds are contact. arXiv:1203.2166v3 [math.SG] (2012)(submitted) • (With Roger Casals and Francisco Presas) Contact blow-up. -
Debashish Goswami Jyotishman Bhowmick Quantum Isometry Groups Infosys Science Foundation Series
Infosys Science Foundation Series in Mathematical Sciences Debashish Goswami Jyotishman Bhowmick Quantum Isometry Groups Infosys Science Foundation Series Infosys Science Foundation Series in Mathematical Sciences Series editors Gopal Prasad, University of Michigan, USA Irene Fonseca, Mellon College of Science, USA Editorial Board Chandrasekhar Khare, University of California, USA Mahan Mj, Tata Institute of Fundamental Research, Mumbai, India Manindra Agrawal, Indian Institute of Technology Kanpur, India S.R.S. Varadhan, Courant Institute of Mathematical Sciences, USA Weinan E, Princeton University, USA The Infosys Science Foundation Series in Mathematical Sciences is a sub-series of The Infosys Science Foundation Series. This sub-series focuses on high quality content in the domain of mathematical sciences and various disciplines of mathematics, statistics, bio-mathematics, financial mathematics, applied mathematics, operations research, applies statistics and computer science. All content published in the sub-series are written, edited, or vetted by the laureates or jury members of the Infosys Prize. With the Series, Springer and the Infosys Science Foundation hope to provide readers with monographs, handbooks, professional books and textbooks of the highest academic quality on current topics in relevant disciplines. Literature in this sub-series will appeal to a wide audience of researchers, students, educators, and professionals across mathematics, applied mathematics, statistics and computer science disciplines. More information -
ANNEXURE 1 School of Mathematics Sciences —A Profile As in March 2010
University Yearbook (Academic Audit Report 2005-10) ANNEXURE 1 School of Mathematics Sciences —A Profile as in March 2010 Contents 1. Introduction 1 1.1. Science Education: A synthesis of two paradigms 2 2. Faculty 3 2.1. Mathematics 4 2.2. Physics 12 2.3. Computer Science 18 3. International Links 18 3.1. Collaborations Set Up 18 3.2. Visits by our faculty abroad for research purposes 19 3.3. Visits by faculty abroad to Belur for research purposes 19 4. Service at the National Level 20 4.1. Links at the level of faculty 20 5. Student Placement 21 5.1. 2006-8 MSc Mathematics Batch 21 5.2. 2008-10 MSc Mathematics Batch 22 6. Research 23 1. Introduction Swami Vivekananda envisioned a University at Belur Math, West Bengal, the headquarters of the Ramakrishna Mission. In his conversation with Jamshedji Tata, it was indicated that the spirit of austerity, service and renun- ciation, traditionally associated with monasticism could be united with the quest for Truth and Universality that Science embodies. An inevitable fruit of such a synthesis would be a vigorous pursuit of science as an aspect of Karma Yoga. Truth would be sought by research and the knowledge obtained disseminated through teach- ing, making knowledge universally available. The VivekanandaSchool of Mathematical Sciences at the fledgling Ramakrishna Mission Vivekananda University, headquartered at Belur, has been set up keeping these twin ide- als in mind. We shall first indicate that at the National level, a realization of these objectives would fulfill a deeply felt National need. 1.1. -
Annual Report
THE INSTITUTE OF MATHEMATICAL SCIENCES C. I. T. Campus, Taramani, Chennai - 600 113. ANNUAL REPORT Apr 2015 - Mar 2016 Telegram: MATSCIENCE Telephone: +91-44-22543100,22541856 Fax:+91-44-22541586 Website: http://www.imsc.res.in/ e-mail: offi[email protected] Foreword The Institute of Mathematical Sciences, Chennai has completed 53 years and I am pleased to present the annual report for 2015-2016 and note the strength of the institute and the distinctive achievements of its members. Our PhD students strength is around 170, and our post-doctoral student strength is presently 59. We are very pleased to note that an increasing number of students in the country are ben- efiting from our outreach programmes (for instance, Enriching Mathematics Education, FACETS 2015, Physics Training and Talent Search Workshop) and we are proud of the efforts of our faculty, both at an individual and at institutional level in this regard. IMSc has started a monograph series last year, with a plan to publish at least one book every year. A book entitled “Problems in the Theory of Modular Forms” as ‘IMSc Lecture Notes - 1’ has been published this year Academic productivity of the members of the Institute has remained high. There were several significant publications reported in national and international journals and our faculty have authored a few books as well. Five students were awarded Ph.D., and three students have submitted their Ph.D. theses. Four students were awarded M.Sc. by Research, and two students have submitted their master’s theses under the supervision of our faculty. -
LIST of PUBLICATIONS (1) (With S. Ramanan), an Infinitesimal Study of the Moduli of Hitchin Pairs. Journal of the London Mathema
LIST OF PUBLICATIONS INDRANIL BISWAS (1) (With S. Ramanan), An infinitesimal study of the moduli of Hitchin pairs. Journal of the London Mathematical Society, Vol. 49, No. 2, (1994), 219{231. (2) A remark on a deformation theory of Green and Lazarsfeld. Journal f¨urdie Reine und Angewandte Mathematik, Vol. 449 (1994), 103{124. (3) (With N. Raghavendra), Determinants of parabolic bundles on Riemann surfaces. Proceedings of the Indian Academy of Sciences (Math. Sci.), Vol. 103, No. 1, (1993), 41{71. (4) (With K. Guruprasad), Principal bundles on open surfaces and invariant functions on Lie groups. International Journal of Mathematics, Vol. 4, No. 4, (1993), 535{ 544. (5) Secondary invariants of Higgs bundles. International Journal of Mathematics, Vol. 6, No. 2, (1995), 193{204. (6) On the mapping class group action on the cohomology of the representation space of a surface. Proceedings of the American Mathematical Society, Vol. 124, No. 6, (1996), 1959{1965. (7) (With K. Guruprasad), On some geometric invariants associated to the space of flat connections on an open surface. Canadian Mathematical Bulletin, Vol. 39, No. 2, (1996), 169{177. (8) A remark on Hodge cycles on moduli spaces of rank 2 bundles over curves. Journal f¨urdie Reine und Angewandte Mathematik, Vol. 370 (1996), 143{152. (9) On Harder{Narasimhan filtration of the tangent bundle. Communications in Anal- ysis and Geometry, Vol. 3, No. 1, (1995), 1{10. (10) (With N. Raghavendra), Canonical generators of the cohomology of moduli of parabolic bundles on curves. Mathematische Annalen, Vol. 306, No. 1, (1996), 1{14. (11) (With M. -
Poly-Time Blackbox Identity Testing for Sum of Log-Variate Constant-Width Roabps
Poly-time blackbox identity testing for sum of log-variate constant-width ROABPs Pranav Bisht ∗ Nitin Saxena † Abstract Blackbox polynomial identity testing (PIT) affords ‘extreme variable-bootstrapping’ (Agrawal et al, STOC’18; PNAS’19; Guo et al, FOCS’19). This motivates us to study log-variate read-once oblivious algebraic branching programs (ROABP). We restrict width of ROABP to a constant and study the more general sum-of-ROABPs model. We give the first poly(s)-time blackbox PIT for sum of constant-many, size-s, O(log s)-variate constant-width ROABPs. The previous best for this model was quasi-polynomial time (Gurjar et al, CCC’15; CC’16) which is comparable to brute-force in the log-variate setting. Also, we handle unbounded-many such ROABPs if each ROABP computes a homogeneous polynomial. Our new techniques comprise– (1) an ROABP computing a homogeneous polynomial can be made syntactically homogeneous in the same width; and (2) overcome the hurdle of unknown variable order in sum-of-ROABPs in the log-variate setting (over any field). 2012 ACM CCS concept: Theory of computation– Algebraic complexity theory, Fixed parameter tractability, Pseudorandomness and derandomization; Computing methodologies– Algebraic algorithms; Mathematics of computing– Combinatoric problems. Keywords: identity test, hitting-set, ROABP, blackbox, log variate, width, diagonal, derandom- ization, homogeneous, sparsity. 1 Introduction Polynomial Identity Testing (PIT) is the problem of testing whether a given multivariate polynomial is identically zero or not. The input polynomial to be tested is usually given in a compact representation– like an algebraic circuit or an algebraic branching program (ABP). -
Indian Roots of Cryptography
Algologic Technical Report # 2/2013 The Indian roots of cryptography S. Parthasarathy [email protected] Ref.: newcryptoroots.tex Ver. code: 20190123a Keywords : Alice, Bob, Sita, Rama, Vatsyayana, Kamasutra, Hemachan- dra, Fibonacci, Hindu, Arab, Numeral, Ramanujan, Agarwal, AKS, IITK Abstract This note is a sequel to my article [2] about the dramatis personae of cryptography. The article, provoked a world-wide reaction. In fact, a related Google search resulted in over 6 million hits, making me a kind of celebrity ! For those who care to be more reasonable and logical, here is some more evidence to strengthen the proposal I made earlier in my article about Sita and Rama. 1 The Indian roots of cryptography The article [2] about Alice and Bob, talks about the dramatis personae of cryptography, and proposes a much more meaningful alternative. The au- thor came across many situations when contributions by India are unfairly understated or ignored completely by the cryptography community. We take a quick look at some of them. One remarkable exception is the book by Kim Plofker [15], a well-documented book which is free of bias and exaggeration. Most books on cryptography invariably include the Caesar’s cipher as an example of substitution cipher. It is strange that they all ignore, or are unaware of another substitution cipher which was in use a few centuries before Caesar’s cipher. According to [1] Cryptography is recommended in the Kama Sutra (ca 400 BCE) as a way for lovers to communicate without inconvenient discovery. 1 The Signal Corps Association [3], gives an interesting explanation of the kama sutra cipher. -
Tata Institute of Fundamental Research
Tata Institute of Fundamental Research NAAC Self-Study Report, 2016 VOLUME 2 VOLUME 2 1 Departments, Schools, Research Centres and Campuses School of Technology and School of Mathematics Computer Science (STCS) School of Natural Sciences Chemical Sciences Astronomy and (DCS) Main Campus Astrophysics (DAA) Biological (Colaba) High Energy Physics Sciences (DBS) (DHEP) Nuclear and Atomic Condensed Matter Physics (DNAP) Physics & Materials Theoretical Physics (DTP) Science (DCMPMS) Mumbai Homi Bhabha Centre for Science Education (HBCSE) Pune National Centre for Radio Astrophysics (NCRA) Bengaluru National Centre for Biological Sciences (NCBS) International Centre for Theoretical Sciences (ICTS) Centre for Applicable Mathematics (CAM) Hyderabad TIFR Centre for Interdisciplinary Sciences (TCIS) VOLUME 2 2 SECTION B3 Evaluative Report of Departments (Main Campus) VOLUME 2 3 Index VOLUME 1 A-Executive Summary B1-Profile of the TIFR Deemed University B1-1 B1-Annexures B1-A-Notification Annex B1-A B1-B-DAE National Centre Annex B1-B B1-C-Gazette 1957 Annex B1-C B1-D-Infrastructure Annex B1-D B1-E-Field Stations Annex B1-E B1-F-UGC Review Annex B1-F B1-G-Compliance Annex B1-G B2-Criteria-wise inputs B2-I-Curricular B2-I-1 B2-II-Teaching B2-II-1 B2-III-Research B2-III-1 B2-IV-Infrastructure B2-IV-1 B2-V-Student Support B2-V-1 B2-VI-Governance B2-VI-1 B2-VII-Innovations B2-VII-1 B2-Annexures B2-A-Patents Annex B2-A B2-B-Ethics Annex B2-B B2-C-IPR Annex B2-C B2-D-MOUs Annex B2-D B2-E-Council of Management Annex B2-E B2-F-Academic Council and Subject -
The Monk Who Is Sold on Geometry: an Interview with Mahan Maharaj
The Monk Who is Sold on Geometry: An Interview with Mahan Maharaj Professor Mahan Mj is a young geometric topologist at Ramakrishna Mission Vivekananda University, who combines an esoteric career as a research mathematician and teacher with that of a monk. He belongs to the monastic order, Ramakrishna Mission, founded in 1897 by Swami Vivekananda, a renowned Hindu philosopher. He is currently a Professor in the Department of Mathematics, Ramakrishna Mission Vivekananda University, whose campus is located just outside Belur Math, the Headquarters of the Mission in Kolkata, India. Mahan Mj was recently awarded the Shanti Swarup Bhatnagar Award in the Mathematical Sciences, India’s topmost national award that recognises scientific contributions made by Indian scientists under the age of 45. Initially reluctant to be interviewed, saying that he believed in the “anonymity that a mathematician’s career affords’’, Mahan Mj graciously relented and spoke to Sujatha Ramdorai. Sujatha Ramdorai (SR): Please tell us a little about your background and early education. Mahan Mj (MM): My early schooling was at St Xavier’s College, Kolkata and then I did an Integrated MSc (Maths) degree at IIT Kanpur. SR: When did it become clear to you that a career in Mathematics was what you preferred? MM: It’s the subject I liked most at school. Nevertheless, due presumably to social conditioning, I opted to join the BTech programme at IIT Kanpur in Electrical Engineering for the “security” it would provide. This was, however, with the intention of switching to Maths after the BTech. I expressed the intention of returning to Kolkata and joining ISI (Indian Statistical Institute) Kolkata BStat, a few months into the programme as I didn’t quite enjoy Engineering studies. -
Lipics-CCC-2021-11.Pdf (1
Deterministic Identity Testing Paradigms for Bounded Top-Fanin Depth-4 Circuits Pranjal Dutta # Ñ Chennai Mathematical Institute, India Department of Computer Science & Engineering, IIT Kanpur, India Prateek Dwivedi # Ñ Department of Computer Science & Engineering, IIT Kanpur, India Nitin Saxena # Ñ Department of Computer Science & Engineering, IIT Kanpur, India Abstract Polynomial Identity Testing (PIT) is a fundamental computational problem. The famous depth-4 reduction (Agrawal & Vinay, FOCS’08) has made PIT for depth-4 circuits, an enticing pursuit. The largely open special-cases of sum-product-of-sum-of-univariates (Σ[k]ΠΣ∧) and sum-product- of-constant-degree-polynomials (Σ[k]ΠΣΠ[δ]), for constants k, δ, have been a source of many great ideas in the last two decades. For eg. depth-3 ideas (Dvir & Shpilka, STOC’05; Kayal & Saxena, CCC’06; Saxena & Seshadhri, FOCS’10, STOC’11); depth-4 ideas (Beecken,Mittmann & Saxena, ICALP’11; Saha,Saxena & Saptharishi, Comput.Compl.’13; Forbes, FOCS’15; Kumar & Saraf, CCC’16); geometric Sylvester-Gallai ideas (Kayal & Saraf, FOCS’09; Shpilka, STOC’19; Peleg & Shpilka, CCC’20, STOC’21). We solve two of the basic underlying open problems in this work. We give the first polynomial-time PIT for Σ[k]ΠΣ∧. Further, we give the first quasipolynomial time blackbox PIT for both Σ[k]ΠΣ∧ and Σ[k]ΠΣΠ[δ]. No subexponential time algorithm was known prior to this work (even if k = δ = 3). A key technical ingredient in all the three algorithms is how the logarithmic derivative, and its power-series, modify the top Π-gate to ∧. 2012 ACM Subject Classification Theory of computation → Algebraic complexity theory Keywords and phrases Polynomial identity testing, hitting set, depth-4 circuits Digital Object Identifier 10.4230/LIPIcs.CCC.2021.11 Funding Pranjal Dutta: Google Ph. -
Classifying Polynomials and Identity Testing
Classifying polynomials and identity testing MANINDRA AGRAWAL1,∗ and RAMPRASAD SAPTHARISHI2 1Indian Institute of Technology, Kanpur, India. 2Chennai Mathematical Institute, and Indian Institute of Technology, Kanpur, India. e-mail: [email protected] One of the fundamental problems of computational algebra is to classify polynomials according to the hardness of computing them. Recently, this problem has been related to another important problem: Polynomial identity testing. Informally, the problem is to decide if a certain succinct representation of a polynomial is zero or not. This problem has been extensively studied owing to its connections with various areas in theoretical computer science. Several efficient randomized algorithms have been proposed for the identity testing problem over the last few decades but an efficient deterministic algorithm is yet to be discovered. It is known that such an algorithm will imply hardness of computing an explicit polynomial. In the last few years, progress has been made in designing deterministic algorithms for restricted circuits, and also in understanding why the problem is hard even for small depth. In this article, we survey important results for the polynomial identity testing problem and its connection with classification of polynomials. 1. Introduction its simplicity. For example, consider the polyno- mials The interplay between mathematics and computer ··· science demands algorithmic approaches to vari- (1 + x1)(1 + x2) (1 + xn) ous algebraic constructions. The area of computa- and tional algebra addresses precisely this. The most fundamental objects in algebra are polynomials x1x2 ···xn. and it is a natural idea to classify the polyno- mials according to their ‘simplicity’. The algorith- The former has 2n − 1 more terms than the later, mic approach suggests that the simple polynomials however, both are almost equally easy to describe are those that can be computed easily.