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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. -
List of Faculty Members Enjoying Iisc Pay Scale Srl
List of faculty members enjoying IISc pay scale Srl. Name Designation Section Centre 1 Sm. Sanghamitra Bandyopadhyay Director M.I.U. BARANAGORE 2 Rahul Roy Professor (HAG) Stat-Math DELHI 3 Probal Chaudhuri Professor (HAG) Stat-Math BARANAGORE 4 Debasis Sengupta Professor (HAG) Appl. S.U. BARANAGORE 5 Alok Goswami Professor (HAG) Stat-Math BARANAGORE 6 Bhabatosh Chanda Professor (HAG) E.C.S.U. BARANAGORE 7 Anup Dewanji Professor (HAG) Appl. S.U. BARANAGORE 8 Arup Bose Professor (HAG) Stat-Math BARANAGORE 9 Dilip Saha Professor (HAG) G.S.U. BARANAGORE 10 Palash Sarkar Professor (HAG) Appl. S.U. BARANAGORE 11 Satya Ranjan Chakravarty Professor (HAG) E.R.U. BARANAGORE 12 Sm. Mausumi Bose Professor (HAG) Appl. S.U. BARANAGORE 13 Nikhil Ranjan Pal Professor (HAG) E.C.S.U. BARANAGORE 14 Bimal Kr. Roy Professor (HAG) Appl. S.U. BARANAGORE 15 R.B. Bapat Professor (HAG) Stat-Math DELHI 16 B.V. Rajarama Bhat Professor (HAG) Stat-Math BANGALORE 17 Arunava Sen Professor (HAG) Economics & Planning Unit DELHI 18 Abhirup Sarkar Professor (HAG) E.R.U. BARANAGORE 19 Ayanendranath Basu Professor (HAG) I.S.R.U. BARANAGORE 20 Goutam Mukherjee Professor (HAG) Stat-Math BARANAGORE 21 Sm. Amita Majumder Professor (HAG) E.R.U. BARANAGORE 22 Nityananda Sarkar Professor (HAG) E.R.U. BARANAGORE 23 Prabal Roy Chowdhury Professor (HAG) Economics & Planning Unit DELHI 24 Subhamoy Maitra Professor (HAG) Appl. S.U. BARANAGORE 25 Tapas Samanta Professor (HAG) Appl. S.U. BARANAGORE 26 Abhay Gopal Bhatt Professor (HAG) Stat-Math DELHI 27 Atanu Biswas Professor (HAG) Appl. S.U. -
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 -
A NEW APPROACH to UNRAMIFIED DESCENT in BRUHAT-TITS THEORY by Gopal Prasad
A NEW APPROACH TO UNRAMIFIED DESCENT IN BRUHAT-TITS THEORY By Gopal Prasad Dedicated to my wife Indu Prasad with gratitude Abstract. We present a new approach to unramified descent (\descente ´etale") in Bruhat-Tits theory of reductive groups over a discretely valued field k with Henselian valuation ring which appears to be conceptually simpler, and more geometric, than the original approach of Bruhat and Tits. We are able to derive the main results of the theory over k from the theory over the maximal unramified extension K of k. Even in the most interesting case for number theory and representation theory, where k is a locally compact nonarchimedean field, the geometric approach described in this paper appears to be considerably simpler than the original approach. Introduction. Let k be a field given with a nontrivial R-valued nonarchimedean valuation !. We will assume throughout this paper that the valuation ring × o := fx 2 k j !(x) > 0g [ f0g of this valuation is Henselian. Let K be the maximal unramified extension of k (the term “unramified extension" includes the condition that the residue field extension is separable, so the residue field of K is the separable closure κs of the residue field κ of k). While discussing Bruhat-Tits theory in this introduction, and beginning with 1.6 everywhere in the paper, we will assume that ! is a discrete valuation. Bruhat- Tits theory of connected reductive k-groups G that are quasi-split over K (i.e., GK contains a Borel subgroup, or, equivalently, the centralizer of a maximal K-split torus of GK is a torus) has two parts. -
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. -
Tata Institute of Fundamental Research Prof
Annual Report 1988-89 Tata Institute of Fundamental Research Prof. M. G. K. Menon inaugurating the Pelletron Accelerator Facility at TIFR on December 30, 1988. Dr. S. S. Kapoor, Project Director, Pelletron Accelerator Facility, explaining salient features of \ Ion source to Prof. M. G. K. Menon, Dr. M. R. Srinivasan, and others. Annual Report 1988-89 Contents Council of Management 3 School of Physics 19 Homi Bhabha Centre for Science Education 80 Theoretical Physics l'j Honorary Fellows 3 Theoretical A strophysics 24 Astronomy 2') Basic Dental Research Unit 83 Gravitation 37 A wards and Distinctions 4 Cosmic Ray and Space Physics 38 Experimental High Energy Physics 41 Publications, Colloquia, Lectures, Seminars etc. 85 Introduction 5 Nuclear and Atomic Physics 43 Condensed Matter Physics 52 Chemical Physics 58 Obituaries 118 Faculty 9 Hydrology M Physics of Semi-Conductors and Solid State Electronics 64 Group Committees 10 Molecular Biology o5 Computer Science 71 Administration. Engineering Energy Research 7b and Auxiliary Services 12 Facilities 77 School of Mathematics 13 Library 79 Tata Institute of Fundamental Research Homi Bhabha Road. Colaba. Bombav 400005. India. Edited by J.D. hloor Published by Registrar. Tata Institute of Fundamental Research Homi Bhabha Road, Colaba. Bombay 400 005 Printed bv S.C. Nad'kar at TATA PRESS Limited. Bombay 400 025 Photo Credits Front Cover: Bharat Upadhyay Inside: Bharat Upadhyay & R.A. A chary a Design and Layout by M.M. Vajifdar and J.D. hloor Council of Management Honorary Fellows Shri J.R.D. Tata (Chairman) Prof. H. Alfven Chairman. Tata Sons Limited Prof. S. Chandrasekhar Prof. -
Sir Michael Atiyah the ASIAN JOURNAL of MATHEMATICS
.'•V'pXi'iMfA Sir Michael Atiyah THE ASIAN JOURNAL OF MATHEMATICS Editors-in-Chief Shing-Tung Yau, Harvard University Raymond H. Chan, Chinese University of Hong Kong Editorial Board Richard Brent, Oxford University Ching-Li Chai, University of Pennsylvania Tony F. Chan, University of California, Los Angeles Shiu-Yuen Cheng, Hong Kong University of Science and Technology John Coates, Cambridge University Ding-Zhu Du, University of Minnesota Kenji Fulcaya, Kyoto University Hillel Furstenberg, Hebrew University of Jerusalem Jia-Xing Hong, Fudan University Thomas Kailath, Stanford University Masaki Kashiwara, Kyoto University Ka-Sing Lau, Chinese University of Hong Kong Jun Li, Stanford University Chang-Shou Lin, National Chung Cheng University Xiao-Song Lin, University of California, Riverside Raman Parimala, Tata Institute of Fundamental Research Duong H. Phong, Columbia University Gopal Prasad, Michigan University Hyam Rubinstein, University of Melbourne Kyoji Saito, Kyoto University Jalal Shatah, Courant Institute of Mathematical Sciences Saharon Shelah, Hebrew University of Jerusalem Leon Simon, Stanford University Vasudevan Srinivas, Tata Institue of Fundamental Research Srinivasa Varadhan, Courant Institute of Mathematical Sciences Vladimir Voevodsky, Northwestern University Jeff Xia, Northwestern University Zhou-Ping Xin, Courant Institute of Mathematical Sciences Horng-Tzer Yau, Courant Institute of Mathematical Sciences Mathematics in the Asian region has grown tremendously in recent years. The Asian Journal of Mathematics (ISSN 1093-6106), from International Press, provides a forum for these developments, and aims to stimulate mathematical research in the Asian region. It publishes original research papers and survey articles in all areas of pure mathematics, and theoretical applied mathematics. High standards will be applied in evaluating submitted manuscripts, and the entire editorial board must approve the acceptance of any paper. -
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. -
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. -
Arxiv:2009.11521V2 [Math.GT] 4 Mar 2021
PROPAGATING QUASICONVEXITY FROM FIBERS MAHAN MJ AND PRANAB SARDAR π Abstract. Let 1 → K −→ G −→ Q be an exact sequence of hyperbolic −1 groups. Let Q1 < Q be a quasiconvex subgroup and let G1 = π (Q1). Under relatively mild conditions (e.g. if K is a closed surface group or a free group and Q is convex cocompact), we show that infinite index quasiconvex subgroups of G1 are quasiconvex in G. Related results are proven for metric bundles, developable complexes of groups and graphs of groups. 1. Introduction The aim of this paper is to provide evidence in favor of the following Scholium. Scholium 1.1. For an exact sequence π 1 → K −→ G −→ Q → 1 of hyperbolic groups, and more generally for hyperbolic metric bundles, quasicon- vexity in fibers propagates to quasiconvexity in subbundles. There are two specific examples in which the exact sequence in Scholium 1.1 has been studied: (1) When K = π1(Σ) is the fundamental group of a closed surface of genus g > 1, and Q < MCG(Σ). Here, the exact sequence comes from the Birman exact sequence π 1 → π1(Σ) −→ MCG(Σ.∗) −→ MCG(Σ) → 1, where MCG(Σ.∗) denotes the mapping class group of Σ equipped with a marked point ∗. (2) When K = Fn is the free group on n generators (n> 2), and Q < Out(Fn). Here, the exact sequence comes from the Birman exact sequence for free arXiv:2009.11521v2 [math.GT] 4 Mar 2021 groups π 1 → Fn −→ Aut(Fn) −→ Out(Fn) → 1. Date: March 5, 2021. 2010 Mathematics Subject Classification. -
Infosys Prize 2017
Infosys Science Foundation INFOSYS PRIZE 2017 The Romanesco broccoli has fascinated photographers the world over. The brilliant chartreuse and the mesmerizing spiral spines belong to an edible flower bud of the species Brassica oleracea. Grown in Italy since the 16th century, this broccoli- cauliflower hybrid is nutritionally rich, with a delicate nutty flavor. Romanesco thus demands as much interest from chefs as from botanists and researchers. But it doesn’t stop there – peer closely and you will see just how incredible it really is. For it is one of the earth’s most stunning natural fractals. In other words, each of its buds is composed of a series of smaller buds, all arranged in yet another logarithmic spiral. The same pattern continues at several diminishing size levels. Studies of fractals found in nature, such as a snowflake or lightning bolts or indeed the Romanesco broccoli, trace a path to modern applications in computer graphics. We tend to divide and study distinct subjects – physics, biology, math, engineering and so on – only to find one interconnected universe. And it gets even more bizarre. The number of spirals on the head of a Romanesco broccoli is a natural approximation of the Fibonacci number. Named after the Italian mathematician, the Fibonacci spiral is a logarithmic spiral where every quarter turn is farther from the origin by a factor of phi, the golden ratio. How about that for a little bit of math in your soup? ENGINEERING AND COMPUTER SCIENCE The Infosys Prize 2017 in Engineering and Computer Science is awarded to Prof. Sanghamitra Bandyopadhyay for her scholarly record in algorithmic optimization and for its significant impact on biological data analysis. -
Contributions to Algebraic Number Theory from India
Contributions to Algebraic Number Theory from India Dipendra Prasad October 19, 2004 There was a conference organised at the Institite of Mathematical Sciences, Madras in 1997 on the occasion of the 50th anniversary of India’s Independence to review contributions by Indians to various branches of mathematics since In- dependence. This is a written account of the lecture I gave then on some of the contributions by Indian mathematicians to Algebraic number theory for the period 1947-1997. There has been a lot of work done in India during these years, and it will be impossible to report on all of it in limited space. We have therefore chosen some of the representative works from the vast literature reflecting to some extent the author’s taste. Since this was a report about work done in the country, works of several very prominent mathematicians from India during this period who worked for most of their scientific career outside India has been omitted. In particular, we do not speak about the work of S. Chowla who has contributed so much to so many areas of Algebraic number theory. We have also restricted ourselves to areas very closely related to Algebraic number theory, and have therefore omitted topics in transcendental and analytic number theory which was reported by others in the conference. We have also omitted from our consideration the arithmetic theory of algebraic groups. In particular, we do not speak on the work of K.G. Ramanathan who initiated the study of arithmetic groups in the country which has flourished into a very strong area of research at the Tata Institute, Bombay.