Professor
Department of Mathematical Sciences
📍 AB2 2F8
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Research Area
Algebraic Geometry, Algebraic Number Theory, Algebraic Topology
Research Interests
1. Construction of Algebraic Cycles as indicated by the Beilinson-Bloch conjectures.
2. Nori motives and related questions and problems.
3. Algebraic varieties that represent modular forms.
4. Various aspects of constructive mathematics and computability. 5. Computational aspects of number theory.
2023 - 2025 : Member (Convenor for 2023 - 2024), Sectional Committee for Mathematical Sciences, Indian National Science Academy, New Delhi
Since 2023 : Member of the Editorial Board, University Texts in the Mathematical Sciences, Springer
Since 2022 : Member of the Advisory Board, Proceedings -- Mathematical Sciences, Indian Academy of Sciences, Bangalore
Since 2022 : INSA Representative in Council of the Indian Statistical Institute
2003 - 2011 : Professor, IMSc (on long leave from Aug 2009)
1996 - 2003 : Associate Professor, IMSc
1995 - 1996 : Professor, ISI
1993 - 1998 : Reader, TIFR (on long leave from Nov. 1995)
1990 - 1991 : Visiting Assistant Professor, Department of Mathematics, University of Chicago, Chicago, U.S.A.
1990 : Visiting Member, Max-Planck-Institut für Mathematik, Bonn, Germany
1989 : Exchange Visitor (Indo-French programme), Université de Paris VII, Paris, France
1989 - 1993 : Fellow, TIFR
1987 - 1989 : Research Associate, TIFR
1982 - 1987 : Research Assistant, TIFR
1982 - 1992 : PhD, University of Mumbai (based on work done at TIFR)
1977 - 1982 : M.Sc. (5-year Integrated), Indian Institute of Technology, Kanpur, India
Fellowship of Indian Academy of Sciences Bangalore, 1997.
Fellowship of National Academy of Sciences Allahabad, 1999.
B. M. Birla award for young scientists, 1999.
DST Swarnajayanti Grant, 2001.
Associate of the ICTP, Trieste, 1999-2001.
NBHM National Lecturer, India, 2004-2005.
Shanti Swarup Bhatnagar Award, 2005.
Debian Developer, 2007.
Fellowship of Indian National Science Academy, New Delhi, 2009.
J. C. Bose Fellowship, 2010-2019.
Fellowship of The World Academy of Sciences, Trieste, 2019.
Kapil Paranjape and Dinakar Ramakrishnan. Modular forms and Calabi-Yau varieties. In Arithmetic and geometry. London Math. Soc. Lecture Note Ser. series, volume 420, Cambridge Univ. Press, Cambridge, 2015, pages 351–372.
Mark Green, Philip A Griffiths and Kapil H Paranjape. Cycles over fields of transcendence degree 1. Michigan Math. J. 52(1):181–187, 2004. URL, DOI
Indranil Biswas and Kapil H Paranjape. The Hodge conjecture for general Prym varieties. J. Algebraic Geom. 11(1):33–39, 2002. URL, DOI
Kapil Hari Paranjape. A geometric characterization of arithmetic varieties. Proc. Indian Acad. Sci. Math. Sci. 112(3):383–391, 2002. URL, DOI
Jishnu Biswas, Gautham Dayal, Kapil H Paranjape and G V Ravindra. Higher Abel-Jacobi maps. In Algebra, arithmetic and geometry, Part I, II (Mumbai, 2000). Tata Inst. Fund. Res. Stud. Math. series, volume 16, Tata Inst. Fund. Res., Bombay, 2002, pages 159–169.
Kapil H Paranjape. Cohomological and cycle-theoretic connectivity. Ann. of Math. (2) 139(3):641–660, 1994. URL, DOI
Hélène Esnault and Kapil H Paranjape. Remarks on absolute de Rham and absolute Hodge cycles. C. R. Acad. Sci. Paris Sér. I Math. 319(1):67–72, 1994.
K H Paranjape and V Srinivas. Self-maps of homogeneous spaces. Invent. Math. 98(2):425–444, 1989. URL, DOI
Kapil Paranjape. Abelian varieties associated to certain $K3$ surfaces. Compositio Math. 68(1):11–22, 1988. URL
Kapil Paranjape and S Ramanan. On the canonical ring of a curve. In Algebraic geometry and commutative algebra, Vol. II. Kinokuniya, Tokyo, 1988, pages 503–516.