School of Mathematics  Tata Institute of Fundamental Research  Homi Bhabha Road  Mumbai, 400 005, India E-mail: rajan@math.tifr.res.in Phone: 91-22-22782665 (o) Fax: 91-22-22804610 (o) Phone: 91-22-22804643 (h)  Phone: 91-9869063353 (m)

My main interests are in arithmetic geometry, automorphic forms and representation theory.

List of Publications

In Journals:

1. (with Vijay M. Patankar), Distinguishing Galois representations by their normalized traces, J. Number Theory, 178 (2017) 118-125. PDF file

2. (with Hassan Azad, Indranil Biswas and Shehryar Sikander), Hermitian symmetric space, flat bundle and holomorphicity criterion, Bull. Sci. Math., 140 (2016) 1-10. PDF file

3. (with Supriya Pisolkar), On the splitting fields of generic elements in Zariski dense subgroups, J. Algebra, 457 (2016) 106-128. PDF file

4. (with Manisha Kulkarni and Vijay M. Patankar), Locally potentially equivalent two dimensional Galois representations and Frobenius fields of elliptic curves, J. Number Theory, 164 (2016) 87-102. PDF file

5. On the irreducibility of irreducible characters of simple Lie algebras, Trans. Amer. Math. Soc., 366 (2014) 6443-6481. PDF file

6. (with Chandrasheel Bhagwat and Supriya Pisolkar) Commensurability and representation equivalent arithmetic lattices, International Mathematics Research Notices 2013; doi: 10.1093/imrn/rns282. PDF file

7. (with Chandrasheel Bhagwat) On a multiplicity one property for the length spectra of even dimensional compact hyperbolic spaces, J. Number Theory, 131 (2011) 2339-2344. PDF file

8. An example of non-homeomorphic conjugate varieties, Math. Res. Letters, 18 (2011), no. 05, 937-942. PDF file

9. (with Vijay Patankar) Locally potentially equivalent Galois representations, J. Ramanujan Math. Soc., 27 No. 1 (2012) 77-90. PDF file

10. (with Chandrasheel Bhagwat) On a spectral analogue of the strong multiplicity one theorem, published online in Inter. Math. Res. Notices (IMRN) Nov. 19, 2010, doi:10.1093/imrn/rnq243. PDF file

11. (with Arati S. Khedekar) On cohomology theory of topological groups, Proc. Indian Acad. Sci.(Math. Sci), 2012, vol. 122, no. 2, 221-242. PDF file

12. On isospectral arithmetical spaces, Amer. J. Math., 2007, vol 129, no. 3, 791-806. PDF file

13. (with Najmuddin Fakhruddin) Congruences for rational points of varieties over finite fields, Math. Ann. 333 (2005) no. 4, 797-809. PDF file

14. (with U. K. Anandavardhanan) Distinguished representations, base change, and reducibility for unitary groups, Inter. Math. Res. Notices, 2005, vol. 14, 841-854. PDF file

15. On the non-vanishing of the first betti number of hyperbolic three manifolds, Math. Annalen, 330 (2004) no. 2, 323-329. PDF file

16. Unique decomposition of tensor products of irreducible representations of simple algebraic groups, Annals of Math. 160 (2004), 683-704. PDF file

17. On the vanishing of the measurable Schur cohomology groups of Weil groups, Compos. Math. 140 (2004), no. 1, 84--98. PDF file

18. On strong multiplicity one for automorphic representations, J. Number Theory 102 (2003), no. 1, 183--190. PDF file

19. (with Dipendra Prasad) On an archimedean analogue of Tate's conjecture, J. Number Theory, 99 (2003) no. 1, 180-184. PDF file

20. (with Kirti N. Joshi) Frobenius splitting and ordinarity, Inter. Math. Res. Notices, 2003, vol. 2, 109-121. PDF file

21. On the image and fibres of solvable base change, Math. Res. Letters, 9 (2002) no. 4, 499-508. PDF file

22. (with Chandrashekhar Khare) On Heegner points of large conductor, Math. Res. Letters., 8 no.3, (2001) 275-278. PDF file

23. (with Chandrashekhar Khare) The density of ramified primes in semimple p-adic Galois representations, Internat. Math. Res. Notices, 2001, no. 12, 601-607. PDF file

24. (with T. N. Venkataramana) On the first cohomology of arithmetic groups, Manuscripta Math., 105 (2001) 537-552. PDF file

25. Refinement of strong multiplicity one for automorphic representations of GL(n), Proc. Amer. Math. Soc. 128 (2000), no. 3, 691--700. PDF file

26. On the image and the fibres of the non-normal cubic lift, C. R. Math. Acad. Sci. Soc. R. Can. 22 (2000), no. 1, 1--6. PDF file

27. Automorphisms of X(11) over characteristic $3$ and the Mathieu group $M\sb {11}$, J. Ramanujan Math. Soc. 13 (1998), no. 1, 63--72. PDF file

28. On strong multiplicity one for $l$-adic representations, Internat. Math. Res. Notices 1998, no. 3, 161--172. PDF file

29. Distribution of values of Hecke characters of infinite order, Acta Arith. 85 (1998), no. 3, 279--291. PDF file

30. On the size of the Shafarevich-Tate group of elliptic curves over function fields, Compositio Math. 105 (1997), no. 1, 29--41. PDF file

31. (with K. Guruprasad), Group cohomology and the symplectic structure on the moduli space of representations, Duke Math. J. 91 (1998), no. 1, 137--149. PDF file

32. Vanishing theorems for cohomologies of automorphic vector bundles, J. Differential Geom. 43 (1996), no. 2, 376--409. PDF file

33. Deformations of complex structures on $\Gamma\backslash{\rm SL}\sb 2({C})$, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), no. 2, 389--395. PDF file

In Conference Proceedings:

1. Some questions on Spectrum and Arithmetic of locally symmetric spaces, Advanced Studies in Pure Mathematics 58, 2010, Algebraic Arithmetic Structures of Moduli Spaces (Sapporo 2007) (eds. H. Nakamura and L. Weng) pp. 137-157. PDF file

2. Recovering modular forms and representations from tensor and symmetric powers, Algebra and Number Theory, Proceedings of the Silver Jubilee Conference, University of Hyderabad, ed. R. Tandon, Hindustan Book Agency, (2005) 281-298. PDF file

3. On Langlands functoriality- Reduction to the semistable case, Algebraic Groups and Arithmetic, (eds.) S. G. Dani and G. Prasad, TIFR, Mumbai (2004), 199-219. PDF file

4. An algebraic Chebotarev density theorem, Proceedings of the International conference on Cohomology of arithmetic groups, L-functions and Automorphic Forms, Mumbai 1998 ed. T. N. Venkatramana, Narosa new Delhi, 2001, 158-169. PDF file

5. (with M. Ram Murty), Stronger multiplicity one theorems for forms of general type on ${\rm GL}\sb 2$, Analytic number theory, Vol. 2 (Allerton Park, IL, 1995), 669--683, Progr. Math., 139, Birkhauser Boston, Boston, MA, 1996. PDF file

Preprints:

1. (with S. Subramanian), A universal Torelli theorem for elliptic surfaces, PDF file

Expository articles:

1. On the work of Lafforgue, Fields Medals and Nevanlinna Prize: 2002, Current Sci. 83 no. 9 (2002) 1088-1090. PDF file

2. Weak Mordell-Weil theorem, Elliptic curves, modular forms and cryptography (Allahabad, 2000), 63--72, Hindustan Book Agency, New Delhi, 2003. PDF file

3. Main Conjecture of Iwasawa Theory, Cyclotomic Fields and Related Topics, 185-219. eds S. D. Adhikari, S. A. Katre and D. Thakur, Bhaskarcharya Pratisthana, Pune 2000. PDF file

4. On the work of R. Borcherds, in The work of the Fields medalists, Current Sci. 75 (1998), no. 12, 1290--1295. PDF file

Lecture notes:

1. On the analytic theory of automorphic $L$-functions, Notes of a course of lectures given at the Summer School on Automorphic Forms and Shimura Varieties held at ICTP, Triete, July 2007. PDF file.