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: Chennai Mathematical Institute, 2004
: Chennai Mathematical Institute, 2006
: University of New Mexico, 2012
Arithmetic jet spaces.
Connections of arithmetic jet spaces to p-adic Hodge theory as well as p-adic modular forms.
, Max Planck Institute, Bonn, Germany (2018 - Present)
,Indian Statistical Institute, Bangalore (2018 - 2018)
, Australian National University, Australia (2012 - 2018)
, University of New Mexico, USA (2006 - 2012)
Selected Recent Publications
Isocrystals associated to arithmetic jet spaces of abelian schemes (with J. Borger), to appear in Advances in Mathematics, arXiv:1712.09346.
Differential characters of Drinfeld modules and de Rham cohomology (with J. Borger), to appear in Algebra and Number Theory, arXiv:1703.05677.
Differential modular forms over totally real fields of non zero integral weights (with D. Banerjee), submitted, arXiv:1806.00191
On Frobenius and Fibers of Arithmetic Jet Spaces (with J. Borger), arXiv:1703.07010
Lift of Frobenius and descent to constants, arXiv:1703.06479.
Invariant rational forms for correspondences of curves, Journal of Number Theory 143:170-184, 2014.
The first p-jet space of an elliptic curve: global functions and lifts of Frobenius (with A. Buium), Mathematical Research Letters, 21(4):677- 689, 2014.
Hecke operators on differential modular forms mod p (with A. Buium), Journal of Number Theory 132(5):966-997, 2012.
The ring of differential Fourier expansions (with A. Buium), Journal of Number Theory 132(5):896-937, 2012.
Differential Overconvergence (with A. Buium), Algebraic methods in dynamical systems, volume 94 of Banach Center Publications, pages 99-129. Polish Acad. Sci. Inst. Math., Warsaw, 2011.
Atul Abhay Dixit
H. N. Mhaskar
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