Department of Mathematics

Indian Institute of Science Education and Research Bhopal

Office: 312, Infinity Building

Phone: (0755)6691269

E-mail: abhand[at]iiserb[dot]ac[dot]in

[**Fall 2023:** MTH410 Representation Theory] [**Winter 2024:**MTH 324/424 Mathematical methods of classical mechanics]

Me and Atreyee Bhattacharya are organizing the Problem solving seminar this year.

I am also involved with the Math Circles of India initiative.

Differential geometry: connections on principal bundles, symmetry and reduction of mechanical systems

Algebra and number theory: modular forms, class groups of number fields, representation theory of GL(n) over finite and local fields

Other interests: Hausdorff measure of self-similar sets, applications of number theory to physics

*Research supported by the SERB grant MTR/2019/000582.*

Mock modularity in CHL models (with Ashoke Sen and Ranveer Kumar Singh) arXiv e-print

Maass lifts of half-integral weight Eisenstein series and theta powers (with Karam Deo Shankhadhar and Ranveer Kumar Singh), *Pacific Journal of Mathematics,* Vol. 321 (2022), No. 1, 1â€“43.

Bhargava's cube and Black Hole Charges (with Nabamita Banerjee, Suvankar Dutta, Ashoke Sen and Ranveer Kumar Singh), *Research in the Mathematical Sciences,* 8 (2021), no. 1, 3.

Zagier's 3/2-weight mock modular form (with Ranveer Kumar Singh), *preprint*.

Dualizing involutions on the metaplectic GL(2) (with Kumar Balasubramanian), *Journal of Pure and Applied Algebra *, 225 (2021), no. 1, 106479, 15 pp.

A note on lower bounds of heights of non-zero Fourier coefficients of Hilbert cusp forms (with Sanoli Gun and P. Rath), *Archiv der Mathematik, *114 (2020), no. 3, 285â€“298.

Class numbers of quadratic fields (with M. Ram Murty), *Hardy-Ramanujan Journal,* 42 (2019), 17-25.

Dirichlet series attached to quasimodular forms (with Karam Deo Shankhadhar). *Journal of Number Theory,* 202 (2019), 91â€“106.

Geodesic reduction via frame bundle geometry. *Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, 6 (2010), 020, 17 pages.

Naveen Kumar (Ph.D.), *ongoing*

Gurleenkaur Nanda (BS-MS Thesis), *Representation theoretic characterization of particles*, 2021-22.

Koustav Mondal (BS-MS Thesis), *Universal quadratic forms *, 2020-21

Ranveer Kumar Singh (BS-MS Thesis),* Applications of number theory in string theory, 2019-20*

Antony James(BS-MS Thesis), *Bhargava's cubes and higher composition laws, 2018-19.*

Ashok Kumar (BS-MS Thesis), *Sieves in number theory*. 2017-18

Merin Abraham (BS-MS Thesis), *Dynamics of singularly perturbed polynomials, 2016-17*.

Sweta Pandey (BS-MS Thesis), *Estimation of Hausdorff measure of fractals, 2014-15*.