Geometry, Algebra, Number Theory, and Their Information Technology Applications

Overview of the work of Kumar Murty (A. Akbary, S. Gun, M. Ram Murty).- On the average value of a function of the residual index (A. Akbary, A. T. Felix).- Applications of the square sieve to a conjecture of Lang and Trotter for a pair of elliptic curves over the rationals (S. Baier, V. M. Patankar).- $R$-group and multiplicity in restriction for unitary principal series of $GSpin$ and $Spin$ (D. Ban, K. Choiy, D. Goldberg).- The $2$-Class Tower of $\mathbb{Q}(\sqrt{-5460})$ (N. Boston, J. Wang).- On the bad reduction of certain $U(2,1)$ Shimura varieties (E. de Shalit, E. Goren).- Density modulo 1 of a sequence associated to a multiplicative function evaluated at polynomial arguments (J.-M. Deshouillers, M. Nasiri-Zare).- Uniqueness Results for a class of $L$-functions (A. Dixit).- Quadratic periods of meromorphic forms on punctured Riemann surfaces (P. Eskandari).- On the local coefficients matrix for coverings of $\SL_2$ (F. Gao, F. Shahidi, D. Szpruch).- Eisenstein series of weight one, $q$-averages of $0$-logarithm and periods of elliptic curves (D. R. Grayson, D. Ramakrishnan).- On zeros of certain cusp Forms of integral weight for full modular group (M. Manickam, Sandeep E. M.).- A note on Burgess bound (R. Munshi).- A smooth Selberg sieve and applications (M. Ram Murty, A. Vatwani).- Explicit arithmetic on abelian varieties (V. Kumar Murty, P. Sastry).- Derived categories of moduli spaces of vector bundles on curves II (M. S. Narasimhan).- Representations of an integer by some quaternary and octonary quadratic forms (B. Ramakrishnan, B. Sahu, A. K. Singh).- A topological realization of the congruence subgroup kernel (J. Scherk).- Fine Selmer groups and isogeny invariance (R. Sujatha, M. Witte).- Distribution of a subset of non-residues modulo $p$ (by R. Thangadurai, V. Kumar).- On solving a generalized Chinese remainder theorem in the presence of remainder errors (G. Xu).- Endomorphism algebras of abelian varieties with special reference to superelliptic