Diophantine approximation on planar curves

Day and Date: Wednesday (April 26, 2017)

Time: 11.30  am to  12:30 pm

Venue: Conference Room, Dept. of Mathematics, First floor SSE building

Abstract: The well-known theorems of Khintchine and Jarnik in Diophantine approximation provide a comprehensive description of the measure theoretic properties of real numbers approximable by rational numbers with a given error. Various generalisations of these fundamental results have been obtained for other settings, in particular, for curves and more generally manifolds. In this talk, I will explain my recent Jarnik type results for a parabola in homogeneous settings. This result is the first of its kind.

Dr. Mumtaz Hussain is a faculty member at La Trobe University (Australia).

Speaker Biography:

Dr Mumtaz Hussain is currently a tenured faculty member at La Trobe university (Australia). Dr Hussain graduated with a PhD from the University of York (UK) after having an M. Phil degree from Quad–i–Azam university (Pakistan).  Prior to his current position Dr Hussain held postdoctoral positions at Aarhus university (Denmark), the university of Newcastle (Australia),  La Trobe university (Australia) and Brandeis university (USA). Dr. Hussain’s main research strengths are in analytic number theory, dynamical systems and ergodic theory. Dr Hussain has a significant number of publications in leading international journals with renowned researcher across the world. Dr Hussain as made significant contributions in developing a comprehensive metrical theory for absolute value linear forms and, further, established links of this theory in signal processing.