This workshop will feature four short courses on various topics in number theory ranging from beginner’s to theadvanced level. Briefly, the short course on the following listed topics.
Ramanujan’s theta functions and series for 1/π will survey the main properties of theta functions that have applications in number theory. In particular, by taking inspirations from Ramanujan, a large number of explicit examples will bediscussed. Introduction to analytical number theory will focus on fundamentals in analytical number theory such as continued fractions, prime number theorem, Riemann zeta function and Euler’s formula. Dynamical methods in number theory will focus on classical and modern applications of ergodic theory and dynamicalsystems in Diophantine problems. Metric number theory will focus on the the quantitative study of density of rational numbers in real number system. In particular, the course will focus on range of ideas and techniques in Diophantine approximation and fractal geometry.
National Center for Mathematics
Abdus Salam School of Mathematical Sciences