פעילויות השבוע

Equidistribution of ”special“ points is a theme of both analytic and geometric interest in number theory: in this talk I plan to deal with the case of CM points on Shimura curves.

The first part will be devoted to a geometric description of the aforementioned curves and of their moduli interpretation.Subsequently, I plan to sketch an equidistribution result of reduction of CM points in the special fiber of a Shimura curve associated to a ramified quaternion algebra. Time permitting, I will mention how Ratner‘s theorem and subconvexity bounds on Fourier coefficients of certain theta series can be used to obtain two different equidistribution results.

One easy way of representing knot is via a knot diagram. However, inferring properties of the knot from its diagram and deciding when two diagrams represent the same knot are quite difficult problems. Surprisingly, when the diagram is sufficiently “twisty“ then some structure starts to emerge. I will discuss two results of this nature: hyperbolicity of highly twisted knot diagrams and uniqueness of highly twisted plat diagrams.

Based on joint works with Yoav Moriah, Tali Pinsky and Jessica Purcell. All relevant notions will be explained in the talk.