Title: Fibonacci and related numbers in determinants

Abstract: There are many references to matrices or determinants that have Fibonacci numbers as elements. In this talk, we show several determinants expressing the Fibonacci and related polynomials. This method is well-applicable to other numbers or polynomials too. In addition, these results, based on the form of the Hessenberg matrix, allow for many applications such as inverse formulas, explicit expressions, and continued fraction...

Title: Singularities of generic mean curvature flows

Abstract: Surfaces evolving by mean curvature flow in R3 can develop rather complicated singularities. However, it was conjectured by Huisken that generically only very simple singularities can form. This conjecture was recently resolved by works of Chodosh-Choi-Mantoulidis-Schulze and Bamler-Kleiner. I will discuss these results, as well as what more we can say.

Professor Szekelyhidi is given a special lecture on some of the introductory...