Mathematics Colloquium: Computing with Modular Forms

Mathematics Colloquium: Computing with Modular Forms


You are cordially invited to attend two colloquia this week given by Wilfried Meidl (RICAM, Austria) on Wednesday, 29 November 2017, in FENS-G055 at 11.30 am, and by İlker İnam (Bilecik Şeyh Edebali University) on Thursday, 30 November 2017, in FENS-L030 at 11 am.

Title: Bent functions and generalized Bent functions

Speaker:: Wilfried Meidl

Date/Time: Wednesday, 29 November 2017,  at 11.30 am

Place: in FENS-G055


Abstract: Bent functions correspond to relative difference sets in the groups Zn2 × Z2 respectively Zn2 × Z2m . Being highly nonlinear, Boolean bent functions have application in cryptography. Whereas there are many constructions of Boolean bent functions, bent functions from Zn2 to Z2m seem to be quite rare. Recently a lot of research has been performed on generalized bent (gbent) functions, which are functions from Zn2 to Z2m satisfying the weaker condi- tion that Hf(1,u) has absolute value 2n/2 for every u  Zn2. In this talk, the main results on gbent functions and bent functions from Zn2 to Z2m are summarized, and some open questions are discussed. 

Title: Computing with Modular Forms 

Speaker:: İlker İnam

Date/Time: Thursday, 30 November 2017, at 11 am

Place:  in FENS-L030


Abstract:  Modular forms are holomorphic functions on the upper half plane that satisfy fundamental symmetry and growth conditions. They have many applications in several branches of mathem- atics and even in physics. Since modular forms are periodic, they are perfect number theoretic objects. Furthermore, the space of modular forms are finite dimensional vector space, hence they are computation-friendly. In this talk, we will introduce modular forms with basic properties and then we will show how one can make computations with them by using Magma Computer Algebra System.