### Schedule for the talks

Tuesday
14:00-14:15 Göral
14:20-14:35 Sertbaş
14:40-14:55 Alkım
15:20-15:35 Süer

1) Speaker: Haydar Göral (Koc University, Turkey)
Title: Heights of Fractions

Abstract: We first define the height function on the field of algebraic numbers. The height function measures the arithmetic complexity of an algebraic number and it has some nice properties. Then, we consider the height of rational numbers and fractions. We show that some certain subsets of rational numbers related to the integers and their sumsets constitute a small portion in the set of fractions.

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2) Speaker: Doga Can Sertbas (Cumhuriyet University, Turkey)

Title: On Harmonic Numbers and Their Generalisations

Abstract: Any partial sum of the harmonic series is called a harmonic number. These numbers are equipped with a lot of combinatorial and analytic properties. In this talk, we mention some of these properties and explain which of these properties hold in some of generalizations of harmonic numbers.

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3) Speaker: Erdem Alkım

Title: Forgotten Properties of Number Theoretic Transform

Abstract: Since Number Theoretic Transform (NTT) is efficient in terms of complexity, it is widely used in post-quantum cryptographic schemes that based on ring version of Learning With Errors (RLWE) problem. Because efficient implementations of NTT use two input butterfly operation, it was widely assumed that degree of the polynomial should be a power of $2$. In this talk, we will show that with adjustments on the butterfly operation NTT can be implemented efficiently for any highly composite degree of polynomial. We will show adjustments for three and five input butterfly operations and also provide generic NTT implementation for the degree $n = 2^i \cdot 3^j \cdot 5^k$ and performance results to show that the algorithm scales comparable results with $n$.

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4) Speaker:  Mojtaba Fadavi (Isfahan University of Technology, Iran)

Title: Encoding into Elliptic Curves over Finite Fields

Abstract: Having an encoding function f : Fq → E(Fq) does not seem easy in general case, and making such function was first mentioned as an open question by Ren ́e Schoof in 1985. In fact, the importance of this encoding functions was emphasized after the introduction of the Identity Based Encryption by Boneh and Franklin. More precisely, many Elliptic curves-based cryptosystems and protocols require this kind of encoding functions from a finite field Fq into Fq-rational points of an elliptic curve. In this presentation I review the history of the probabilistic and deterministic encoding functions and if we have sufficient time I can state some recent progress of this area.

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5) Speaker: Ergün Süer (Bilgi University, Turkey)

Title: Plancherel Formula for SU(2)

Abstract: In this work, we study a constructive proof of the Plancherel formula for the compact group SU(2) by using the Weyl’s integration formula. The arguments of the proof make it possible to generalize the formula to non-compact groups SL(2, C) and SL(2, R). The work consists of several parts. First, we derive the Plancherel formula for finite groups. In the second part, we generalize it to arbitrary compact groups by proving the Peter-Weyl Theorem. In final part, we classify the irreducible representations of SU(2) and give a constructive proof as stated at beginning.