Title: Digits of the sum of proper divisors

Abstract: Let s(n) denote the sum of proper divisors of a positive 

integer n. In 1992, Erdös, Granville, Pomerance, and Spiro 

conjectured that if A is a set of integers with asymptotic 

density zero then the preimage set s^{-1}(A) also has 

asymptotic density zero. In this talk, we will discuss the verification 

of this conjecture when A is  the set of integers with 

missing digits (also known as ellipsephic integers) by giving a 

quantitative estimate on the size of the set s^{-1}(A). We 

then discuss the further digital properties of the sum of proper 

divisors function. This talk is based on the joint works with Giulia 

Cesana, Cécile Dartyge, Charlotte Dombrowsky, Paul Pollack and Lola Thompson.

Title: In Silico Çalışmalarda İstatistiksel Öğrenme

Abstract: Biyolojik ve kimyasal süreçlerin laboratuvar ortamı (in vivo/in vitro) yerine bilgisayar simülasyonları, matematiksel modeller ve istatistiksel öğrenme yaklaşımları aracılığıyla incelenmesini ifade eden in silico yöntemler, günümüzde deneysel araştırmaların zaman ve maliyet kısıtlarını aşmada kritik bir rol oynamaktadır. In silico veri analitiğinde karşılaşılan etiket kıtlığı, yüksek boyutluluk ve belirsizlik yönetimi gibi temel istatistiksel problemlere odaklanan bu seminerde, hesaplamalı biyo-istatistik ve toksikoloji alanında yürütülen bağımsız araştırmalar özetlenecektir. Seminer kapsamında, kısıtlı etiketli verilerde sahte etiketleme ve özellik ağırlıklandırma ile çalışan Genelleştirilmiş Yarı Denetimli Regresyon Sinir Ağı (GSSRNN) mimarisi, PFAS kimyasallarının çok boyutlu organ risklerini spektral ayrıştırma (PCA) ve Gaussian Karma Modelleri (GMM) ile skalerleştiren Bileşik Toksisite İndeksi (CTI), içme suyundaki arsenik maruziyetini Monte Carlo simülasyonlarıyla modelleyen açık kaynak kodlu Python tabanlı risk analiz kütüphanesi ve itfaiyecilerde mesleki PFAS maruziyetine bağlı genotoksisite risklerinin değerlendirilmesi sezgisel, matematiksel ve istatistiksel öğrenme odaklı bir çerçevede sunulacaktır.

Title: Vanishing Behaviors: From Burnside's Theorem to Group Classification

Abstract: Given a finite group G, the relationship between its conjugacy classes and irreducible characters is a central topic in group theory. A classical theorem of Burnside establishes that every non-linear irreducible character of G vanishes on at least one conjugacy class; equivalently, each non-linear row of the character table contains a zero. This result reveals a deep connection between the arithmetic properties of irreducible characters and the underlying structure of the group.

In this talk, we investigate how the presence, distribution, and patterns of zeros in the character table influence the structure of G. We discuss how such vanishing behavior can be used to derive information about important group-theoretic properties. We also highlight developments that build on Burnside’s observation, illustrating how a closer analysis of zeros of characters provides a useful perspective for understanding and classifying finite groups.

Title: The arithmetic of function fields: From Drinfeld modules to generalizations of elliptic sheaves

Abstract: Number fields and function fields over finite fields share many properties, and this analogy plays an important role in modern arithmetic geometry. On the function field side, the role of elliptic curves is played by Drinfeld modules. 

I will start with an introduction to Drinfeld modules and their similarities with elliptic curves. I will then explain Drinfeld's reformulation of these objects as elliptic sheaves together with some known generalizations. In the second part of the talk, I will present my own work on generalized D-elliptic sheaves and their uniformization. I will end with some ongoing works and future directions.

No background on function field arithmetic will be assumed.