FGC-HRI-IPM Joint Number Theory Seminar

FGC, HRI and IPM are holding a joint biweekly zoom Number Theory seminar for 2022.

When: Tuesdays
Where: Zoom
Seminar mailing list: google group


Speaker: Abbas Maarefparvar (IPM, Iran)
Title: On BRZ exact sequence for finite Galois extensions of number fields
Abstract: In this talk, I will shortly explain how to use some cohomological results of Brumer-Rosen and Zantema to obtain a four-term exact sequence, called ``BRZ’’ standing for these authors, which reveals some information about strongly ambiguous ideal classes (coinciding with relative Polya group) of a finite Galois extension of number fields. As an application of the BRZ, I will reprove some well known results in the literature. Then, as a minor modification on relative Polya group for a finite extension of number fields, I will introduce the notion of ``relative Ostrowski quotient'' and give some new approaches of the BRZ exact sequence. The main part of my talk is concerning a joint work with Ali Rajaei and Ehsan Shahoseini.
Date: June 14, 2022

Speaker: Somnath Jha (IIT Kanpur, India)
Title: Fine Selmer group of elliptic curves over global fields
Abstract: The (p-infinity) fine Selmer group (also called the 0-Selmer group) of an elliptic curve is a subgroup of the usual p-infinity Selmer group of an elliptic curve and is related to the first and the second Iwasawa cohomology groups. Coates-Sujatha observed that the structure of the fine Selmer group over the cyclotomic Z_p extension of a number field K is intricately related to Iwasawa's \mu-invariant vanishing conjecture on the growth of p-part of the ideal class group of K in the cyclotomic tower. In this talk, we will discuss the structure and properties of the fine Selmer group over certain p-adic Lie extensions of global fields. This talk is based on joint work with Sohan Ghosh and Sudhanshu Shekhar.
Date: May 31, 2022
Video link

Speaker: Hamza Yesilyurt (Bilkent University, Ankara, Turkey)
Title: A Modular Equation of Degree 61
Abstract: A modular equation of degree n is an equation that relates classical theta functions with arguments q and q^n. The theory of modular equations started with the works of Landen, Jacobi and Legendre. The theory gained popularity again with enormous contributions made by Ramanujan. In this talk we will give a brief introduction to the theory of modular equations and then obtain a new modular equation of degree 61 by using a generalization of a theta function identity due to David M. Bressoud. This is a joint work with Ahmet Güloğlu.
Date: May 17, 2022
Video link

Speaker: Chirantan Chowdhury (University of Duisburg-Essen)
Title: Motivic Homotopy Theory of Algebraic Stacks
Abstract: In this talk, we extend the stable motivic homotopy theory from schemes to a large class of algebraic stacks using the language of ∞-categories. This includes quasi-separated algebraic spaces, local quotient stacks (for example moduli of vector bundles). We also extend the six functor formalism and prove statements like localization and purity. We start the talk by motivating the need of such specific class of algebraic stacks which shall lead up to the construction of the stable homotopy functor and the four functors f∗ , f∗, − ⊗ − and Hom(−, −). We then briefly explain the motivation of ”Enhanced operation map” due to Liu and Zheng which helps us to construct the exceptional functors. The talk ends by stating the other properties of these six functors like localization and purity.
Date: April 19, 2022
Video link

Speaker: Farzad Aryan (Göttingen University)
Title: On the Riemann Zeta Function
Abstract :I will discuss the Riemann zeta function and the significance of its zeros to prime numbers. Also, I will look at the distribution of zeta zeros and mention some of my related works on the subject.
Date: April 5, 2022
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Speaker: Semih Ozlem (Yeditepe University, Turkey)
Title: On the motivic Galois group of a number field
Abstract : Aim of this talk is to briefly introduce the motivic Galois group and state a potential answer to Langlands' conjecture regarding the relation of Langlands' group and motivic Galois group.
Date: March 15, 2022
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Speaker: Cristian David Gonzalez Aviles (Universidad de La Serena, Chile)
Title : Totally singular algebraic groups
Abstract : I will define the groups of the title and discuss some examples. When they are of positive dimension, these groups exist only over an imperfect field. We will see examples in dimension 1 related to the purely inseparable forms of the additive group studied by Russell in 1970. We will also see some examples of arbitrarily high dimensions. I hope to convince the audience that this class of algebraic groups is both interesting and quite large!
Date: February 1, 2022
Video link