FGC-HRI-IPM Joint Number Theory Seminar
When: Wednesdays
Where: Zoom
Meeting ID: 85613860958
Seminar mailing list: google group
Past Seminar Series
Talks
Speaker: Firtina Kucuk, University College, Dublin
Title: Factorization of algebraic p-adic Rankin-Selberg L-functions
Abstract: I will give a brief review of Artin formalism and its p-adic variant.
Artin formalism gives a factorization of L-functions whenever the associated Galois representation decomposes.
I will explain why establishing the p-adic Artin formalism (or its algebraic counterpart via the Iwasawa Main Conjectures)
is a non-trivial problem when there are no critical L-values. In particular, I will focus on the case where the Galois
representation arises from a self-Rankin-Selberg product of a newform, and present the results in this direction including the one I obtained in my PhD thesis.
Date: April 3, 2024
Speaker: Emre Sertoz, Leiden University
Title: Computing linear relations between univariate integrals
Abstract: The study of integrals of univariate algebraic functions (1-periods) provided the impetus to develop much
of algebraic geometry and transcendental number theory. This old saga is now at a point of resolution. In 2022, Huber
and Wüstholz gave a "qualitative description" of all linear relations with algebraic coefficients between 1-periods.
New techniques for determining symmetries of complex tori allow us to develop algorithms to
explicate these qualitative relations and decide the transcendence of 1-periods. This is a work-in-progress with Joël Ouaknine (MPI SWS) and James Worrell (Oxford).
Date: March 20, 2024
Speaker: Hamed Mousavi, King's College London
Title: Pointwise Ergodic Theorem Along Primes
Abstract: In this talk, we will be exploring the pointwise convergence of ergodic averages along
the primes. Our discussion will begin by explaining the contributions of Birkhoff, as
well as the efforts made by Bourgain and Wierdl in this direction, which was concluded
by Mirek’s proof of pointwise ergodic convergence for primes. Additionally, we will be
presenting some of our own results on structure theorems in the endpoint case Lplogq,
along with a pointwise ergodic theorem in the Gaussian setting. Moving forward, we will
briefly mention the breakthrough result made by Krause-Mirek-Tao on bilinear ergodic
averages. This will be departing point in our current project on the pointwise ergodic
theorem for bilinear averages along prime numbers. If time allows, we will provide a toy
model example in linear theory, which will demonstrate a typical method used in this
area of study.
Date: March 6, 2024
Speaker: Haydar Goral, Izmir (Turkey)
Title: Counting arithmetic progressions modulo p
Abstract: In 1975, Szemeredi gave an affirmative answer to Erdös and Turan's conjecture
which states that any subset of positive integers with a positive upper density contains arbitrarily
long arithmetic progressions. Szemeredi-type problems have also been extensively studied in subsets
of finite fields. While much work has been done on the problem of whether subsets of finite fields
contain arithmetic progressions, in this talk we concentrate on how many arithmetic progressions
we have in certain subsets of finite fields. The technique is based on certain types
of Weil estimates. We obtain an asymptotic for the number of k-term arithmetic progressions
in squares with a better error term. Moreover our error term is sharp and best possible
when k is small, owing to the Sato-Tate conjecture. This work is supported by the Scientific and Technological Research Council of Turkey with the project number 122F027.
Date: February 21, 2024
Speaker: Simon Myerson, University of Warwick
Title: A two dimensional delta method and applications to quadratic forms
Abstract: We develop a two dimensional version of the delta symbol method and apply it to
establish quantitative Hasse principle for a smooth pair of quadrics defined over Q in at least 10
variables. This is a joint work with Pankaj Vishe (Durham) and Junxian Li (Bonn).
Date: February 7, 2024