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Abstracts for PLeaSANT

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A discriminated problem about discriminants

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Speaker: 
Wadim Zudilin
Affiliation: 
Radboud University Nijmegen/MPIM
Date: 
Tue, 07/04/2026 - 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
PLeaSANT

Fairly optimal lower bounds are known for the discriminants of number fields are known but they seem to be far from the truth in the case of monogenic number fields, that is, for the discriminants of (monic) irreducible polynomials with integer coefficients. This problem appears in the 1990 review of Odlyzko as Open Problem 2.5, with attribution to Serre "and others." I will try to update on the recent development and connections with Lehmer's question on the Mahler measure.

A Habiro formalism for CM points

Posted in
Speaker: 
Pengcheng Zhang
Affiliation: 
MPIM
Date: 
Mon, 13/04/2026 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
PLeaSANT
In this talk, we will present a Habiro-ring-like object encoding the information of CM points and singular moduli, which may contribute to a Habiro formalism for CM points.
 
We will start with the original Habiro ring defined by Habiro, explain how to view elements in the Habiro ring as power series expansions at roots of unity as well as functions on roots of unity, and sketch Habiro's proof of the injectivity of these associations via congruences of cyclotomic polynomials.
 
We will then recall the theory of s

Maximal degree extension needed to define an isogeny over a finite field

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Speaker: 
Stevan Gajovic
Affiliation: 
MPIM
Date: 
Mon, 20/04/2026 - 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
PLeaSANT

The Honda-Tate theorem classifies abelian varieties over finite fields up to isogenies. We use this theorem to answer the following question: if two abelian varieties over $\mathbb{F}_q$ of dimension $g$ become isogenous over some extension of $\mathbb{F}_q$, but not over any proper subfield, how large can the degree of this extension be (in terms of $g$)?

Multiple zeta star values, limits, and pi-power identities

Posted in
Speaker: 
Steven Charlton
Affiliation: 
Universität zu Köln
Date: 
Tue, 28/04/2026 - 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
PLeaSANT

Multiple zeta (star) values are a multivariable generalisation of Riemann zeta values like $\zeta(2)=\pi^2/6$ and $\zeta(3)$; their arithmetic nature (irrational or transcendental) is still largely conjectural.  They play a rather important role in high-energy physics calculations, acting as a bridge between number theory and particle physics.  One of the main goals is to understand their algebraic structure, and all of the relations and identities they satisfy.

 

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