Upcoming seminars June 9 (Thu), 2022, 10:0011:00, TBA Title: On the probability distribution of $2$Selmer groups of quadratic twist families of elliptic curves over global function fields Speaker: Sun Woo Park (University of WisconsinMadison / NIMS) Abstract: We present recent progress on computing the probability distribution of $2$Selmer groups of quadratic twist families of a nonisotrivial elliptic curve $E$ over global function fields $\mathbb{F}_q(t)$ of characteristic coprime to $2$ and $3$. The elliptic curves we consider satisfy the condition that the Galois groups of the field extensions generated by their $2$torsion points are isomorphic to $S_3$. The key component of this talk will focus on how the Riemann hypothesis over $\mathbb{F}_q(t)$ allows one to show that the probability distribution conforms to the PoonenRains heuristics with explicit error bounds, a simplification of previous wellstudied approaches on computing the desired distribution over the rational numbers $\mathbb{Q}$. July 21 (Thu), 2022, 10:0011:00, online Title: TBA Speaker: Gilyoung Cheong (UC Irvine) Abstract: TBA 
Past seminars March 31 (Thu), 2022, 10:0011:00, online Title: Continued fraction expansions in real quadratic field and an invariant measure of GaussKuzmin type in dimension two Speaker: Junyeong Park (Seoul National University) Abstract: We investigate a twodimensional dynamical system that models a Euclidean algorithm for algebraic integers in the real quadratic field of discriminant five. It represents certain nonsimple continued fraction expansions. A Markov partition is exhibited, which we use to prove that the transfer operator has a dominant eigenvalue. As a consequence, we show that it has a unique invariant probability measure which is absolutely continuous with respect to the Lebesgue measure. The system is expanding in a nonuniform way. This is joint work with Dohyeong Kim. April 21 (Thu), 2022, 10:0011:00, online Title: On Stevenhagen's conjecture Speaker: Peter Koymans (University of Michigan) Abstract: In this talk we will study the negative Pell equation, which is the conic $C_D : x^2  D y^2 = 1$ to be solved in integers $x, y \in \mathbb{Z}$. We shall be concerned with the following question: as we vary over squarefree integers $D$, how often is $C_D$ soluble? Stevenhagen conjectured an asymptotic formula for such $D$. Fouvry and Klüners gave upper and lower bounds of the correct order of magnitude. We will discuss a proof of Stevenhagen's conjecture, and potential applications of the new proof techniques. This is joint work with Carlo Pagano. May 12 (Thu), 2022, 17:0018:00, online Title: Polarizations of abelian varieties over finite fields via canonical liftings Speaker: Stefano Marseglia (Utrecht University) Abstract: We describe all polarizations for all abelian varieties over a finite field in a fixed isogeny class corresponding to a squarefree Weil polynomial, when one variety in the isogeny class admits a canonical liftings to characteristic zero, i.e., a lifting for which the reduction morphism induces an isomorphism of endomorphism rings. This is joint work with Jonas Bergström and Valentijn Karemaker. May 19 (Thu), 2022, 17:0018:00, online Title: Arithmetic of $\theta$critical $p$adic $L$functions Speaker: Kazim Büyükboduk (University College Dublin) Abstract: In joint work with Denis Benois, we give an étale construction of Bellaïche's $p$adic $L$functions about $\theta$critical points on the Coleman–Mazur eigencurve. I will discuss applications of this construction towards leading term formulae in terms of $p$adic regulators on what we call the thick Selmer groups, which come attached to the infinitesimal deformation at the said $\theta$critical point along the eigencurve, and an exotic ($\Lambda$adic) $\mathcal{L}$invariant. Besides our interpolation of the Beilinson–Kato elements about this point, the key input to prove the interpolative properties of this $p$adic $L$function is a new $p$adic Hodgetheoretic "eigenspacetransition via differentiation" principle. 

Please send one of the organizers an email if you are interested in giving a talk. If you want to receive regular email announcement, please send an email with your name/affiliation, in title of "subscribe", to jilee.math@gmail.com.
The first number theory seminar started March 10th, 2005 and it became a regular seminar since then. For more information on
the early history of the number theory seminar, see the
article (by SoonYi Kang in KIAS News Letter, Fall 2005) and
the following archive files. Archive: 2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  
Number Theory Group at KIAS
Choi, YounSeo 