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G-BRL CNU Number Theory Seminar에 관심을 가져주셔서 감사합니다.

2025년 상반기 세미나 일정을 아래와 같이 안내드립니다.

세미나 일정

Date: 25. 04. 04 (Fri) 10:00~
Speaker: Junyeong Park (Chonnam National University)
Title: Arithmetic BF theory

Abstract: In this talk, I first briefly recall the notion of TQFT (Topological Quantum Field Theory). Then I introduce an arithmetic BF theory over number fields.

Date: 25. 04. 04 (Fri) 11:00~
Speaker: OH GYEONGWON (Chonnam National University)
Title: The conductor density of abelian extensions with local conditions and its applications

Abstract: In this talk, I investigate the enumeration of cyclic extensions of odd prime degree $\ell$ over $\mathbb{Q}$ subject to specified local conditions. By ordering these extensions according to their conductors, we derive an asymptotic count with a power-saving error term. As a consequence of our results, I also introduce some applications, such as the distribution of $L$-values and Diophantine stability.

Date: 25. 04. 17 (Thu) 16:30~
Speaker: Jinwoo Choi (Seoul National University)
Title: On a weak form of Ennola's conjecture about certain cubic number fields
Abstract: Unlike the case of real quadratic fields, it is in general hard to determine a complete set of fundamental units for a given family of non-Galois totally real cubic number fields. Ennola’s conjecture is one of unsolved problems on a pair of fundamental units of such a family. St\'ephane Louboutin suggested a weak form of Ennola’s conjecture and provided a conditional proof of it. In this seminar, I introduce the weak form of Ennola's conjecture and complete its conditional proof. This can be done by showing that two main assumptions Louboutin made in his previous work hold true. This is a joint work with Prof. Dohyeong Kim.

Date: 25. 04. 23 (Wed) 16:30~ (전남대학교 사범대학 교육융합관 401호)

Speaker: Hwajong Yoo (Seoul National University)
Title: The rational cuspidal subgroup of J_0(N)

Abstract: We introduce generalized Ogg's conjecture which asserts that the rational torsion subgroup of J_0(N) is equal to the rational cuspidal subgroup of J_0(N).  And then we discuss how to compute the rational cuspidal subgroup of J_0(N) when N is a prime power.

Date: 25. 05. 08 (Thu) 16:30~
Speaker: Yong-Gyu Choi (KAIST)
Title: Degenerations of D-shtukas over ramified legs
Abstract: The canonical integral models of Shimura varieties associated with reductive groups that are anisotropic modulo center are expected to be proper. However, an analogous property is known to be false for the moduli stack of shtukas over global function fields. More precisely, given a proper smooth curve X over a finite field and a parahoric group scheme G over X corresponding to a maximal order of a central division algebra D over the function field of X, Eike Lau obtained a numerical criterion for the properness of the moduli stack of bounded G-shtukas with legs in the split locus of D. As a consequence, there exists an instance where the moduli stack of bounded G-shtukas is not proper over the split locus of D.

Based on the work of Arasteh Rad—Hartl and Bieker, the moduli stack of bounded G-shtukas is allowed to have legs in the ramification locus of D. We extend Lau's result to the case where the legs are allowed to lie in the ramification locus, showing in particular that the moduli stack of G-shtukas can be proper when the legs are restricted to the split locus of D, but not proper when the legs run over the whole curve. This is joint work with Wansu Kim and Junyeong Park.

Date: 25. 05. 23 (Fri) 10:00~
Speaker: Chang Heon Kim (Sungkyunkwan University)
Title: Arithmetic of generalized Hecke operators

Abstract: Generalized Hecke operators originated from the replication formula in Monstrous
Moonshine by Conway, Norton, Koike, Ferenbaugh, etc. In this talk we will extend these operators
to apply to harmonic Maass functions on modular curves of higher genera. Then these operators can be applied to weakly holomorphic modular forms of weight 0, deriving numerous arithmetic properties of
Fourier coefficients (e.g. congruences of Fourier coefficients, Zagier dualities, etc). Further, these operators can be extended to weakly holomorphic modular forms of nonzero weights.  Additionally, we will identify the conditions under which the action of these operators preserves holomorphicity. This is a joint work with Daeyeol Jeon, Soon-Yi Kang and Gyeong Seok Min.

Date: 25. 06. 26 (Thu) 16:30~ 

Speaker: Taeyeoup Kang (POSTECH)
Title: Estimation of the Jacquet-Rallis orbital integral via stratification

Abstract: Orbital integrals are objects that appear in the geometric side of the relative trace formula, which is a powerful tool in Langlands program. Computing them in general is a difficult problem and little results are known. Recently, Cho, Kang, and Lee proposed a new method for computing standard orbital integrals by assigning a stratification and do smoothening. By extending this idea, I will explain our work on one of the relative orbital integrals, called the Jacquet-Rallis case. This case appears in the fundamental lemma for the unitary case and in the arithmetic fundamental proposed by Wei Zhang, without an explicit computation. We estimate the Jacquet-Rallis orbital integral via stratification. This is a joint work in progress with Sungmun Cho.

Date: 25. 06. 27 (Fri) 10:00~ 

Speaker: Yugo Takanashi (University of Tokyo)

Title: On the formal degree conjecture for G2

Abstract:

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