세미나 종류: DASOM 세미나

강연자: Jun Ueki

소속: Ochanomizu University

장소: 129동 301호, 309호

강연1

일시: Mar 31(tuesday) 14:00-15:00

장소: 129동 301호

제목: The p-adic class numbers of Zp-towers and the Lang--Trotter conjecture

초록: We recall basic analogies between knots and primes in arithmetic topology with emphasis on Weber’s problem on class numbers, and point out the p-adic convergence of the class numbers in Zp-towers of number fields, function fields, knots, and graphs. We further ask a question on analogue of a well-known theorem and conjecture on the densities of super singular primes etc.

(Based on a joint work with Hyuga Yoshizaki and that with Reo Kobayashi.)

강연2

일시: Apr 2(thursday) 14:00-15:00

장소: 129동 301호

제목: Hilbert ramification theoy, Chebotarev links, and anabelian geometry for 3-manifolds

초록: We recall basic analogies between knots and primes in arithmetic topology with emphasis on ramification theory. We also introduce a set of knots that behaves like that of prime numbers, and present an analogue of the classical Neukirch—Uchida theorem, which originally asserts that if two number fields have isomorphic absolute Galois groups, then the fields are isomorphic. 

We also discuss the profinite rigidity of multivariable twisted Alexander polynomials and the taut/Teichmuller polynomials of fibered hyperbolic links. 

(Based on a joint work with Nadav Gropper and Yi Wang, and that with Tam Cheetham-West, Biao Ma, Youheng  Yao.)

강연3

일시: Apr 3 (friday) 14:00-15:00

장소: 129동 309호

제목: The ring of finite algebraic numbers in the "poor man's adele ring" and its positive characteristic analogues

초록: Within the ring A=(prod_p Z/pZ) / (bigoplus_p Z/pZ), p running through the set of prime numbers, J. Rosen introduced a Q-subalgebra P^0_A, which is a “finite analogue''of the ring of algebraic numbers from a viewpoint of the periods of motives, and characterized it by linear recurrent sequences. Fundamental theories of P^0_A have been established by Rosen, Rosen–Takeyama–Tasaka–Yamamoto, Anzawa–Funakura, and others. We review their works, present their positive characteristic analogues, and ask further questions. 

(Based on a joint work with D.Matsuzuki and H.Sakamoto.)