The DASOM Lecture Series is designed to foster deep interaction across the diverse research areas of the Center, including homogeneous dynamics, arithmetic dynamics, Teichmüller dynamics, and number theory. By inviting leading international scholars for focused lecture series rather than single talks, we create sustained opportunities for intellectual exchange, collaborative discussion, and cross-fertilization of ideas among members of the DASOM community. The lecture series also serves as a platform for strengthening international research cooperation, supporting long-term collaborations, and integrating global perspectives into the Center’s research program.
Lecture Series 1 (Number theory)
Speaker: Jun Ueki (Ochanomizu University)
Scheduled for March 31(Tue), 14:00-15:00
Place: Room 301, Building 129
Title: The p-adic class numbers of Zp-towers and the Lang--Trotter conjecture
Abstract: 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.)
Scheduled for April 2 (Tue), 14:00-15:00
Place: Room 301, Building 129
Title: Hilbert ramification theoy, Chebotarev links, and anabelian geometry for 3-manifolds
Abstract: 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.)
Scheduled for April 3 (Fri), 14:00-15:00
Place: Room 309, Building 129
Title: The ring of finite algebraic numbers in the "poor man's adele ring" and its positive characteristic analogues
Abstract: 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.)
Lecture Series 2
Speaker: Tengren Zhang (National University of Singapore)
Scheduled and Place
April 29 (Wed) 16:00 – 17:30 / Room 104, Building 129
May 6 (Wed) 16:00 – 17:30 / Room 104, Building 129
May 8 (Fri) 16:00 – 17:30 / Room 104, Building 129
May 13 (Wed) 16:00 – 17:30 / Room 112, Building 24
Title: Patterson-Sullivan theory for transverse groups
Abstract: In recent years, there has been significant progress in developing a Patterson–Sullivan theory for transverse groups in higher-rank Lie groups. In this series of talks, I will introduce the notions of transverse groups, Anosov groups, and relative Anosov subgroups via convergence group actions. I will then discuss the definition and construction of Patterson–Sullivan measures in this setting and describe recent advances in the theory for such groups.