ZMC&NTT-IFM合同セミナー

ZEN数学センター（ZMC）では、下記の研究集会の開催を予定しております。ご興味ある方のご参加をお待ちしております。

・会場の収容に限りがございますので、参加を希望される方は、お手数ではございますが、加藤文元（fumiharu_kato@zen.ac.jp）までご一報ください。

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ZMC&NTT-IFM合同セミナー・日程：10月22日（水）午後
・場所：ZEN大学逗子キャンパス
　神奈川県逗子市新宿3丁目12-11
　JR横須賀線「逗子」駅より徒歩15分13:00〜13:30 Fumiharu Kato (ZEN university / ZMC）

13:40〜14:10 Masato Wakayama (ZEN university & NTT-IFM）
14:40〜15:40 Zeev Rudnick (Tel-Aviv university)
16:00〜17:00 Shai Haran (Technion)

Speaker: Fumiharu Kato (ZEN university / ZMC）
Title: Sharp bounds for the number of rational points on algebraic curves and dimension growth over all global fields
Abstract: Joint work with Gal Binyamini (Weizmann) & Raf Cluckers (Lille). I will talk on our recent results on the bounds of K-rational points, where K is a number field, of height at most H on hyper surfaces X of degree d. In many cases, our bounds depends quadratically on d with the optimal exponents of H, which leads to new results on Heath-Brown's and Serre's dimension growth conjecture for global fields. I will also mention on analogous results for global fields in positive characteristic. The proofs are given by the p-adic determinant method, and the optimal dependence on d is achieved using a technical improvement in the treatment of high multiplicity points on mod p reductions of algebraic curves.

Speaker: Masato Wakayama (ZEN university & NTT-IFM）
Title: Light-matter interactions and number theory
Abstract: The quantum Rabi model (QRM) describes the coupling of a two-state system to a bosonic field mode. There are also several imporatnat related/generalized models such as the asymmetric QRM, two photon QRM, quantum Rabi-Stark models, which describe the fundamental mechanism of light-matter interaction. In this talk, we introduce mathematical challenges, particularly number theoretic ones, that arise from the study of the spectrum (energy states) of the target Hamiltonian that describes such quantum interactions, along with several conjectures.

Speaker: Zeev Rudnick (Tel Aviv University)
Title: Number theory and spectral theory of the Laplacian
Abstract: I will discuss some of the interactions between number theory and the spectral theory of the Laplacian. Some have very classical background, such as the connection with lattice point problems. Others are newer, including connections between random matrix theory, the zeros of the Riemann zeta function, and spectral statistics on the moduli space of hyperbolic surfaces.

Speaker: Shai Haran (Technion)
Title: Non additive geometry
Abstract: The usual dictionary between geometry and commutative algebra is not appropriate for Arithmetic geometry because addition is a singular operation at the "Real prime". We replace Rings, with addition and multiplication, by Props (=strict symmetric monoidal category generated by one object), or by Bioperad (=two closed symmetric operads acting on each other): to a ring we associate the prop of all matrices over it, with matrix multiplication and block direct sums as the basic operations, or the bioperad consisting of all raw and column vectors over it. We define the "commutative" props and bioperads, and using them we develop a generalized algebraic geometry, following Grothendieck footsteps closely. This new geometry is appropriate for Arithmetic (and potentially also for Physics).