The ZEN Mathematics Center (ZMC) is pleased to announce the upcoming research conference detailed below. We look forward to welcoming interested participants.・As venue capacity is limited, we kindly request those wishing to attend to notify Fumihito Kato (<a href="mailto:fumiharu_kato@zen.ac.jp" target="_blank" rel="noopener noreferrer nofollow">fumiharu_kato@zen.ac.jp</a>).＝＝＝＝＝＝＝＝＝＝ ZMC &amp; NTT-IFM Joint Seminar・Date: Wednesday, October 22, Afternoon ・Location: ZEN University Zushi Campus 3-12-11 Shinjuku, Zushi City, Kanagawa Prefecture 15-minute walk from JR Yokosuka Line “Zushi” Station13:00〜13:30 Fumiharu Kato (ZEN university / ZMC） 13:40〜14:10 Masato Wakayama (ZEN university &amp; 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) &amp; 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&apos;s and Serre&apos;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 &amp; 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 &quot;Real prime&quot;. 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 &quot;commutative&quot; 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).

ZMC&NTT-IFM  Joint Seminar

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（<a href="mailto:fumiharu_kato@zen.ac.jp" target="_blank" rel="noopener noreferrer nofollow">fumiharu_kato@zen.ac.jp</a>）までご一報ください。＝＝＝＝＝＝＝＝＝＝ ZMC&amp;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 &amp; 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) &amp; 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&apos;s and Serre&apos;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 &amp; 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 &quot;Real prime&quot;. 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 &quot;commutative&quot; 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).

ZMC&NTT-IFM合同セミナー

<ul><li>Conference Name: ZMC Conference 2025</li><li>Title: Anabelian Geometry and its Computer Formalization</li><li>Dates: July 1 - July 4, 2025</li><li>Venue: Floor 12, Dwango Seminar Room, KABUKIZA TOWER, 4-12-15 Ginza, Chuo-ku, Tokyo, 104-0061 JAPAN</li><li>Organizers:<ul><li>Johan Commelin (Utrecht)</li><li>Yuichiro Hoshi (RIMS, Kyoto)</li><li>Fumiharu Kato (ZMC)</li><li>Kiran Kedlaya (UCSD)</li><li>Adam Topaz (Alberta)</li></ul></li><li>Conference Theme: Recently, more and more people have become interested in the formalization of mathematics by computers, and are becoming more and more aware that Lean4 formalizations and verifications of mathematics have the potential to significantly change the way of doing the research mathematics in the future. These formalizations have already been applied to various areas of arithmetic geometry, and at this conference we would like to discuss the potential of Lean4 formalization of anabelian geometry. In this conference, we would like to discuss not only the latest research presentations on anabelian geometry, but also the construction of libraries related to anabelian geometry. We will also work in small groups to actually work on the formalization of mathematics related to anabelian geometry by Lean4. The conference will also include a session on automatic formalization by machine learning.</li><li>Participation: Reservation required, free</li><li>Reservation: click here（<a href="https://docs.google.com/forms/d/e/1FAIpQLSd7Jg4PWJ-RATxazSjwc2cj3W1lY2iaS1-YSwn7Hbw6bliIvg/viewform?usp=dialog）">https://docs.google.com/forms/d/e/1FAIpQLSd7Jg4PWJ-RATxazSjwc2cj3W1lY2iaS1-YSwn7Hbw6bliIvg/viewform?usp=dialog）</a></li></ul>

ZMC Conference 2025

<ul><li>Conference Name: ZMC Conference 2025</li><li>Title: Anabelian Geometry and its Computer Formalization</li><li>Dates: July 1 - July 4, 2025</li><li>Venue: Floor 12, Dwango Seminar Room, KABUKIZA TOWER, 4-12-15 Ginza, Chuo-ku, Tokyo, 104-0061 JAPAN</li><li>Organizers:<ul><li>Johan Commelin (Utrecht)</li><li>Yuichiro Hoshi (RIMS, Kyoto)</li><li>Fumiharu Kato (ZMC)</li><li>Kiran Kedlaya (UCSD)</li><li>Adam Topaz (Alberta)</li></ul></li><li>Conference Theme: Recently, more and more people have become interested in the formalization of mathematics by computers, and are becoming more and more aware that Lean4 formalizations and verifications of mathematics have the potential to significantly change the way of doing the research mathematics in the future. These formalizations have already been applied to various areas of arithmetic geometry, and at this conference we would like to discuss the potential of Lean4 formalization of anabelian geometry. In this conference, we would like to discuss not only the latest research presentations on anabelian geometry, but also the construction of libraries related to anabelian geometry. We will also work in small groups to actually work on the formalization of mathematics related to anabelian geometry by Lean4. The conference will also include a session on automatic formalization by machine learning.</li><li>Participation: Reservation required, free</li><li>Reservation:<a href="https://docs.google.com/forms/d/e/1FAIpQLSd7Jg4PWJ-RATxazSjwc2cj3W1lY2iaS1-YSwn7Hbw6bliIvg/viewform?usp=dialog" target="_blank" rel="noopener noreferrer nofollow"> click here</a></li></ul>

ZMCカンファレンス2025 開催のお知らせ

Upon the approval of ZEN University, the former IUGC was renamed ZEN Mathematics Center (ZMC). The ZMC will be managed by the following organization. •   Director: Fumiharu Kato •   Deputy Director: Ivan Fesenko •   Administrative Staff: Akiko Takagi •   Technical Staff: Daisuke Seshita, Toshihiko Nakazawa

Announcement of name change to ZEN Mathematics Center (ZMC)

2024年11月12日（火）、旧IUGCはZEN数学センター（ZEN Mathematics Center）と改称しました。 今後、以下の体制で運営していきます。<ul><li>所長：加藤 文元</li><li>副所長：イヴァン・フェセンコ</li><li>事務スタッフ：高木 章子</li><li>テクニカルスタッフ：瀬下 大輔、中澤俊彦</li></ul>

TOPICS

ZMC&NTT-IFM Joint Seminar

ZMC Conference 2025

Announcement of name change to ZEN Mathematics Center (ZMC)