Location: 

Mathematical Institute (Aobayama campus) https://maps.app.goo.gl/zcUcVf2zutWY3Zr89 ,or 

Science Complex A (Aobayama campus) https://maps.app.goo.gl/U8mZQsw3L7NhrrmA6

2 sessions on different days!!

Speakers: Piotr Achinger (Warsaw), Ko Aoki (Bonn), Alberto Merici (Heidelberg)

2025年9月24日（水） Wednesday 24 September 

Place: Room 202, Science Complex A (合同A棟202)

13:30--15:00 Piotr Achinger (Warsaw)

Title: Tame fundamental groups of rigid spaces 

Abstract:
The fundamental group of a complex variety is finitely presented. The talk will survey algebraic variants (in fact, distant corollaries) of this fact, in the context of variants of the etale fundamental group. We will then zoom in on "tame" etale fundamental groups of p-adic analytic spaces. Our main result is that it is (topologically) finitely generated (for a quasi-compact and quasi-separated rigid space over an algebraically closed field).  The proof uses logarithmic geometry beyond its usual scope of finitely generated monoids to (eventually) reduce the problem to the more classical one of finite generation of tame fundamental groups of algebraic varieties over the residue field. This is joint work with Katharina Hübner, Marcin Lara, and Jakob Stix.

2025年9月25日（木）Thursday 25 September 

Place: Room 305, Mathematical Institute (数学棟305)

13:30--15:00 Alberto Merici (Heidelberg)

Title: Descent for logarithmic invariants and applications

Abstract:
Following a suggestion by Mathew, I will explain how to identify some arithmetic invariants of logarithmic schemes with (non-log) invariants of the associated infinity root stack of Talpo and Vistoli. A key ingredient is a form of descent for logarithmic invariants that we call "saturated descent”. As an application, we deduce comparison theorems of logarithmic invariants from classical (non-logarithmic) comparisons and construct variants of Beilinson/Bloch--Esnault--Kerz fiber squares for semi-stable varieties over a local field.
This is a joint work with F. Binda, T. Lundemo and D. Park.

15:15--16:45 Ko Aoki (Bonn)

Title: Higher motives

Abstract:
I talk about my thesis work in progress. I first explain how to categorify the idea of motives of algebraic varieties. Now we parametrize six operations rather than cohomology theories, which I call “2-motives.” To formulate this, we need the theory of presentable (∞, 2)-categories, which was initiated by Stefanich and has been recently advanced by me. I then explain Scholze’s idea for relating this to the transmutation philosophy of Drinfeld and Bhatt–Lurie. I present my theorem precisely realizing this idea. Moreover, I describe the analytic version of this theorem, which is useful for constructing various realizations, such as the p-adic de Rham realization and the Habiro realization.

Lunch before each session

Dinner: Thu 25 Sep

2025年8月8日（金）Friday 8 August (2 talks!)

Place: Room 202, Science Complex A, Aobayama Campus. Not the mathematics building!

= 合同A棟202室（数学棟ではありません！）

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Talk 1

Time: 13:45--15:15

Speaker: Christopher Frei (TU Graz)

Title: Asymptotics for solubility of unit equations over real quadratic fields

Abstract: For a real quadratic field K and positive integer r, we prove an asymptotic formula for the number of rational integers of bounded absolute value that can be written as a sum of r units of the ring of integers of K. This is joint work with M. Widmer and V. Ziegler and answers partially a question posed by M. Jarden and W. Narkiewicz. 

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Talk 2

Time: 15:30--17:00

Speaker: Bruno Chiarellotto (University of Padua, Italy)

Title: "The life of  Alexander Grothendieck"

Abstract: In the 20th century we speak about the mathematics before and after Alexander Grothendieck. Starting from his interesting life we will try to introduce his mathematics.

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Lunch: Those who join meet at 12:45 at the entrance of the cafeteria in front of Mathematical Institute.

2025年７月28日（月）Monday 28 July 

Time: 13:00--14:30

Room: 数学棟201 Lecture room 201, Mathematical Institute 

Speaker: 星明考 氏（新潟大学）Akinari Hoshi (Niigata University)

Title: 

Rationality problem for fields of invariants, norm one tori and Hasse norm principle

Abstract: 

The aim of this talk is to give a survey of recent developments in the rationality problem for fields of invariants, e.g. Noether's problem, rationality problem for algebraic tori, norm one tori and quasi-monomial actions.

I will give some explicit examples of (non-)stably (resp. retract) rational fields

which are weaker concepts than the rationality.

Negative results may be obtained by using (stable) birational invariants, e.g. flabby class, unramified Brauer (cohomology) group which is an avatar of the Artin-Mumford invariant.

By Colliot-Thelene and Voisin's result (2012, Duke Math. J.), an explicit example of

non-vanishing of the unramified cohomology group of degree three provides an explicit counter-example of the integral Hodge conjecture.

A counter-example of Noether's problem for N\rtimes A_6 over C is also given

where A_6 is the alternating group of degree 6 and N=(Z/10Z)^9.

As an application, we present recent results about Hasse norm principle for K/k where K/k is a finite separable field extension of a global field k.

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Dinner: beer 

2025年7月17日（木）Thursday 17 July 

Time: 13:30--15:00

Room: 数学系研究棟305 = Lecture Room 305, Mathematical Institute

Speaker: 三井健太郎 氏（琉球大学）Kentaro Mitsui (University of the Ryukyus)

Title: 

Actions of degenerating abelian varieties on their Mumford models

Abstract: 

Mumfordは，完備環上で分裂トーラス還元を持つアーベル多様体について，相対的コンパクトモデルを構成した．このモデルはMumfordモデルと呼ばれ，一般には一意的でないが有用である．中村郁氏との共同研究において，完備離散付値環上のアーベル多様体のネロンモデルについて，ネロンモデルが作用するような対称性の高い相対的コンパクトモデルをMumfordモデルに基づき構成した．この対称性は，連結成分群と単位成分群に関する二種類の対称性からなる．本講演では，一般の完備環上のMumfordモデルについて，後者の対称性を解説する．

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Lunch: 12:30

2025年6月23日（月）Monday 23 June 

Time: 10:30--12:00

Room: 数学棟201 Lecture room 201, Mathematical Institute 

Speaker: 阿部健 氏（同志社大学）Takeshi Abe (Doshisha University)

タイトル：一般形超曲面の部分多様体に関するいくつかの結果

アブストラクト：非特異な一般型の複素射影多様体$X$にはZariski閉真部分集合$Z$（例外集合と呼ばれる）が存在し，Zを含まないXの部分多様体は一般型になる，との予想がある．この講演では，$X$が$n$次元射影空間$\mathbb{P}^{n}$内のvery generalな次数$d$の一般型超曲面の場合に，上記の予想に関するEin,Voisin,Clemens-Ranによる先行結果を紹介してから，講演者による僅かな改良結果をのべる．また，$n$次元射影空間$\mathbb{P}^{n}$とその中のvery generalな次数$d$の一般型超曲面$D$の組$(\mathbb{P}^{n},D)$に対して，Clemens-Ranの結果の対数版が成り立つことを紹介する．

 2025年5月8日（木）Thursday 8 May 

13:30--15:00

数学棟305 [Lecture Room 305, Mathematical Institute]

Speaker: Paul Helminck (Tohoku University)

Title: 

Gluing coamoebas of hyperplane arrangements to obtain pair-of-pants decompositions of complex varieties

Abstract: 

In this talk, I will discuss a general technique for expressing the topological structure of a complex algebraic variety in terms of glued hyperplane complements in projective space. In the case of a Riemann surface, this recovers well-known pair-of-pants decompositions. Here the hyperplane complement consists of the projective line minus three points. 

At the beginning of the talk, I will give a short elementary introduction to various concepts in algebraic geometry and algebraic topology to explain the relevant framework for the remainder of the talk. I will then move over to the main theorem of the talk, which says that the topology of a hyperplane complement can be recovered in terms of the associated angle set, or coamoeba, of the hyperplanes. Loosely speaking, this shows that the essential topological data associated to a hyperplane complement lies in the possible angles resulting from the hyperplane equations, so that the radii can be forgotten. 

To prove this result, I will introduce the more general notion of a quasi-polyhedral fibration and show that these define homotopy equivalences. This will require a general semi-algebraic form of the Smale-Vietoris theorem combined with a limiting argument. The angle map for a hyperplane complement is a particular example of a quasi-polyhedral fibration, so this automatically shows that the angles of the hyperplanes recover the topology of the complement. We then extend this theorem to the Kato-Nakayama space of a suitable smooth toric compactification of the complement and show that the extended angle set (or coamoeba) is homotopy equivalent to the Kato-Nakayama space. This allows us to glue extended angle sets along boundary divisors to obtain generalized pair-of-pants decompositions. This is part of a project with Yassine El Maazouz.

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Official lunch (= an ordinary casual lunch): We meet at 12:30 at the entrance of the cafeteria in front of Mathematical Institute.