Autumn School on Topos and Applications将于2025年9月23日开班，现开启报名，请注意以下事项：

【开课说明】

课程日期：2025年9月23日（报到）— 28日（离会）

日程安排：9月24日-28日上午 短课程，9月24日-27日下午 报告

主办单位：武汉大学数学与统计学院、国家天元数学中部中心、中法联合数学研究中心

会议地点：雷军科技楼B102报告厅

【课程介绍】

1. Olivia Caramello（University of Insubria and Grothendieck Institute）

课程题目：Introduction to relative topos theory

摘要：Relativity techniques for schemes have played a key role in Grothendieck’s refoundation of algebraic geometry. The theory of relative toposes consists in an analogous, but much more general and powerful, set of tools for toposes, applicable to many fields of mathematics. The course will provide an introduction to the new foundations for relative topos theory, formulated in the language of stacks and fibrations, that we have been developing since 2020 with our collaborators.

We shall notably present the following central topics:

(1)The relative “presheaf-bundle” adjunction

(2)Representation theorems for relative toposes

(3)Relative sites

(4)Relative Diaconescu’s theorem

(5)The notion of existential fibred site

(6)The problem of ‘relativization’ of ordinary topos-theoretic notions and results

(7)Applications to artificial intelligence and meta-learning

2. Laurent Lafforgue (2002 Fields Medalist)（Huawei, Lagrange Research Center）

课程题目：Moduli problems, classifying toposes, invariants, and the six operations formalism

摘要：Grothendieck discovered toposes as the common culmination of two a priori very different lines of thought: on the one hand the geometric problem of moduli spaces, on the other hand the topological-algebraic development of cohomological and homological invariants. The aim of the course will be to introduce these two themes and the new forms that Grothendieck has given them in the extremely general framework of toposes. We shall present :

- the notion of stack and that of topos associated with a stack,

- the different notions of classifying toposes,

- the general redefinition of cohomological and homotopic invariants in the context of toposes,

- the “six operations formalism” as a topossic generalisation and deepening of Poincaré duality,

- fundamental open questions that have yet to be tackled systematically.

3. Aurelien Sagnier（Huawei Paris Research Center）

课程题目：Topos Theory and Artificial Intelligence : examples, interactions, hints for possible future exploration

摘要：In these lectures I will try to present some material for possible interactions of Topos Theory and Artificial Intelligence.

The choice of the different materials (from the state of the art) exposed is personal and thus non exhaustive but the choice and the thematics was heavily influenced by the deep theoretical insights of Olivia Caramello and Laurent Lafforgue.

This series of lectures will be organized around five general thematics :

(1)Concrete examples in topos theory.

(2)Sheaf Learning.

(3)Moduli spaces and machine learning.

(4)Logic and machine learning.

(5)Transformers, Large Language Models (LLM) and toposes.

【学员待遇】

本次课程不需缴纳学费，为外地学员提供食宿（名额40，2人合住），为非本校的武汉市其他高校学员提供餐补（名额10），其他费用自理。本校学生可旁听课程，无资助。

【报名流程及联系人】

1、报名及录取方式：点击此处提交报名申请（https://www.wjx.cn/vm/Yr9ZAtT.aspx#），由组委会评选后成为正式学员。

2、报名截止日期：2025年8月25日下午17:00，我们将尽快通过邮件通知报到时间及地点。

3、联系人：邓老师  电话：027-87287715         邮箱：tmcc@whu.edu.cn