Minicourse on the Hodge conjecture-清华大学求真书院

短期课程

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来源： 05-16

时间：2023-05-16~2023-05-30

地点：Lecture Hall, Floor 3 Jin Chun Yuan West Bldg Tencent Meeting ID: 579 9724 2693

主讲人：James Lewis University of Alberta, Canada

Time

Lecture 1. May 16 (09:50-11:25)

Lecture 2. May 17 (09:50-11:25)

Lecture 3. May 19 (09:50-11:25)

Lecture 4. May 22 (15:20-16:55)

Lecture 5. May 23 (09:50-11:25)

Lecture 6. May 24 (09:50-11:25)

Lecture 7. May 26 (09:50-11:25)

Lecture 8. May 29 (15:20-16:55)

Lecture 9. May 30 (09:50-11:25)

Speaker

Research Areas

Algebraic Geometry, Algebraic Cycles

Research Interests

Regulators and the arithmetic and geometry of algebraic cycles

Personal Website

https://www.math.ualberta.ca/Lewis_JD.html

Course Description

✔ Introduction

✔ Formalism of mixed Hodge structures

✔ The Hodge conjecture

✔ Milnor's K-theory, algebraic de Rham cohomology theory and de Rham cycle class map

✔ Deligne's absolute Hodge cycles and a recent work of C. Voisin

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Tropical Hodge conjecture for Abelian varieties
AbstractThe classical Hodge conjecture states that for a smooth projective variety any rational (p,p)-class can be represented by an algebraic cycle. The first non-trivial case for abelian varietie
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Reflections on the Hodge Conjecture from an Arithmetic Geometer
Speaker James D. Lewis is Professor at University of Alberta. His current research interests are in regulators of (higher) algebraic cycles into Hodge cohomology theories (such as Beilinson's absolute Hodge cohomology). With his colleague Matt Kerr, together initially with Stefan Mueller-Stach, they provided over the course of 10 years an explicit description of the Beilinson-Bloch regulators i...
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