MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal
22.05.17 24.05.17

Chow Lectures 2017

Wei-Liang Chow (October 1, 1911, Shanghai – August 10, 1995, Baltimore) was a celebrated mathematician best known for his work in algebraic geometry, though he also made important contributions to other areas such as differential geometry, differential equations, and control theory. Within algebraic geometry he is known among other things for his work on intersection theory (Chow's moving lemma, Chow ring), for Chow's theorem on algebraicity of projective analytic varieties, and for many other achievements.

Chow was born in Shanghai, had his school education in the United States, and graduated from the University of Chicago in 1931. He obtained his PhD in Leipzig in 1936, where he worked with van der Waerden (who was a professor at the University of Leipzig), introducing in particular Chow coordinates. Subsequently, Chow was a professor in Nanjing, Princeton and at Johns Hopkins University were he worked until 1977.

The idea behind the Chow lectures - which almost coincide with Chow's 80th Phd anniversary - is to give students the opportunity to enjoy lectures by internationally renowned experts on active fields of modern mathematics and to create a stimulating research environment.

Inaugural speaker for the Chow lectures 2017 is Claire Voisin (Collège de France). Claire Voisin is mainly known for her works on algebraic geometry and its relation to Hodge theory. Among her fundamental achievements are counterexamples to the Kodaira problem and a solution of the generic case of Green's conjecture. She obtained several distinctions such as the European Mathematical Society Prize in 1992, the Servant Prize in 1996, the Sophie Germain Prize in 2003 and the Clay Research Award in 2008. In 2016 she received the Gold medal from the French National Centre for Scientific Research – the highest scientific research award in France.

In addition, there will be a historical introduction by Norbert Schappacher (Université de Strasbourg).

Plan of preparatory sessions (subject to change)


  1. Varieties vs. Manifolds
    • Definition of complex manifold and Kähler manifold
    • Smooth projective complex varieties are compact Kähler manifolds, Chow's Theorem
    • Running example: projective n-space over C
  2. Hodge theory
    • Definition of Hodge structure, Hodge classes and Hodge numbers
    • Hodge decomposition theorem
    • (real and complex) De Rham cohomology, Comparison Theorem
    • Idea for Hodge decomposition: Direct sum decomposition of differential forms with complex coefficients


  1. Motivation: Cycle class map
  2. Definition of Chow groups and Chow rings
  3. How to compute Chow groups
    • Pushforward, pullback, localisation sequence
    • Examples: Affine and projective space
    • Further examples (if time allows): correspondences, Chow groups of projective bundles and blow ups

See this file with the easy exercises. The participants of the Preparatory Lectures should solve the exercises BEFORE they are coming to the first lecture.

We want to stress that the Exercises are meant to teach basic definitions and concepts. They are all easy and should not require too much time, but playing around with the objects we will be dealing with will significantly improve the level of understanding when visiting the Chow and the Preparatory Lectures.

We will NOT repeat the notions introduced in the Exercises during our Preparatory Lectures, but assume that they are known. Of course, participants are welcome and encouraged to ask questions about the Exercises before, during and after our Preparatory Lectures.

The organisers of the preparatory lectures are:


09:30 - 10:30
10:30 - 11:00
11:00 - 12:00
12:00 - 14:00
14:00 - 15:00 Claire Voisin (Collège de France, France)
15:00 - 15:30
15:30 - 16:30 Jean-Michel Coron (Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions, France)
Colloquium of the Max Planck Institute: Some methods to use the nonlinearities for controlling systems


Karim Adiprasito

Universität Leipzig

Daniele Agostini

Humboldt-Universität zu Berlin

Carlos Améndola

TU Berlin

Hannah Bergner

Albert-Ludwigs-Universität Freiburg

Valeria Bertini

Université de Strasbourg

Lara Bossinger

University of Cologne

Emma Brakkee

University of Bonn

Paul Breiding

TU Berlin

Dominik Burek

Institute of Mathematics of the Jagiellonian University

Peter Bürgisser

TU Berlin

Alberto Castaño Domínguez

Technische Universität Chemnitz

Aleksander Czarnecki

Jagiellonian University in Cracow

Ferran Dachs Cadefau

Martin-Luther-Universität Halle-Wittenberg

Andreas Demleitner

Universität Bayreuth

Philipp di Dio

Uni Leipzig/MPI Leipzig

Eliana Duarte

MIS MPI Leipzig

Lina Elz

HTWK Leipzig

Hannes Fiedler

HTWK Leipzig

Davide Frapporti

Universität Bayreuth

Luca Giovenzana

Chemnitz University

Franco Giovenzana

Chemnitz university

Lukas Grunau

HTWK Leipzig

Marvin Hahn

University of Tübingen

Enno Keßler

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Yeongrak Kim


Charlie Kirst

HTWK Leipzig

Hanveen Koh

Johns Hopkins University

Kathlén Kohn

TU Berlin

Igor Krylov

Max Planck Institute of mathematics

Lukas Kühne

University Bonn

Mario Kummer

Max Planck Institute for Mathematics in the Sciences

Benjamin Kutschan

TU Berlin

Sara Lamboglia

University of Warwick

Michal Lason

University of Bern

Christian Lehn

Technische Universität Chemnitz

Yumeng Li

Free University Berlin

Songbo Ling

Universität Bayreuth

Raeez Lorgat

Massachusetts Institute of Technology

Katrin Lubashevsky

HTWK Leipzig

Renjie Lyu

Universiteit van Amsterdam

Madhusudan Manjunath

Queen Mary University of London

Jochen Merker

HTWK Leipzig

Mateusz Michalek

University of California

Giosuè Emanuele Muratore

Università Degli Studi Roma Tre

Amir Niknejad

College of Mount Saint Vincent

Joe Palacios


Marta Panizzut

TU Berlin

Nebojsa Pavic

University of Sheffield

Dario Portelli

Universita` di Trieste

Rohini Ramadas

University of Michigan

René Recktenwald

Albert-Ludwigs-Universität Freiburg

Yue Ren

MPI MIS Leipzig

David Sabonis

TU Munich & University of Copenhagen

Camilo Sarmiento

Leipzig University

Mahsa Sayyary Namin

Max Planck Institute for Mathematics in the Sciences

Joshua Schäfer

HTWK Leipzig

Norbert Schappacher

Université de Strasbourg

Anne Schirmer

HTWK Leipzig

Bernd Schober

University of Toronto

Matthias Schwarz

Universität Leipzig

Emre Sertöz

MPI MIS Leipzig

Christian Sevenheck

TU Chemnitz

Muhammad Shabbir

University of Luebeck

Kristin Shaw

Technische Universitaet Berlin

Robert Silversmith

University of Michigan

Tanya Kaushal Srivastava

FU Berlin

Bernd Sturmfels

MPI MIS Leipzig

Do Thi Anh

Philipps-Marburg university

Jürgen Tolksdorf

Max Planck Institute/University Leipzig

Josue Tonelli Cueto

Technische Universität Berlin

Jacinta Torres


Martin Ulirsch

University of Michigan

Emanuele Ventura

MPI Leipzig

Elmiro Vetere


Claire Voisin

Collège de France

Phung Xuan Kien

University of Strasbourg

Scientific Organizers

Karim Adiprasito

Hebrew University of Jerusalem and Universität Leipzig

Christian Lehn

Technische Universität Chemnitz

Mateusz Michalek

Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig and Polish Academy of Sciences

Matthias Schwarz

Universität Leipzig

Administrative Contact

Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail