國家理論科學研究中心學術演講
 NCTS Seminar in Algebraic Geometry

Day 1

(1)

 Time     :      August 2 (Monday) AM 10:30

 Topic    :      Degree formulae: introduction and motivations

 Abstract:

     We will discuss strange phenomena that an homotopy theorist encounters in trying to study algebraic geometry. Lack of algebraic morphisms as opposed to "topological" morphisms between two algebraic varieties Y and X results in unexpected information we can draw on Y and X from the simple existence of any morphism between them. Some of these information is encoded in the so called "degree formulae".

(2) 

 Time     :      August 2 (Monday) PM 1:30

 Topic    :      Degree formulae: examples and  applications

 Abstract:

    The simplest cases of degree formulae will be analized and some of the most immediate consequences on quadratic forms (due to Rost) will be sketched. The Bloch-Kato conjecture in algebraic K-theory and the need of degree formulae with prescribed characteristic numbers: algebraic Morava K-theories and the higher degree formulae. Towards a systematization in generating degree formulae.

Lecture Room B,

National Center for Theoretical Sciences

4th Floor, The 3rd General Building,

National TsingHua University

Day 2

 Time     :      August 4 (Wednesday) AM 9:00

 Topic    :      The technology making this possible: (stable) homotopy

                     category of schemes

 Abstract:

      The use of homotopy theory in algebraic geometry has been made possible by the existence of certain hybrid categories with both algebraic and homotopy theoretical content. The technology lying at the base has been initially discovered by Quillen and is a certain kind of localization we can perform on suitable categories, called model categories. We will explain how this specializes to our case, what illnesses it cures and what are the sideffects, if abused.

Lecture Room B,

National Center for Theoretical Sciences

4th Floor, The 3rd General Building,

National TsingHua University