The Chern–Dold character and the Milnor–Hirzebruch problem

• 主讲人：Victor Buchstaber (Steklov Mathematical Institute, Moscow Steklov International Mathematical Center, MSU)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2024-05-23 21:00 - 2024-05-23 22:00
• 地点： Online

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Recording: https://meeting.tencent.com/v2/cloud-record/share?id=85cd23a4-6bec-4499-8afc-ec20faa1ea00&from=3&is-single=false&record_type=2

 

Abstract: The talk is devoted to problems and results related to the Chern numbers of complex, algebraic and toric manifolds.

Our goal is to present a recent result of Buchstaber and Veselov: The exponential generating series of complex cobordism classes of theta divisors of principally polarized Abelian varieties realizes the exponential of the formal group of geometric cobordisms.

This result is based on Buchstaber's construction (1970) of the Chern–Dold character in the theory of complex cobordism.

We will discuss applications of this result to well-known problems in algebraic topology and algebraic geometry, including the hitherto open Milnor–Hirzebruch problem (1958) on Chern numbers of irreducible smooth algebraic manifolds.

 

Bio: Professor Victor Buchstaber was born 01 April 1943. In 1966 he graduated from Moscow Lomonosov State University (MSU). He is a Doctor of Physical and Mathematical Sciences, Corresponding Member of the Russian Academy of Sciences, Professor of the Department of Higher Geometry and Topology at the Moscow State University, Chief Researcher of the Department of Geometry and Topology at the Steklov Mathematical Institute RAS, Vice-President of the Moscow Mathematical Society, Corresponding Fellow of the Royal Society of Edinburgh (UK), Emiritus Professor at the University of Manchester (UK), Honorary Doctor at the Voronezh State University (Russia).

Areas of his scientific interests: algebraic topology, functional equations, theory of Abelian functions, mathematical physics, applied mathematics.

He is author of more than 300 scientific publications. Monograph “Toric Topology” by V.M. Buchstaber and T.E. Panov (AMS, 2015) became world famous.

Victor Buchstaber has a large scientific school. More than 30 dissertations were defended under his scientific supervision. Many of his students became famous scientists and received worldwide recognition.