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Date : May, 21-22, 25-26

Time : 16:00--18:00

Place : seminar room 1423

Organizers : Jinsung PARK (KIAS)

Speakers : Yuri A. Kordyukov (Russian Academy of Sciences, Ufa, Russia)

Abstract : The main purpose of these lectures is to describe an analytic approach to Lefschetz formulas for flows on foliated manifolds based on transversal index theory for foliations.
For a non-singular flow on compact foliated manifold, which preserves the folition and is transverse to it, we introduce the Lefschetz distribution on the real line. We will state a formula for this distribution, which can be considered as a dynamical Lefschetz formula for the flow.
We will discuss some related topics, which we need: index theory for transversally elliptic operators, the leafwise de Rham complex and Hodge theory for foliations, noncommutative geometry of foliations, $L^2$ index theory for tangentially elliptic operators.
We will also discuss some perspectives and open problems, in particular, the Guillemin-Patterson conjecture for Anosov flows and the Deninger program of analogies between arithmetic algebraic geometry and dynamical systems on foliated manifolds. 

Contact - Local Staff : Kangwon LEE (kwlee@kias.re.kr)