[PHK_seminar] [Cohomology], K. Ono

[Petr Somberg]

You  are invited to Professor Kaoru  Ono's  Eduard  Cech lecture  at
15.00 in the blue lecture room  in the rear  building of the
Institute  of Mathematics  (Zitna 25)   which  is  also available   via

ZOOM link: https://www.math.cas.cz/CechLectureZoom

live on Youtube: https://www.math.cas.cz/CechLectureYoutube


Title: Some Developments in Lagrangian Floer Theory

Abstract:  Andreas Floer initiated what is now called
Floer theory in the middle of 1980’s. I start
with some background such as the Arnold
conjecture for fixed points of Hamiltonian
diffeomorphisms, which motivates him to
build Floer (co)homology.
After mentioning his construction, I will
sketch a general story of Floer theory for
Lagrangian submanifolds and explain some
applications based on my joint work with Kenji
Fukaya, Yong-Geun Oh and Hiroshi Ohta.
I would also like to speak on a recent joint
work with Bohui Chen and Bai-Ling Wang on
Lagrangian Floer theory on symplectic orbifolds.
In particular, we introduced the
notion of dihedral twisted sectors, which is a
counterpart of the twisted sector (inertia orbifold) in orbifold
Gromov-Witten theory due to
Weimin Chen and Yongbin Ruan.

There will be coffee and refreshment before the lecture

  Professor Ono  shall deliver   a continuation  of his Eduard  Cech
lecture    on our PHK seminar  the next  Wednesday at the  usual schedule.

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 And here is the preliminary program starting from the next week on:

Here is the title and abstract in seminars.

Title: Lagrangian Floer theory on symplectic orbifolds
Abstract:  W. Chen and Y. Ruan developed Gromov-Witten theory on
symplectic orbifolds,
where an imporatn notion, the inertia orbifold (twisted sector) plays an
important role.
When a Lagrangian is contained in the regular part, Lagrangian Floer
theory was studied
by C.-H. Cho and M. Poddar.  In joint works with B. Chen and B.-L. Wang,
we introduce
the notion of dihedral twisted sector associated with a Lagrangian in a
symplectic orbifold.
After reviewing some preliminaries on orbifolds such as orbifold
morphisms, I will present
the notion of dihedral twisted sector associated with a Lagrangian in a
symplectic orbifold
and explain how to construct Lagrangian Floer theory in symplectic
orbifolds.  This talk is
based on a joint work with B. Chen and B.-L. Wang.

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Title:  Some applications of Lagrangian Floer theory
Abstract:  I will explain a bit more on general story of Lagrangian
Floer theory, which I touch
in Eduard Cech Lecture.  Firstly, we will presentLagrangian Floer theory
such as the construction
of the filtered $A_{\infty}$-structure, (weak) Mauer-Cartan equation,
bulk deformation, etc.
Then we explain its efficiency through some application such as the case
of Lagrangian torus fibers
in compact K\”ahler toric manifolds,   This is mainly based on joint
works with K. Fukaya, Y.-G. Oh, H. Ohta.