Modern Interactions between
Algebra, Geometry and Physics
Workshop
Date
June 27 (Mon) , 2016 - June 29 (Wed) , 2016Venue
TOKYO ELECTRON House of Creativity 3F, Lecture Theater, KatahiraCampus, Tohoku University

Invited Speakers
Xiuxiong Chen (Stony Brook)
Toshiki Mabuchi (Osaka)
Shinichiroh Matsuo (Nagoya)
Hiroshi Iritani (Kyoto)
Yuji Odaka (Kyoto)
Kazushi Ueda (Tokyo)
Giovanni Landi (University of Trieste)
Kenta Tottori (Tohoku)

1Time schedule
Date
27(Mon)28(Tue)29(Wed)Time
11:00 - 12:30
12:30 - 15:00
15:00 - 16:30
18:00 11:00 - 12:30
12:30 - 13:45
13:45 - 14:45
15:00 - 16:30
11:00 - 12:30
12:30 - 14:15
14:15 - 14:45
15:00 - 16:30

Speaker
Kazushi Ueda(Tokyo)
Lunch and Discussion
Xiuxiong Chen (Stony Brook)
Reception (Restaurant Hagi)
Hiroshi Iritani (Kyoto)
Lunch and Discussion
Giovanni Landi (University of Trieste)
Shinichiroh Matsuo (Nagoya)Toshiki Mabuchi (Osaka)
Lunch and Discussion
Kenta Tottori (Tohoku)
Yuji Odaka (Kyoto)

Title and Abstract• Kazushi Ueda(Tokyo)
Title: Residue mirror symmetry for Grassmannians
Abstract: Motivated by recent works on localizations in A-twisted gauged
linear sigma models, we discuss a generalization of toric residue
mirror symmetry by Batyrev-Materov to complete intersections inGrassmannians. This is a joint work with Bumsig Kim, Jeongseok
Oh, and Yutaka Yoshida.
• Xiuxiong Chen (Stony Brook)
Title: A recent update on Kähler geometry
Abstract: There is a long standing conjecture which relates the existenceof Kähler Einstein metrics with positive scalar curvature to thestability of underlying polarization, which goes back to Yau in
1980s. In this lecture, we will give an expository account of its
resolution by Chen-Donaldson-Sun in 2012 and in addition, we will2

also go over several new proofs (namely, proofs based on continuity
path, the Kähler ricci flow and variation method respectively) tothis important result emerging in recent years.
• Hiroshi Iritani (Kyoto)
Title: Mirror symmetry for toric stacks
Abstract: I will describe Landau-Ginzburg mirror symmetry for big andequivariant quantum cohomology of toric stacks. I will also discuss the convergence of the mirror isomorphism and how quantum
D-modules change under toric flips. Part of this talk is based on
joint work with Tom Coates, Alessio Corti and Hsian-Hua Tseng.
• Giovanni Landi (University of Trieste)
Title Line bundles over noncommutative spaces
Abstract: We give a Pimsner algebra construction of noncommutative circle bundles. In particular, noncommutative lens spaces are given
as ‘direct sums of line bundles’ and exhibited as ‘total spaces’ ofcertain principal bundles over noncommutative weighted projective spaces. We naturally gets an analogue of the classical Gysin
sequence which relates K-theory classes of the total space algebra
to that of the base space algebra. In turn this is used to selectT-dual noncommutative bundles.
• Shinichiroh Matsuo (Nagoya)
Title: The perturbation of the Seiberg-Witten equations
Abstract: We will introduce a new class of perturbations of the SW equations. It is naturally crystallised through Weitzenbock formulaeand oﬀers flexibility in the way the SW invariants are constructed.
The part of this talk is based on a joint work with Mikio Furuta.
• Toshiki Mabuchi (Osaka)
Title: An extremal Kähler version of the Yau-Tian-Donaldson conjecture3

Abstract: The Yau-Tian-Donaldson conjecture for Kähler-Einstein cases wasaﬃrmatively solved by Chen-Donaldson-Sun and Tian. However,its generalized version including extremal Kähler cases is stillopen. In this talk, I’d like to discuss the general case focussingon what is the right choice of the definition of K-stability in thisgeneral case.
• Kenta Tottori (Tohoku)
Title: Calabi’s conjecture of the Kähler-Ricci soliton type
Abstract: As a generalization of Calabi’s conjecture, Zhu introduced theKähler-Ricci soliton version of this conjecture. In this talk, wediscuss this conjecture on a compact Fano manifold (more generally, a compact Kähler manifold with a holomorphic vector field
which has a zero point) and prove it by using a geometric flow. Iftime allows, we will also talk about the case of a nowhere vanishing
holomorphic vector field.
• Yuji Odaka (Kyoto)
Title: Gromov-Hausdorﬀ compactification of moduli variety of KählerEinstein varieties
Abstract: Kähler-Einstein (KE) metric on a variety is a certain class of
canonical metric and Gromov-Hausdorﬀ distance gives a way to
get a canonical limit of (sequence/family) of varieties when combined with the KE metrics, appropriately rescaled to make thediameters bounded. We use such diﬀerential geometric tools to an
algebraic geometry question - compactify algebraic moduli spacesof varieties, which are often classical moduli varieties, and closely
look at the structure we get at the boundary. There is a crucial
diﬀerence with positive curvature case ( Fano manifold ) andnon-negative curvature case.

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