Algebraic
Geometry in East Asia
Online Seminar
This
is a joint effort of many algebraic geometers in East Asia. We aim to create a
platform for algebraic geometers and students for further interaction and
cooperation.
The
seminar will take place on Friday at GMT 1:00 or GMT 7:00, unless otherwise
specified, in order to accommodate most participants in East Asia.
To
receive the announcement and the Zoom password, please send an empty mail with
the title "Subscription" to the following address:
ageaseminar A@T gmail.com
This is a mirror site of
https://sites.google.com/ncts.ntu.edu.tw/ageaseminar
Last updated 2020/11/23
Upcoming Talks:
2021/1/22 GMT 7:008:00
Sho Tanimoto (Kumamoto University)
Title: Classifying sections of del Pezzo fibrations
Abstract:
Mori invented a technique called as
Bend and Break lemma which claims that if we deform a curve with fixed points,
then it breaks into the union of several curves such that some of them are
rational. This technique has wide applications ranging from rationally
connectedness of smooth Fano varieties, Cone theorem for smooth projective
varieties, to boundedness of smooth Fano varieties. However, a priori there is
no control on breaking curves so in particular, an outcome of Bend and Break
could be a singular point of the moduli space of rational curves. With Brian
Lehmann, we propose Movable Bend and Break conjecture which claims that a free
rational curve of enough high degree can degenerate to the union of two free
rational curves in the moduli space of stable maps, and we confirm this
conjecture for sections of del Pezzo fibrations over an arbitrary smooth projective curve. In
this talk I will explain some of ideas of the proof of MBB for del Pezzo fibrations as well as its
applications to Batyrev’s conjecture and Geometric
Mann’s conjecture. This is joint work with Brian Lehmann.
2021/1/22 GMT 8:159:15
Fei Hu (University of Oslo)
Title: Some comparison problems on
correspondences
Abstract:
Although the transcendental part of
Weil's cohomology theory remains mysterious, one may
try to understand it by investigating the pullback actions of morphisms, or
more generally, correspondences, on the cohomology
group and its algebraic part.
Inspired by a result of Esnault
and Srinivas on automorphisms of surfaces as well as recent advances in complex
dynamics, Truong raised a question on the comparison of two dynamical degrees,
which are defined using pullback actions of dynamical correspondences on cycle
class groups and cohomology groups, respectively. An
affirmative answer to his question would surprisingly imply Weil’s Riemann
hypothesis.
In this talk, I propose more general comparison problems
on the norms and spectral radii of the pullback actions of certain correspondences
(which are more natural in some sense). I will talk about their connections
with Truong’s dynamical degree comparison and the standard conjectures. Under
certain technical assumption, some partial results will be given. I will also
discuss some applications to Abelian varieties and surfaces. This talk is based
on joint work with Tuyen Truong.
2020/12/4 GMT 1:002:00
Jakub
Witaszek (University of Michigan)
Title: On
the fourdimensional Minimal Model Program for singularities and families in
positive characteristic
Abstract:
I
will discuss new developments on the fourdimensional Minimal Model Program in positive
characteristic. This is based on a joint work with Christopher Hacon.
2020/12/4 GMT 2:153:15
YuWei
Fan (UC Berkeley)
Title:
Stokes matrices, surfaces, and points on spheres
Abstract:
Moduli
spaces of points on nspheres carry natural actions of braid groups. For n=0,1,
and 3, we prove that these symmetries extend to actions of mapping class groups
of positive genus surfaces, through exceptional isomorphisms with certain
moduli of local systems. This relies on the existence of group structure for
spheres in these dimensions. We also apply the exceptional isomorphisms to the
study of Stokes matrices and exceptional collections of triangulated
categories. Joint work with Junho Peter Whang.
Date 
Time 
Speaker 
Title 
2020/12/04 
GMT
1 
Jakub
Witaszek(Michigan) 

2020/12/04 
GMT
2:15 
YuWei
Fan (UC Berkeley) 

2020/12/18 
GMT
7 
Chen
Jiang (Fudan) 

2020/12/18 
GMT
8:15 
Ya Deng (IHES) 

2021/01/08 
GMT
1 
Junliang Shen (MIT) 

2021/01/08 
GMT
2:15 
Yohsuke Matsuzawa (Brown Univ.) 

2021/01/22 
GMT
7 
Sho Tanimoto
(Kumamoto University) 

2021/01/22 
GMT
8:15 
Fei
Hu (University of Oslo) 

2021/02/05 
GMT
7 
Lei
Zhang (USTC) 

2021/02/19 
GMT
7 
Joonyeong Won (KIAS) 

2021/02/19 
GMT
7 
Soheyla Feyzbakhsh
(Imperial College) 





More Confirmed Speakers:
Organizers: Yujiro Kawamata
(Tokyo), Xiaotao Sun (Tianjin), JongHae
Keum (KIAS, Seoul), Jungkai Chen (NTU, Taipei), Conan
Nai Chung Leung (CUHK, Hong Kong), Phung Ho Hai
(VAST, Hanoi), De Qi Zhang (NUS, Singapore), Yusuke Nakamura (Tokyo), Baohua Fu (CAS, Beijing), Kiryong
Chung (Kyungpook National Univ., Daegu), HsuehYung Lin (IPMU, Tokyo)
Archive:
2020/08/07 GMT 8:009:00
Caucher Birkar (University of Cambridge)
Title:
Geometry and moduli of polarised varieties
Abstract:
In this talk I will discuss projective
varieties polarised by ample divisors (or more
generally nef and big divisors) and outline some
recent results about the geometry and moduli spaces of such varieties.
2020/08/14
GMT 7:008:00
Yukinobu
Toda (Kavli IPMU) (video)
Title: On
dcritical birational geometry and categorical DT theories
Abstract:
In this talk, I will explain an
idea of dcritical birational geometry, which deals with certain
"virtual" birational maps among schemes with dcritical structures.
One of the motivations of this new framework is to categorify wallcrossing
formulas of DonaldsonThomas invariants. I will propose an analogue of D/K
equivalence conjecture in dcritical birational geometry, which should lead to
a categorification of wallcrossing formulas of DT invariants.
The main result in this talk is
to realize the above story for local surfaces. I will show the window theorem
for categorical DT theories on local surfaces, which is used to categorify
wallcrossing invariance of genus zero GV invariants, MNOP/PT correspondence,
etc.
2020/08/14
GMT 8:159:15
HuaiLiang
Chang (HKUST) (video)
Title:
BCOV Feynman structure for Gromov Witten invariants
Abstract:
Gromov
Witten invariants Fg encodes the numbers of genus g
curves in Calabi Yau threefolds. They play a role in enumerative geometry and
are not easy to be determined.
In 1993 Bershadsky,
Cecotti, Ooguri, Vafa exhibited a hidden "Feynman structure"
governing all Fg’s at once. Their argument was via
path integral while its counterpart in mathematics had been missing for
decades.
In 2018, considering the moduli
of a special kind of algebro geometric objects,
"Mixed Spin P fields", is developed and provides the wanted
"Feynman structure". In this talk we will see genuine ideas behind
these features.
2020/08/28 GMT 7:008:00
Xun Yu
(Tianjin University) (video)
Title: Automorphism groups of smooth
hypersurfaces
Abstract:
I
will discuss automorphism groups of smooth hypersurfaces in the projective
space and explain an approach to classify automorphism groups of smooth quintic threefolds and smooth
cubic threefolds. This talk is based on my joint
works with Professor Keiji Oguiso
and Li Wei.
2020/08/28 GMT
8:159:15
Tuyen Trung Truong
(University of Oslo) (video)
Title: Rationality of quotients of
Abelian varieties and computer algebra
Abstract:
This
talk concerns the question of what variety of the form X/G, where X is an
Abelian variety and G a finite subgroup of Aut(X), is
rational. It is motivated by some interesting geometric and dynamical system
questions. Most of the work so far concerns the case where X is of the form E^m where E is an elliptic curve, and G is a finite
subgroup of Aut(E). I will review the current known
results and approaches, and explain why it could be necessary to use computer
algebra to resolve the question, and a brief discussion on works in this
direction (including my ongoing joint work with Keiji
Oguiso).
2020/09/11 GMT 2:153:15
Jeongseok Oh (KIAS) (video)
Title: Counting sheaves on CalabiYau 4folds
Abstract:
We define a localised Euler class for
isotropic sections, and isotropic cones, in SO(N) bundles. We use this to give
an algebraic definition of BorisovJoyce sheaf counting invariants on CalabiYau 4folds. When a torus acts, we prove a localisation result. This talk is based on the joint work
with Richard. P. Thomas.
2020/09/25 GMT 7:008:00
Jie Liu
(Chinese Academy of Sciences) (video)
Title:
Strictly nef subsheaves in tangent bundle
Abstract:
Since the seminal works of Mori
and SiuYau on the solutions to Hartshorne conjecture
and Frankel conjecture, it becomes apparent that the positivity of the tangent
bundle of a complex projective manifold carries important geometric
information. In this talk, we will discuss the structure of projective
manifolds whose tangent bundle contains a locally free strictly nef subsheaf and present a new characterisation
of projective spaces. This is a joint work with Wenhao
Ou (AMSS) and Xiaokui Yang
(YMSC).
2020/09/25 GMT 8:309:30
Junyan Cao (Université Côte d'Azur) (video)
Title: On
the OhsawaTakegoshi extension theorem
Abstract:
Since it was established, the OhsawaTakegoshi extension theorem turned out to be a
fundamental tool in complex geometry. We establish a new extension result for
twisted canonical forms defined on a hypersurface with simple normal crossings
of a projective manifold with a control on its L^{2} norme. It is a joint work with Mihai Păun.
2020/10/9 GMT 7:008:00
Frank Gounelas (Göttingen
University) (video)
Title: Curves
on K3 surfaces
Abstract:
I will survey the recent completion (joint with
ChenLiedtke) of the remaining cases of the conjecture that a projective K3
surface contains infinitely many rational curves. As a consequence of this
along with the BogomolovMiyaokaYau inequality and
the deformation theory of stable maps, I will explain (joint with Chen) how in
characteristic zero one can deduce the existence of infinitely many curves of
any geometric genus moving with maximal variation in moduli on a K3 surface. In
particular this leads to an algebraic proof of a theorem of Kobayashi on
vanishing of global symmetric differentials and applications to 0cycles.
2020/10/9
GMT 8:159:15
Toshiyuki Katsura (University of Tokyo) (video)
Title: Counting Richelot
isogenies of superspecial curves of genus 2
Abstract:
Recently,
supersingular elliptic curve isogeny cryptography has
been extended to the genus2 case by using superspecial
curves of genus 2 and their Richelot isogeny graphs.
In view of this situation, we examine the structure of Richelot
isogenies of superspecial curves of genus 2, and give
a characterization of decomposed Richelot isogenies.
We also give a concrete formula of the number of such decomposed Richelot isogenies up to isomorphism between superspecial principally polarized abelian surfaces. This
is a joint work with Katsuyuki Takashima (Mitsubishi Electic Co.).
2020/10/23 GMT 7:008:00
Takahiro Shibata (National
University of Singapore) (video)
Title: Invariant subvarieties
with small dynamical degree
Abstract:
Given a selfmorphism on an algebraic
variety, we can consider various dynamical problems on it. Motivated by an
arithmeticdynamical problem, we consider invariant subvarieties
whose first dynamical degree is less than that of the ambient variety. We give
an estimate of the number of them in certain cases.
2020/10/23 GMT 8:159:15
Sheng Meng (KIAS) (video)
Title: Dynamical equivariant minimal model
program
Abstract:
I will describe the minimal model
program (MMP) in the study of complex dynamics and how MMP can be applied to
many conjectures with dynamical or arithmetical flavours.
Several open questions will also be proposed in this talk.
2020/11/06 GMT 1:002:00
Hong
Duc Nguyen
(Thang Long University) (video)
Title: Cohomology
of contact loci
Abstract:
We
construct a spectral sequence converging to the cohomology
with compact support of the $m$th contact locus of a
complex polynomial. The first page
is explicitly described in terms of a log resolution and coincides with the
first page of McLean's spectral sequence converging to the Floer
cohomology of the $m$th
iterate of the monodromy, when the polynomial has an
isolated singularity. Inspired by this connection we conjecture that the Floer cohomology of the $m$th iterate of the monodromy of
$f$ is isomorphic to the compactly supported cohomology
of the $m$th contact locus of $f$, and that this
isomorphism comes from an isomorphism of McLean spectral sequence with ours.
2020/11/06 GMT 1:002:00
Qizheng Yin (Peking University) (video)
Title:
The Chow
ring of Hilb(K3) revisited
Abstract:
The
Chow ring of hyperKähler varieties should enjoy
similar properties as the Chow ring of abelian varieties. In particular, a Beauville type decomposition is believed (by Beauville himself) to exist for all hyperKähler varieties. In this talk, we discuss a general
approach towards the Beauville type decomposition of
the Chow ring. We carry it out explicitly for the Hilbert scheme of points of
K3 surfaces, and prove the multiplicativity of the resulting decomposition.
Joint work with Andrei Negut and Georg Oberdieck.
2020/11/20 GMT 7:008:00
Jinhyung Park (Sogang
University) (video)
Title: A CastelnuovoMumford
regularity bound for threefolds with mild
singularities
Abstract:
The
EisenbudGoto regularity conjecture says that the CastelnuovoMumford regularity of an embedded projective
variety is bounded above by degree  codimension +1, but McCulloughPeeva recently constructed highly singular counterexamples
to the conjecture. It is natural to make a precise distinction between mildly
singular varieties satisfying the regularity conjecture and highly singular
varieties not satisfying the regularity conjecture. In this talk, we consider
the threefold case. We prove that every projective threefold with rational
singularities has a nice regularity bound, which is slightly weaker than the
conjectured bound, and we show that every normal projective threefold with
CohenMacaulay Du Bois singularities in codimension
two satisfies the regularity conjecture. The codimension two case is particularly
interesting because one of the counterexamples to the regularity conjecture
appears in this case. This is joint work with Wenbo Niu.
2020/11/20 GMT 7:008:00
Evgeny Shinder (University of Sheffield) (video)
Title: Semiorthogonal decompositions
for singular varieties
Abstract:
I
will explain a semiorthogonal decomposition for derived categories of singular
projective varieties into derived categories of finitedimensional algebras,
due to Professor Kawamata, generalizing the concept
of an exceptional collection in the smooth case. I will present known
constructions of these for nodal curves (Burban),
torsionfree toric surfaces (KarmazynKuznetsovShinder) and two nodal threefolds
(Kawamata). Finally, I will explain obstructions
coming from the K_{1} group, and how it translates to
maximal nonfactoriality in the nodal threefold case.
This is joint work with M. Kalck and N. Pavic.
2020/12/4 GMT
1:002:00
Jakub Witaszek (University of Michigan) (video)
Title: On the fourdimensional Minimal Model
Program for singularities and families in positive characteristic
Abstract:
I will discuss new developments on the fourdimensional
Minimal Model Program in positive characteristic. This is based on a joint work
with Christopher Hacon.
2020/12/4 GMT
2:153:15
YuWei Fan (UC Berkeley) (video)
Title: Stokes matrices, surfaces, and points
on spheres
Abstract:
Moduli spaces of points on nspheres carry natural
actions of braid groups. For n=0,1, and 3, we prove that these symmetries
extend to actions of mapping class groups of positive genus surfaces, through
exceptional isomorphisms with certain moduli of local systems. This relies on
the existence of group structure for spheres in these dimensions. We also apply
the exceptional isomorphisms to the study of Stokes matrices and exceptional
collections of triangulated categories. Joint work with Junho
Peter Whang.
2020/12/18 GMT
7:008:00
Chen Jiang (Fudan University) (video)
Title: Positivity in hyperk\"{a}hler manifolds via RozanskyWitten
theory
Abstract:
For a hyperk\"{a}hler manifold $X$ of dimension $2n$, Huybrechts
showed that there are constants $a_0, a_2, \dots, a_{2n}$
such that
$$\chi(L) =\sum_{i=0}^n\frac{a_{2i}}{(2i)!}q_X(c_1(L))^{i}$$
for any line bundle $L$ on $X$, where $q_X$ is the BeauvilleBogomolovFujiki
quadratic form of $X$. Here the polynomial
$\sum_{i=0}^n\frac{a_{2i}}{(2i)!}q^{i}$ is called the RiemannRoch
polynomial of $X$.
In this talk, I will discuss recent progress on the
positivity of coefficients of the RiemannRoch
polynomial and also positivity of Todd classes. Such positivity results follows from a Lefschetztype
decomposition of the root of Todd genus via the Rozansky—Witten
theory, following the ideas of Hitchin, Sawon, and NieperWißkirchen.
2020/12/18 GMT
8:159:15
Ya Deng (IHES) (video)
Title: Big Picard theorem for varieties
admitting a variation of Hodge structures
Abstract:
In 1972, A. Borel proved
generalized big Picard theorem for any hermitian
locally symmetric variety $X$: any holomorphic map from the punctured disk to
$X$ extends to a holomorphic map of the disk into any projective
compactification of $X$. In particular any analytic map from a quasiprojective
variety to $X$ is algebraic. Period domains, introduced by Griffiths in 1969,
are classifying spaces for Hodge structures. They are transcendental
generalizations of hermitian locally symmetric
varieties. In this talk, I will present a generalized big Picard theorem for
period domains, which extends the recent work by BakkerBrunebarbeTsimerman.
2021/1/8 GMT 1:002:00
Junliang Shen (MIT) (video)
Title: Intersection cohomology
of the moduli of of 1dimensional sheaves and the
moduli of Higgs bundles
Abstract:
In general, the topology of the moduli space of semistable sheaves on an algebraic variety relies heavily
on the choice of the Euler characteristic of the sheaves. We show a striking
phenomenon that, for the moduli of 1dimensional semistable
sheaves on a toric del Pezzo
surface (e.g. P^2) or the moduli of semistable Higgs
bundles with respect to a divisor of degree > 2g2 on a curve, the
intersection cohomology (together with the perverse
and the Hodge filtrations) of the moduli space is independent of the choice of
the Euler characteristic. This confirms a conjecture of Bousseau
for P^2, and proves a conjecture of Toda in the case of certain local CalabiYau 3folds. In the proof, a generalized version of Ngô's support theorem plays a crucial role. Based on joint
with Davesh Maulik.
2021/1/8 GMT
2:153:15
Yohsuke Matsuzawa (Brown University) (video)
Title: Vojta's
conjecture and arithmetic dynamics
Abstract:
I will discuss applications of Vojta's
conjecture to some problems in arithmetic dynamics, concerning the growth of
sizes of coordinates of orbits, greatest common divisors among coordinates, and
prime factors of coordinates. These problems can be restated and generalized in
terms of (local/global) height functions, and I proved estimates on asymptotic
behavior of height functions along orbits assuming Vojta's
conjecture. One of the key inputs is an asymptotic estimate of log canonical
thresholds of (X, f^{n}(Y)), where f : X>X is a
selfmorphism and Y is a closed subscheme of X.
As corollaries, I showed that Vojta's conjecture implies Dynamical LangSiegel conjecture
for projective spaces (the sizes of coordinates grow in the same speed),and existence of primitive prime divisors in higher
dimensional setting.
Sponsors: National Center for Theoretical Sciences