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BEGIN:VEVENT
SUMMARY:Xiao-Gang Wen/文小刚 (MIT)
DTSTART:20201227T013000Z
DTEND:20201227T023000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/1
DESCRIPTION:Title: Algebraic higher symmetry and local higher fusion category: symmet
ry as a shadow of topological order\nby Xiao-Gang Wen/文小刚 (MIT)
as part of ICCM 2020\n\n\nAbstract\nI will discuss a most general form of
symmetry --algebraic higher symmetry\, which include symmetry described by
group and higher group. Algebraic higher symmetry\, in its most general f
orm\, is beyond group and higher group. It is described by local higher fu
sion category. I also discuss a holographic point of view for symmetry: sy
mmetry is a shadow of topological order in one higher dimension (ie a fusi
on higher category with trivial center).\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Si Li/李思 (Tsinghua University)
DTSTART:20201227T030000Z
DTEND:20201227T040000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/2
DESCRIPTION:Title: Configuration space integrals and index theory\nby Si Li/李
思 (Tsinghua University) as part of ICCM 2020\n\n\nAbstract\nWe explain a
geometric formulation of the low energy effective theory of sigma models
in terms of bundles of factorization algebras. Appropriate regularization
for Integrals over configuration spaces arises naturally from quantum fiel
d theories and will in general give rise to index type theories. As a case
study in dimension two\, we introduce a geometric renormalization metho
d for regularized integrals over configuration spaces of Riemann surfaces
in 2d chiral quantum field theory. It provides a mathematical tool to fo
rmulate correlation functions of non-local operators in a chiral CFT that
will lead to an algebraic analogue of elliptic index theory.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sijue Wu/邬思珏 (University of Michigan)
DTSTART:20201227T030000Z
DTEND:20201227T040000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/3
DESCRIPTION:Title: The Quartic Integrability and Long Time Existence of Steep Water W
aves in 2d\nby Sijue Wu/邬思珏 (University of Michigan) as part of
ICCM 2020\n\n\nAbstract\nIt is known since the work of Dyachenko & Zakharo
v in 1994 that for the weakly nonlinear 2d infinite depth water waves\, th
ere are no 3-wave interactions and all of the 4-wave interaction coefficie
nts vanish on the resonant manifold. In this talk I will present a recent
result that proves this partial integrability from a different angle. We c
onstruct a sequence of energy functionals Ej (t)\, directly in the physica
l space\, that involves material derivatives of order j of the solutions f
or the 2d water wave equation\, so that d dtEj (t) is quintic or higher or
der. We show that if some scaling invariant norm\, and a norm involving on
e special derivative above the scaling of the initial data are of size no
more than ε\, then the lifespan of the solution for the 2d water wave equ
ation is at least of order O(ε−3 )\, and the solution remains as regula
r as the initial data during this time. If only the scaling invariant norm
of the data is of size ε\, then the lifespan of the solution is at least
of order O(ε−5/2 ). Our long time existence results do not impose size
restrictions on the slope of the initial interface and the magnitude of t
he initial velocity\, they allow the interface to have arbitrary large ste
epnesses and initial velocities to have arbitrary large magnitudes.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinxin Xue/薛金鑫 (Tsinghua University)
DTSTART:20201227T030000Z
DTEND:20201227T040000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/4
DESCRIPTION:Title: Arnold diffusion in geodesic dynamics of blackholes\nby Jinxin
Xue/薛金鑫 (Tsinghua University) as part of ICCM 2020\n\n\nAbstract\nW
e consider the geodesics dynamics of a particle moving in a blackhole back
ground that is a small perturbation of Schwarzschild and Kerr. We show tha
t there are some remarkable chaotic dynamical behaviors including Arnold d
iffusion\, oscillatory motions and chaotic carrousel motions around the ev
ent horizon. We also explain the implication of KAM in this setting\, rela
ted to two observable phenomena: photon ring and QPO.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiangdong Ye/叶向东 (USTC)
DTSTART:20201227T060000Z
DTEND:20201227T070000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/5
DESCRIPTION:Title: Nilpotent structures in dynamical systems\nby Xiangdong Ye/叶
向东 (USTC) as part of ICCM 2020\n\n\nAbstract\nTopological dynamics and
ergodic theory are two branches of dynamical systems. They are closely re
lated and have applications in other fields of mathematics. In this talk I
will explain why nilpotent structures arise naturally in the study of dyn
amical systems and how they are related to combinatorial number theory."\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qingyuan Jiang/姜清元 (University of Edinburgh)
DTSTART:20201227T060000Z
DTEND:20201227T070000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/6
DESCRIPTION:Title: Derived categories and Chow theory of Quot-schemes of Grassmannian
type\nby Qingyuan Jiang/姜清元 (University of Edinburgh) as part o
f ICCM 2020\n\n\nAbstract\nQuot-schemes of Grassmannian type naturally ari
se as resolutions of degeneracy loci of maps between vector bundles over a
scheme. In this talk we will talk about the recent results on the relatio
nships of the derived categories and Chow groups among these Quot-Schemes.
This framework provides a unified way to understand many known formulae s
uch as blowup formula\, Cayley's trick\, projectivization formula and form
ula for Grassmannain type flops and flips\, as well as provide new phenome
na such as virtual flips. We will also discuss applications to the study o
f moduli of linear series on curves\, blowup of determinantal ideals\, gen
eralised nested Hilbert schemes of points on surfaces\, and Brill--Noether
problem for moduli of stable objects in K3 categories.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiu Yu/邱宇 (Tsinghua University)
DTSTART:20201227T060000Z
DTEND:20201227T070000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/7
DESCRIPTION:Title: Cluster exchange groupoids and framed quadratic differentials\
nby Qiu Yu/邱宇 (Tsinghua University) as part of ICCM 2020\n\n\nAbstract
\nWe introduce the cluster exchange groupoids to show that any connected c
omponent (which are all isomorphic) of the moduli space of framed quadrati
c differentials on a decorated marked surface S_Delta is simply connected.
We also improve the result of Bridgeland-Smith\, that such a space can be
identified with the principal component of the space of stability conditi
ons on the associated Calabi-Yau-3 categories of S_Delta. If time permits\
, we will discuss q-deformations on Calabi-Ya categories\, stability condi
tions and quadratic differentials.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziming Ma/馬梓銘 (The Chinese University of Hong Kong)
DTSTART:20201227T071500Z
DTEND:20201227T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/8
DESCRIPTION:Title: The geometry of Maurer-Cartan equation near degenerate Calabi-Yau
varieties\nby Ziming Ma/馬梓銘 (The Chinese University of Hong Kong
) as part of ICCM 2020\n\n\nAbstract\nIn this talk\, we construct a dgBV a
lgebra PV(X) associated to a possibly degenerate Calabi- Yau variety X equ
ipped with local thickening data. This gives a version of the Kodaira-Spen
cer dgLa which is applicable to degenerated spaces including both log smoo
th or maximally degenerated Calabi-Yau. We use this to prove an unobstruct
edness result about the smoothing of degenerated Log Calabi-Yau varieties
X satisfying Hodge-deRham degeneracy property for cohomology of X\, in the
spirit of kontsevich-katzarkov-pantev. If time permitted\, I will describ
e construction of certain class of mirror vector bundles from Lagrangian m
ulti sections using deformation of pairs. This is based on joint works wit
h Kwokwai Chan\, Naichung Conan Leung and Yat-Hin Suen.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bing Wang/王兵 (USTC)
DTSTART:20201227T071500Z
DTEND:20201227T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/9
DESCRIPTION:Title: The local entropy along Ricci flow\nby Bing Wang/王兵 (USTC)
as part of ICCM 2020\n\n\nAbstract\nWe localize the entropy functionals o
f G. Perelman and generalize his no-local-collapsing theorem and pseudo-lo
cality theorem. Our generalization is technically inspired by further deve
lopment of Li-Yau estimates along the Ricci flow. It has various applicati
ons\, including to show the continuous dependence of the Ricci flow with r
espect to the initial metric in Gromov-Hausdorff topology with Ricci curva
ture bounded below\, and to show the compactness of the moduli of Kähler
manifolds with bounded scalar curvature and a rough locally almost Euclide
an condition.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kang Zuo/左康 (Universität Mainz)
DTSTART:20201227T071500Z
DTEND:20201227T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/10
DESCRIPTION:Title: Higgs Bundle in Geometry and Arithmetic A Proposal\nby Kang Z
uo/左康 (Universität Mainz) as part of ICCM 2020\n\n\nAbstract\nThe not
ion of a Higgs bundle originated from the theory of elementary particles\,
more precisely from the notion of the Higgs boson (field) in particle phy
sics. The Yukawa coupling\, named after Hideki Yukawa\, is used in the Sta
ndard Model in particle physics to describe the coupling between the Higgs
bosons\, a.k.a. the God particle\, and the quarks and leptons. A major de
velopment in complex nonabelian Hodge theory was made by Hitchin\, Donadls
on\, Uhlenbeck-Yau and Simpson in the so-called Hitchin-DonaldsonUhlenbeck
-Yau-Simpson correspondence\, a powerful tool in complex algebraic/analyti
c geometry. In this talk I will raise a proposal for exploring \, exploiti
ng and extending further our newly developed theories of Higgs bundles in
algebraic and arithmetic geometry. We will focus principally on the follow
ing two programs: • The Shafarevich Program: We work on moduli spaces of
polarized varieties in our approach to (1) the Shafarevich conjecture on
the finiteness of isomorphism classes of families of higher dimensional va
rieties and (2) a folklore conjecture on the bigness of the fundamental gr
oup of moduli spaces. • p -adic Nonabelian Hodge Theory: We develop and
explore further a theory of Higgs bundles on varieties over p-adic fields.
Three directions of applications are (1) to Faltings p-adic Simpson corre
spondence and its relation to Scholze’s OBdR-functor\, (2) revisiting Gr
othendieck anabelian geometry via nonabelian Hodge-Tate comparison and (3)
to the construction of motivic local systems over p-adic curves in connec
tions to Drinfeld’s work on the Langlands program via Abe’s solution o
f Deligne’s conjecture on p to ` companions. The proposal will therefore
demonstrate that the concept of Higgs bundle in various generalized setti
ngs plays a fundamental role in connecting different fields in algebraic g
eometry and topology via Yukawacoupling and in arithmetic geomety via p-ad
ic Higgs de Rham flow\, a p-adic analogue of Yang-Mills-Higgs equation ove
r the archimadean field. Remarkably the both notions originally came from
particle physics and String theory via Calabi-Yau manifolds. I have discus
sed with Steven Lu\, Ruiran Sun and Jinbang Yang on various parts of the p
roposal. I thank them very much.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin/覃帆 (Shanghai Jiao Tong University)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/11
DESCRIPTION:Title: Dual canonical bases and cluster algebras\nby Fan Qin/覃帆
(Shanghai Jiao Tong University) as part of ICCM 2020\n\n\nAbstract\nOne of
Fomin and Zelevinsky’s main motivations for cluster algebras was to stu
dy the dual canonical bases. Correspondingly\, it had been long conjecture
d that the quantum cluster monomials (certain monomials of generators) bel
ong to the dual canonical bases up to scalar multiples. In a geometric fra
mework for cluster algebras\, Fock and Goncharov expected that cluster alg
ebras possess bases with good tropical properties. In this talk\, we consi
der a large class of quantum cluster algebras called injective-reachable (
equivalently\, there exists a green to red sequence). We study their tropi
cal properties. Then we introduce the (common) triangular basis\, which is
a Kazhdan-Lusztig type basis with good tropical properties. We verify the
above motivational conjecture in full generality.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miaofen Chen/陈苗芬 (East China Normal University)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/12
DESCRIPTION:Title: Fargues-Rapoport conjecture in the non-basic case\nby Miaofen
Chen/陈苗芬 (East China Normal University) as part of ICCM 2020\n\n\nA
bstract\nRapoport and Zink introduce the p-adic period domain (also called
the admissible locus) inside the rigid analytic p-adic flag varieties. Ov
er the admissible locus\, there exists a universal crystalline Qp-local sy
stem which interpolates a family of crystalline representations. The weakl
y admissible locus is an approximation of the admissible locus in the sens
e that these two spaces have the same classical points. In a joint work wi
th Fargues and Shen\, we prove the Fargues-Rapoport conjecture for basic l
ocal Shimura datum which gives a group theoretic characterization when the
admissible locus and the weakly admissible locus coincide. In this talk\,
we will give a similiar criterion for non-basic local Shimura datum which
generalizes the work of Hartl for GLn.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Jiang/江辰 (Shanghai Centre for Mathematical Sciences\, Fud
an)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/13
DESCRIPTION:Title: Positivity in hyper kahler manifolds via Rozansky—Witten theory
\nby Chen Jiang/江辰 (Shanghai Centre for Mathematical Sciences\, Fu
dan) as part of ICCM 2020\n\n\nAbstract\nFor a hyperk\\"{a}hler manifold $
X$ of dimension $2n$\, Huybrechts showed that there are constants $a_0\, a
_2\, \\dots\, a_{2n}$ such that $$\\chi(L) =\\sum_{i=0}^n\\frac{a_{2i}}{(2
i)!}q_X(c_1(L))^{i}$$\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Yuan/袁伟 (Sun Yat-sen University)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/14
DESCRIPTION:Title: Volume comparison with respect to scalar curvature\nby Wei Yu
an/袁伟 (Sun Yat-sen University) as part of ICCM 2020\n\n\nAbstract\nIn
Riemannian geometry\, volume comparison theorem is one of the most fundame
ntal results. The classic results concern volume comparison involving rest
rictions on Ricci curvature. In this talk\, we will investigate the volume
comparison with respect to scalar curvature. In particular\, we show that
one can only expect such results for small geodesic balls of metrics near
V-static metrics. As for closed manifolds\, we give a volume comparison t
heorem for metrics near stable Einstein metrics. In particular\, it provid
es partially affirmative answers to both a conjecture of Schoen about hype
rbolic manifolds and a conjecture proposed by Bray concerning the positive
scalar curvature case respectively.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guan Huang/黄冠 (Tsinghua University)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/15
DESCRIPTION:Title: Recent progress in Birkhoff conjecture for strictly convex billia
rd tables\nby Guan Huang/黄冠 (Tsinghua University) as part of ICCM
2020\n\n\nAbstract\nThe famous Birkhoff conjecture claims that all the int
egrable planar billiard systems are those induced by convex domains with a
n ellipse or a circle as boundary. We will discuss the recent progress of
Birkhoff conjecture\, particularly\, the results obtained for nearly ellip
tic domains. This talk is partially based on joint work with Kaloshin and
Sorrentino.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Zheng/郑浩 (Shanghai Centre for Mathematical Sciences\, Fuda
n)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/16
DESCRIPTION:Title: Categorical computation\nby Hao Zheng/郑浩 (Shanghai Centre
for Mathematical Sciences\, Fudan) as part of ICCM 2020\n\n\nAbstract\nWe
propose that topological quantum computation is a categorification of qua
ntum computation and present some mathematical results that are useful for
realizing categorical computation by topological materials.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiajun Zhang/张家军 (SYSU)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/17
DESCRIPTION:Title: Modelling and analysis of non-Markovian biochemical reaction netw
orks\nby Jiajun Zhang/张家军 (SYSU) as part of ICCM 2020\n\n\nAbstr
act\nModeling intracellular processes has long relied on the Markovian ass
umption. However\, as soon as a reactant interacts with its environment\,
molecular memory definitely exists and its effects cannot be neglected. Si
nce the Markov theory cannot translate directly to modeling and analysis o
f non-Markovian processes\, this leads to many significant challenges. We
develop a formulation\, namely the stationary generalized chemical-master
equation\, to model intracellular processes with molecular memory. This fo
rmulation converts a non-Markovian question to a Markovian one while keepi
ng the stationary probabilistic behavior unchanged. Both a stationary gene
ralized Fokker–Planck equation and a generalized linear noise approximat
ion are further developed for the fast evaluation of fluctuations. These f
ormulations can have broad applications and may help us discover new biolo
gical knowledge.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ke Deng/邓柯 (Center for Statistical Science\, Tsinghua Universi
ty)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/18
DESCRIPTION:Title: Understanding Chinese Texts via Statistical Inference\nby Ke
Deng/邓柯 (Center for Statistical Science\, Tsinghua University) as part
of ICCM 2020\n\n\nAbstract\nWith the growing availability of digitized te
xt data both publicly and privately\, there is a great need for effective
computational tools to automatically extract information from texts. Becau
se the Chinese language differs most significantly from alphabet-based lan
guages in not specifying word boundaries\, most existing Chinese text-mini
ng methods require a prespecified vocabulary and/or a large relevant train
ing corpus\, which may not be available in some applications. We proposed
a family of statistical approaches that can achieve multiple NLP tasks\, s
uch as word discovery\, name entity recognition\, word segementation\, sem
amtic understanding and relation extraction\, simultaneously with little t
raining information. These approaches are particularly useful for mining d
omain-specific texts where the underlying vocabulary is unknown and/or the
texts of interest differ significantly from standard training corpora.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guodong Zhou/周国栋 (East China Normal University)
DTSTART:20201227T091500Z
DTEND:20201227T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/19
DESCRIPTION:Title: Formal deformations and cohomology theory of Rota-Baxter algebras
of any weight\nby Guodong Zhou/周国栋 (East China Normal Universit
y) as part of ICCM 2020\n\n\nAbstract\nThis paper studies Rota-Baxter alge
bras of any weight\, say\, associative algebras endowed with Rota-Baxter o
perators. We develop a cohomology theory for Rota-Baxter algebras of any w
eight and justify it by interpreting lower degree cohomology groups as for
mal deformations and abelian extensions of Rota-Baxter algebras. We make e
xplicit the $L_\\infty$-algebra structure over the cochain complex definin
g cohomology groups and introduce the notion of homotopy Rota-Baxter algeb
ras as Maurer-Cartan elements of this $L_\\infty$-algebra.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ping Xi/郗平 (Xi'an Jiao Tong University)
DTSTART:20201227T091500Z
DTEND:20201227T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/20
DESCRIPTION:Title: Equidistribution of quadratic roots and applications to prime num
ber theory\nby Ping Xi/郗平 (Xi'an Jiao Tong University) as part of
ICCM 2020\n\n\nAbstract\nGiven an irreducible quadratic polynomial of fixe
d discriminant\, the quadratic roots mod $m$ are expected to be equidistri
buted as $m$ runs over reasonable sets. We will give a short historical su
rvey on this topic\, as well as our recent progress on the case of friable
moduli. Moreover\, a reasonable equidistribution can also lead to non-tri
vial multiplicative structures in prime number theory\, and an application
to a special case of Schinzel hypothesis will be discussed in this talk.
The underlying tools will include Gauss’s correspondence in the theory o
f binary quadratic forms and arithmetic exponent pairs for trace functions
developed by Jie Wu and the speaker.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Lv/吕鑫 (East China Normal University)
DTSTART:20201227T091500Z
DTEND:20201227T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/21
DESCRIPTION:Title: The irregularity of trigonal fibrations\nby Xin Lv/吕鑫 (Ea
st China Normal University) as part of ICCM 2020\n\n\nAbstract\nLet $f: S
\\to B$ be a non-trivial fibration of curves of genus $g$. Xiao conjecture
d an upper bound of the relative irregularity $q_f$ in terms of the genus
$g$. In this talk\, we consider this problem for trigonal fibrations.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Xia/夏超 (Xiamen Uinversity)
DTSTART:20201227T091500Z
DTEND:20201227T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/22
DESCRIPTION:Title: A sharp lower bound for the first (nonzero) Steklov eigenvalue\nby Chao Xia/夏超 (Xiamen Uinversity) as part of ICCM 2020\n\n\nAbstra
ct\nEscobar has conjectured that for a compact manifold with boundary whic
h has nonnegative Ricci curvature and boundary principal curvatures bounde
d below by 1\, the first (nonzero) Steklov eigenvalue is greater than or e
qual to 1，with equality holding only on a Euclidean ball. This conjectur
e is true in two dimensions due to Payne and Escobar. In this talk\, we pr
esent a resolution to this conjecture in the case of nonnegative sectional
curvature in any dimensions. We will also give a sharp comparison result
between the first (nonzero) Steklov eigenvalue and the boundary first eige
nvalue. Our tool is a weighted Reilly type formula due to Qiu-Xia and a Po
hozaev type identity. The talk is based on a joint work with Changwei Xion
g.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huichun Zhang/张会春 (SYSU)
DTSTART:20201227T091500Z
DTEND:20201227T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/23
DESCRIPTION:Title: Some results on the Lipschitz Regularity of harmonic maps between
singular spaces\nby Huichun Zhang/张会春 (SYSU) as part of ICCM 20
20\n\n\nAbstract\nIn this talk\, we will introduce some results on the pro
gram about the Lipschitz regularity and gradient estimates for harmonic ma
ps from/between the singular metric spaces with curvature bounded from bel
ow/above in the sense of comparison triangles. This talk is based on some
joint works with Xi-Ping Zhu\, Xiao Zhong\, and Huabin Ge and Wenshuai Jia
ng.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qin Li/李勤 (Southern University of Science and Technology)
DTSTART:20201227T091500Z
DTEND:20201227T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/24
DESCRIPTION:Title: Quantization of Kapranov $L_\\infty$ structure and Bargmann-Fock
sheaves on Kahler manifolds\nby Qin Li/李勤 (Southern University of
Science and Technology) as part of ICCM 2020\n\n\nAbstract\nIn this talk\,
I will introduce a quantization of Kapranov $L_\\infty$ structure on K\\"
ahler manifolds\, which gives rise to a special class of solutions of Fedo
sov equations. These solutions give rise to one-loop exact BV quantization
using Costello's theory of effective renormalization. By using these Fed
osov connections\, we will also construct a sheaf of modules over deformat
ion quantization algebra which we call Bargmann-Fock sheaves. This in part
icular give rise to a representation of Berezin-Toeplitz quantization on H
ilbert spaces.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinshan Zeng/曾锦山 (Jiangxi Normal University)
DTSTART:20201227T091500Z
DTEND:20201227T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/25
DESCRIPTION:Title: On ADMM in Deep Learning: Convergence and Saturation-Avoidance\nby Jinshan Zeng/曾锦山 (Jiangxi Normal University) as part of ICCM 2
020\n\n\nAbstract\nIn this talk\, we introduce an alternating direction me
thod of multipliers (ADMM) for deep neural networks training with sigmoid-
type activation functions (called sigmoid-ADMM pair)\, mainly motivated by
the gradient-free nature of ADMM in avoiding the saturation of sigmoid-ty
pe activations and the advantages of deep neural networks with sigmoid-typ
e activations (called deep sigmoid nets) over their rectified linear unit
(ReLU) counterparts (called deep ReLU nets) in terms of approximation. In
particular\, we prove that the approximation capability of deep sigmoid ne
ts is not worse than deep ReLU nets by showing that ReLU activation fucnti
on can be well approximated by deep sigmoid nets with two hidden layers an
d finitely many free parameters but not vice-verse. We also establish the
global convergence of the proposed ADMM for the nonlinearly constrained fo
rmulation of the deep sigmoid nets training to a Karush-Kuhn-Tucker (KKT)
point at a rate of order O(1/k). Compared with the widely used stochastic
gradient descent (SGD) algorithm for the deep ReLU nets training (called R
eLU-SGD pair)\, the proposed sigmoid-ADMM pair is practically stable with
respect to the algorithmic hyperparameters including the learning rate\, i
nitial schemes and the pro-processing of the input data. Moreover\, we fin
d that to approximate and learn simple but important functions the propose
d sigmoid-ADMM pair numerically outperforms the ReLU-SGD pair.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianping Jiang/姜建平
DTSTART:20201227T091500Z
DTEND:20201227T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/26
DESCRIPTION:Title: The high dimensional Ising model with free boundary conditions\nby Jianping Jiang/姜建平 as part of ICCM 2020\n\n\nAbstract\nWe stud
y the critical Ising model with free boundary conditions on finite domains
in $\\mathbb{Z}^d$ with $d\\geq4$. Under the assumption\, so far only pro
ved completely for high $d$\, that the critical infinite volume two-point
function is of order $|x-y|^{-(d-2)}$ for large $|x-y|$\, we prove the sam
e is valid on large finite cubes with free boundary conditions\, as long a
s $x\, y$ are not too close to the boundary. We also prove that the scalin
g limit of the near-critical (small external field) Ising magnetization fi
eld with free boundary conditions is Gaussian with the same covariance as
the critical scaling limit\, and thus the correlations do not decay expone
ntially. This is very different from the situation in low $d$ or the expec
ted behavior in high $d$ with bulk boundary conditions. This is joint work
with F. Camia and C.M. Newman.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Kou (Harvard University)
DTSTART:20201228T003000Z
DTEND:20201228T013000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/27
DESCRIPTION:Title: Statistical inference of dynamic systems via constrained Gaussian
processes\nby Samuel Kou (Harvard University) as part of ICCM 2020\n\
n\nAbstract\nParameter estimation of nonlinear dynamical system models fro
m noisy and sparse experimental data is a vital task in many fields\; it h
as challenged the existing inference methods\, especially when there are u
nobserved system components. We propose a fast Bayesian inference method t
o estimate the ODE parameters with real data from biological/physical expe
riments via constrained Gaussian process. Our method utilizes Gaussian pro
cesses that are explicitly conditioned on the functional manifold that des
cribes the ODE system. Using this constrained Gaussian process under the B
ayesian paradigm\, our method completely avoids the use of numerical solve
r and thus achieves dramatic saving in computational time. At the same tim
e\, our method also offers accurate inference\, including uncertainly quan
tification. Our approach is distinct from the existing ones owing to its r
igorous construction under the Bayesian framework. We demonstrate the spee
d and accuracy of the method using realistic examples\, including examples
with unobserved system components.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (MIT)
DTSTART:20201228T003000Z
DTEND:20201228T013000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/28
DESCRIPTION:Title: Cohomology of the moduli of Higgs bundles\nby Junliang Shen (
MIT) as part of ICCM 2020\n\n\nAbstract\nThe moduli space of Higgs bundles
and Hitchin‘s integrable system lie at the crossroads of mathematical
physics\, representaton theory\, and geometry. In this talk\, we focus on
the structure of cohomology for the moduli of Higgs bundle from the viewpo
ints of the non-abelian Hodge theorey\, hyper-Kähaler geometry\, and mirr
or symmetry. In particular\, we will discuss recent progress on the P=W co
njecture and Hausel-Thaddeus' topological mirror symmetry conjecture. Base
d on joint work with Mark de Cataldo and Davesh Maulik.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yun Shi (University of Illinois at Urbana-Champaign)
DTSTART:20201228T003000Z
DTEND:20201228T013000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/29
DESCRIPTION:Title: subschemes on some local toric Calabi-Yau threefolds\nby Yun
Shi (University of Illinois at Urbana-Champaign) as part of ICCM 2020\n\n\
nAbstract\nDonaldson-Thomas (DT) theory is an enumerative theory which pro
duces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau
3-fold. Motivic Donaldson-Thomas theory\, originally introduced by Kont
sevich-Soibelman\, is a categorification of the DT theory. This categorifi
cation contains more refined information of the moduli space. In this talk
\, I will give a brief introduction to motivic DT theory following the d
efinition of Bussi-Joyce-Meinhardt\, in particular the role of d-critical
locus structure in the definition of motivic DT invariant. I will also
discuss a result on this structure on the Hilbert schemes of zero dimensio
nal subschemes on some local toric Calabi-Yau threefolds. This is joint wo
rk in progress with Sheldon Katz.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Zhang (Southeast University)
DTSTART:20201228T003000Z
DTEND:20201228T013000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/30
DESCRIPTION:Title: Stratifications on good reductions of Shimura varieties\nby C
hao Zhang (Southeast University) as part of ICCM 2020\n\n\nAbstract\nI wil
l first explain definitions and basic geometric properties of various stra
tifications on good reductions of Hodge type Shimura varieties. Then I wil
l discuss analogous properties for Hodge type compactifications and Rapopo
rt-Zink spaces\, and for good reductions of Shimura varieties of abelian t
ype. This talk is partially based on a joint work with Xu Shen.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zongru Li (Harvard University)
DTSTART:20201228T013000Z
DTEND:20201228T023000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/31
DESCRIPTION:Title: Mirror duality between fractional complete intersection Calabi--Y
au spaces\nby Zongru Li (Harvard University) as part of ICCM 2020\n\n\
nAbstract\nRecently\, Hosono\, Lian\, Takagi\, and Yau investigated the fa
mily of K3 surfaces arising from double covers branched along six lines in
\\(\\mathbb{P}^{2}\\) and proposed a singular version of mirror symmetry.
In this talk\, I will give a construction of mirror pairs of certain sing
ular Calabi--Yau varieties. We will discuss the topological test as well a
s the quantum test on these singular Calabi--Yau pairs. The talk is based
on the joint works with Shinobu Hosono\, Bong H. Lian and S.-T. Yau.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rencang Li (University Of Texas At Arlington)
DTSTART:20201228T013000Z
DTEND:20201228T023000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/32
DESCRIPTION:Title: Orthogonal Multi-View Subspace Learning\nby Rencang Li (Unive
rsity Of Texas At Arlington) as part of ICCM 2020\n\n\nAbstract\nMulti-vie
w data are increasingly collected for a variety of applications in the rea
l world. They contain complementary\, redundant\, and corroborative conten
ts and so provide more informative than single_x005fview data when it come
s to characterize objects of the real-world. It is rather natural for huma
n beings to perceive the world through comprehensive information collected
by multiple sensory organs\, but it is an open question on how to endow m
achines with analogous cognitive capabilities to do the same.One of the fu
ndamental challenges is how to represent and summarize multi-view data in
such a way that comprehensive information concealed in multi-view data can
be properly exploited by multi-view learning models. In this talk\, we wi
ll present a unified framework for multi-view subspace learning to learn i
ndividual orthogonal projections for all views. The framework integrates t
he correlations within multiple views\, supervised discriminant capacity\,
and distance preservation in a concise and compact way. It not only inclu
des several existing models as special cases\, but also inspires new novel
models. Besides the framework\, we will discuss highly efficient numerica
l methods to solve the associated optimization problems. The methods are b
uilt upon an iterative Krylov subspace method which can easily scale up fo
r large size datasets. Extensive experiments are conducted on various real
-world datasets for the multi-view discriminant analysis and multi-view mu
lti-label classification tasks. The experimental results demonstrate that
the proposed models are consistently competitive to and often better than
the state-of-the-art methods.This is a joint work with Li Wang (UT Arlingt
on)\, Lei-hong Zhang (Soochow University)\, and Chungen Shen (University o
f Shanghai for Science and Technology).\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaotong Shen (University of Minnesota)
DTSTART:20201228T013000Z
DTEND:20201228T023000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/33
DESCRIPTION:Title: Likelihood inference for a large causal network\nby Xiaotong
Shen (University of Minnesota) as part of ICCM 2020\n\n\nAbstract\nInferen
ce of causal relations between interacting units in a directed acyclic gra
ph (DAG)\, such as a regulatory gene network\, is common in practice\, imp
osing challenges because of a lack of inferential tools.In this talk\, I w
ill present constrained likelihood ratio tests for inference of the connec
tivity as well as directionality subject to nonconvex acyclicity constrain
ts in a Gaussian directed graphical model. Particularly\,for testing of co
nnectivity\, the asymptotic distribution is either chi-squared or normal d
epending on if the number of testable links in a DAG model is small\; for
testing of directionality\, the asymptotic distribution is the minimum of
d independent chi-squared variables with one-degree of freedom or a genera
lized Gamma distribution depending on if d is small\, where d is the numbe
r of breakpoints in a hypothesized pathway.Computational methods will be d
iscussed\, in addition to some numerical examples to infer a directed path
way in a gene network. This work is joint with Chunlin Li and Wei Pan of t
he University of Minnesota.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mao Sheng (USTC)
DTSTART:20201228T013000Z
DTEND:20201228T023000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/34
DESCRIPTION:Title: Arithmetic semisimplicity theorem\nby Mao Sheng (USTC) as par
t of ICCM 2020\n\n\nAbstract\nIn this lecture\, I would like to talk on an
arithmetic version of the Deligne' semisimplicity theorem.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Huang (Emory University)
DTSTART:20201228T030000Z
DTEND:20201228T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/35
DESCRIPTION:Title: Interlacing methods in Extremal Combinatorics\nby Hao Huang (
Emory University) as part of ICCM 2020\n\n\nAbstract\nExtremal Combinatori
cs studies how large or how small a collection of finite objects could be\
, if it has to satisfy certain restrictions. In this talk\, we will discus
s how eigenvalue interlacing leads to various interesting results in Extre
mal Combinatorics\, including the Erdos-Ko-Rado Theorem and its degree ver
sion\, an isodiametric inequality for discrete cubes\, and the resolution
of a thirty-year-old open problem in Theoretical Computer Science\, the Se
nsitivity Conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihang Zhu (University of Maryland)
DTSTART:20201228T030000Z
DTEND:20201228T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/36
DESCRIPTION:Title: Twisted orbital integrals and affine Deligne-Lusztig varieties\nby Yihang Zhu (University of Maryland) as part of ICCM 2020\n\n\nAbstra
ct\nAffine Deligne-Lusztig varieties are certain algebraic varieties whose
definition has a strong Lie theory flavor. They play an important role in
the study of Shimura varieties\, which is one of the central topics in th
e Langlands Program. On the other hand\, (twisted) orbital integrals on a
Lie group are natural objects in harmonic analysis\, which also appear in
the Langlands Program. We will discuss a recent method of using twisted or
bital integrals to study the geometry of affine Deligne-Lusztig varieties.
The talk is based on a paper joint with Rong Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kuan-Wen Lai (Universtiy of Mass)
DTSTART:20201228T030000Z
DTEND:20201228T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/37
DESCRIPTION:Title: Fourier-Mukai equivalences arising from Cremona transformations\nby Kuan-Wen Lai (Universtiy of Mass) as part of ICCM 2020\n\n\nAbstrac
t\nIt is widely conjectured that a cubic fourfold is rational if and only
if its derived category contains a summand that comes from a K3 surface. T
his question suggests the study about how the birational geometry of cubic
fourfolds is determined by their associated K3 surfaces\, or more general
ly\, by their K3 categories. This talk aims to introduce two examples of e
quivalences between K3 categories constructed from Cremona transformations
\, i.e.\, birational automorphisms of projective spaces\, as well as some
of their applications.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siyuan Lu (McMaster University\, Canada)
DTSTART:20201228T030000Z
DTEND:20201228T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/38
DESCRIPTION:Title: Rigidity of Riemannian Penrose inequality with corners and its im
plications\nby Siyuan Lu (McMaster University\, Canada) as part of ICC
M 2020\n\n\nAbstract\nMotivated by the rigidity case in the localized Riem
annian Penrose inequality\, we show that suitable singular metrics attaini
ng the optimal value in the Riemannian Penrose inequality is necessarily s
mooth in properly specified coordinates. If applied to hypersurfaces enclo
sing the horizon in a spatial Schwarzschild manifold\, the result gives th
e rigidity of isometric hypersurfaces with the same mean curvature.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Wing Hong Luk
DTSTART:20201228T030000Z
DTEND:20201228T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/39
DESCRIPTION:Title: Singularities in general relativity\nby Jonathan Wing Hong Lu
k as part of ICCM 2020\n\n\nAbstract\nIn this talk\, I will survey some re
cent mathematical results regarding the nature of singularities in general
relativity.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu-Shen Lin (Boston University)
DTSTART:20201228T030000Z
DTEND:20201228T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/40
DESCRIPTION:Title: On the comparison of the family Floer mirrors and GS/GHK Mirrors<
/a>\nby Yu-Shen Lin (Boston University) as part of ICCM 2020\n\n\nAbstract
\nStrominger-Yau-Zaslow conjecture serves as the guiding principle for mir
ror symmetry in the past decade. In particular\, SYZ spirit provides a rec
ipe for constructing the mirrors. Instead of the original conjecture\, the
re is the algebraic approach of Kontsevich-Soibelman\, Gross-Siebert and t
he symplectic approach of using family Floer homology. It is natural to as
k to ask if the two approaches give the same mirror. In this talk\, I will
discuss some situations with the existence of special Lagrangian fibratio
ns for some log Calabi-Yau surfaces. Furthermore\, we will compare the fam
ily Floer mirror with the Gross-Hacking-Keel mirror and finite cluster var
ieties. Part of the talk is based on the joint work with Man-Wai Cheung.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianguo Liu (Duke University)
DTSTART:20201228T030000Z
DTEND:20201228T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/41
DESCRIPTION:Title: Contact line dynamics for merging and splitting of droplets: grad
ient flow formulation and computations\nby Jianguo Liu (Duke Universit
y) as part of ICCM 2020\n\n\nAbstract\nThe capillary effects caused by the
interfacial energy dominates the dynamics of small droplets and takes the
form of mean curvature flow of the capillary surface coupled with contact
line dynamics. For the volume preserving motion\, this is modeled by a fr
ee boundary incompressible potential flow. A gradient flow on a Hilbert ma
nifold is used for effective numerical methods. We propose unconditionally
stable first/second order numerical schemes based on explicit moving boun
dary updates and a semi-Lagrangian method. To enforce impermeable obstacle
constraint\, a projection method for a variational inequality is further
adapted to simulate the unavoidable merging and splitting of droplets. Th
e phase transition for the emerged contact lines are detected and equipped
with contact line mechanism. We also compare the purely geometric droplet
dynamics with hydrodynamic models.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuxin Chen (Princeton University)
DTSTART:20201228T030000Z
DTEND:20201228T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/42
DESCRIPTION:Title: Solving Random Quadratic Systems of Equations Is Nearly as Easy a
s Solving Linear Systems\nby Yuxin Chen (Princeton University) as part
of ICCM 2020\n\n\nAbstract\nThis talk considers the fundamental problem o
f solving quadratic systems of equations in n variables. We propose a nove
l method\, which starting with an initial guess computed by means of a spe
ctral method\, proceeds by minimizing a nonconvex functional as in the Wir
tinger flow approach. There are several key distinguishing features\, most
notably\, a distinct objective functional and novel update rules\, which
operate in an adaptive fashion and drop terms bearing too much influence o
n the search direction. These careful selection rules provide a tighter in
itial guess\, better descent directions\, and thus enhanced practical perf
ormance. On the theoretical side\, we prove that for certain unstructured
models of quadratic systems\, our algorithms return the correct solution i
n linear time\, i.e. in time proportional to reading the data as soon as t
he ratio between the number of equations and unknowns exceeds a fixed nume
rical constant. We extend the theory to deal with noisy systems and prove
that our algorithms achieve a statistical accuracy\, which is nearly un-im
provable. We complement our theoretical study with numerical examples show
ing that solving random quadratic systems is both computationally and stat
istically not much harder than solving linear systems of the same size---h
ence the title of this work. For instance\, we demonstrate empirically tha
t the computational cost of our algorithm is about four times that of solv
ing a least-squares problem of the same size.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yau Shing-Tung (Havard University)
DTSTART:20201228T083000Z
DTEND:20201228T093000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/43
DESCRIPTION:Title: Existence of black hole due to GR and dynamics of particles aroun
d it\nby Yau Shing-Tung (Havard University) as part of ICCM 2020\n\n\n
Abstract\n我们讨论广义相对论中关于证明黑洞存在性的数
学理论发展及其几何原理。\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chunhe Li (华南师范大学)
DTSTART:20201228T070000Z
DTEND:20201228T074500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/44
DESCRIPTION:Title: The isometric embedding in rotationally symmetric warped product
space:existence and uniqueness\nby Chunhe Li (华南师范大学) as p
art of ICCM 2020\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinbang Yang
DTSTART:20201228T070000Z
DTEND:20201228T074500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/45
DESCRIPTION:Title: Comparison on p-adic Simpson correspondence and p-adic Riemann-Hi
lbert correspondence\nby Jinbang Yang as part of ICCM 2020\n\n\nAbstra
ct\nIn 2005\, Faltings constructed an equivalence between the category of
Higgs bundles and that of generalized representations of the \\'etale fund
amental group for curves over a p-adic field. In 2013\, Scholze introduced
a fully faithful functor from the category filtered de Rham bundles to th
at of $\\mathbb B_{dR}^+$-local systems. In this talk\, I will show that f
or a filtered de Rham bundle the first graded piece of the $\\mathbb B_{
dR}^+$-local systems is just the generalized representation attached to it
s graded Higgs bundle. This is a joint work with Kang Zuo.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Zhang (USTC)
DTSTART:20201228T070000Z
DTEND:20201228T074500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/46
DESCRIPTION:Title: Pluricanonical system in positive characteristic\nby Lei Zhan
g (USTC) as part of ICCM 2020\n\n\nAbstract\nPluricanonical system plays a
n important role in the classification of varieties. Concerning this issue
\, abundance and effectivity are the two most important problems. To study
the two problems\, the key point is how to construct pluricanonical secti
ons. There have been many methods to construct pluricanonical sections in
characteristic zero. In this talk\, we discuss pluricanonical systems on v
arieties in positive characteristic. We will summarize the recent progress
es and explain how to adapt the techniques from characteristic zero to pos
itive characteristic case.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pu Zhang (上海交通大学)
DTSTART:20201228T070000Z
DTEND:20201228T074500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/47
DESCRIPTION:Title: 单态射范畴\, Gorenstein 投射模和倾斜理论\nby Pu
Zhang (上海交通大学) as part of ICCM 2020\n\n\nAbstract\n我们将
报告由quiver和双模确定的两种单态射范畴的各种性质，
它们与Gorenstein投射模，半Gorenstein投射模，倾斜理论，奇
点范畴之间的关系.我们将构造Hilbert型为(3\,2)的6维局部
代数上一类（无穷多个）半Gorenstein投射模而非torsionless
模（从而非Gorenstein投射模）的例子.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenglong Yu (Tsinghua University)
DTSTART:20201228T053000Z
DTEND:20201228T063000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/48
DESCRIPTION:Title: Calabi-Yau varieties via cyclic covers and arithmetic ball quotie
nts\nby Chenglong Yu (Tsinghua University) as part of ICCM 2020\n\n\nA
bstract\nIn this talk\, we consider Calabi-Yau varieties arising from cycl
ic covers of smooth projective varieties branching along simple normal cro
ssing divisors. The crepant resolutions give families of smooth Calabi-Yau
manifolds. In some cases\, the corresponding period maps factor through b
all quotients. We give a classification of such examples for cyclic covers
of some Fano varieties\, especially for the product of three projective l
ines. This generalizes the work of Sheng-Xu-Zuo. Some of the Calabi-Yau ma
nifolds obtained are related to the Borcea-Voisin construction and studied
in Rohde’s thesis. This is joint work with Zhiwei Zheng.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Zhang (National University of Singapore)
DTSTART:20201228T053000Z
DTEND:20201228T063000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/49
DESCRIPTION:Title: Twisted Automorphic Descent and the Global Gan-Gross-Prasad Conje
cture\nby Lei Zhang (National University of Singapore) as part of ICCM
2020\n\n\nAbstract\nIn this talk\, we will discuss the theory of Twisted
Automorphic Descent and constructions of concrete cuspidal automorphic mod
ules by means of the global Arthur parameters via endoscopy classification
. Among the consequences of the theory\, we establish one direction of Glo
bal Gan-Gross-Prasad Conjecture in full generality for all classical group
s. This is a joint project with Dihua Jiang.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuang Miao (Wuhan University)
DTSTART:20201228T053000Z
DTEND:20201228T063000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/50
DESCRIPTION:Title: The stability of blow up solutions to critical Wave Maps beyond e
quivariant setting\nby Shuang Miao (Wuhan University) as part of ICCM
2020\n\n\nAbstract\nIn 2006\, Krieger\, Schlag and Tataru (KST) constructe
d a family of type II blow up solutions to the 2+1 dimensional wave map eq
uation with unit sphere as its target. This construction provides the firs
t example of blow up solutions to the energy-critical Wave Maps. A key fea
ture of this family is that it exhibits a continuum of blow up rates. Howe
ver\, from the way it was constructed\, the stability of this family was n
ot clear and it was believed to be non-generic. In this talk I will presen
t our recent work on proving the stability and rigidity of the KST family\
, beyond the equivariant setting. This is based on joint works with Joachi
m Krieger and Wilhelm Schlag.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Wu (Tsinghua University)
DTSTART:20201228T053000Z
DTEND:20201228T063000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/51
DESCRIPTION:Title: Crossing probabilities in 2D critical lattice models\nby Hao
Wu (Tsinghua University) as part of ICCM 2020\n\n\nAbstract\nThis talk has
two parts. In the first part\, we discuss Ising model which is one of the
most studied models in statistical physics. We consider critical Ising mo
del in two-dimensional and give crossing probabilities of multiple interfa
ces in the critical Ising model in polygon with alternating boundary condi
tions. Similar formulas also hold for other critical lattice models\, for
instance level lines of discrete Gaussian free field. However\, the situat
ion is different when one considers level lines of metric graph Gaussian f
ree field. This leads to the second part of this talk. In the second part\
, we discuss Gaussian free field (GFF). Discrete GFF and metric graph GFF
converge to the same continuum GFF. However\, their crossing probabilities
are distinct. We will explain the difference and show how to calculate th
em.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiangdi Huang (中科院数学与系统科学研究院)
DTSTART:20201228T070000Z
DTEND:20201228T074500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/52
DESCRIPTION:Title: Global classical and weak solutions to the three-dimensional full
compressible Navier-Stokes system with vacuum and large oscillations\
nby Xiangdi Huang (中科院数学与系统科学研究院) as part of ICC
M 2020\n\n\nAbstract\nFor the three-dimensional full compressible Navier
–Stokes system describing the motion of a viscous\, compressible\, heat-
conductive\, and Newtonian polytropic fluid\, we establish the global exis
tence and uniqueness of classical solutions with smooth initial data which
are of small energy but possibly large oscillations where the initial den
sity is allowed to vanish. Moreover\, for the initial data\, which may be
discontinuous and contain vacuum states\, we also obtain the global existe
nce of weak solutions. These results generalize previous ones on classical
and weak solutions for initial density being strictly away from a vacuum\
, and are the first for global classical and weak solutions which may have
large oscillations and can contain vacuum states.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changzheng Li (Sun Yat-Sen University)
DTSTART:20201228T070000Z
DTEND:20201228T074500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/53
DESCRIPTION:Title: Eigenvalue problems and quantum cohomology\nby Changzheng Li
(Sun Yat-Sen University) as part of ICCM 2020\n\n\nAbstract\nIn this talk\
, we will discuss some problems on the eigenvalues of linear operators on
the quantum cohomology of a Fano manifold\, induced by the quantum multipl
ications.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bangti Jin (UCL\, UK)
DTSTART:20201228T070000Z
DTEND:20201228T074500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/54
DESCRIPTION:Title: Numerical methods for time-fractional diffusion\nby Bangti Ji
n (UCL\, UK) as part of ICCM 2020\n\n\nAbstract\nDuring the past decade\,
parabolic equations involving a fractional-order derivative in time have r
eceived much attention\, and a large number of numerical methods have been
developed. Many of these existing methods were developed by assuming that
the solution is sufficiently smooth\, which however is generally not true
. In this talk\, I will describe our works on developing and analyzing and
robust numerical schemes that do not assume solution regularity directly\
, but only data regularity.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kelin Xia/夏克林 (新加坡南洋理工大学)
DTSTART:20201228T070000Z
DTEND:20201228T074500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/55
DESCRIPTION:Title: Persistent representations based deep learning for drug design\nby Kelin Xia/夏克林 (新加坡南洋理工大学) as part of ICCM 20
20\n\n\nAbstract\nEffective molecular representation is key to the success
of machine learning models for molecular data analysis. In this talk\, we
will discuss a series of persistent representations\, including persisten
t homology\, persistent spectral models\, and persistent Ricci curvature a
nd their combination with deep learning models. Unlike traditional graph a
nd network models\, these filtration-induced persistent models can charact
erize the multiscale topological and geometric information\, thus signific
antly reduce molecular data complexity and dimensionality. Feature vector
s are obtained from various persistent attributes derived from topological
and geometric invariants\, such as homology\, cohomology\, eigenvalues\,
and Ricci curvature. They are inputted into deep learning models\, in part
icular\, random forest\, gradient boosting tree and convolutional neural n
etwork (CNN). Our persistent representations based molecular fingerprints
can significantly boost the performance of learning models in drug design.
\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bin Shu (华东师范大学)
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/56
DESCRIPTION:Title: Super Vust theorem and a duality for principal finite W-superalge
bras\nby Bin Shu (华东师范大学) as part of ICCM 2020\n\n\nAbstra
ct\nIn this talk\, I will introduce a super version of Vust theorem for a
general linear Lie superalgebra\, which gives rise to a duality involving
any given nilpotent even matrix. The duality can be extended to the princi
pal finite W-superalgebras. This is a joint work with Changjie Cheng and Y
ang Zeng.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weizhe Zheng (AMSS)
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/57
DESCRIPTION:Title: Weil猜想、平展上同调和超积\nby Weizhe Zheng (AMSS)
as part of ICCM 2020\n\n\nAbstract\nWeil猜想是关于有限域上代数
簇Zeta函数的重要猜想。本报告将回顾Weil猜想和平展上同
调的关系，介绍分解定理等后续发展，并简介超积上同
调的一些新进展。\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qifeng Li (Institute for Basic Science)
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/58
DESCRIPTION:Title: The VMRT structures and the deformation rigidity of rational homo
geneous spaces\nby Qifeng Li (Institute for Basic Science) as part of
ICCM 2020\n\n\nAbstract\nIn a series of works of Hwang and Mok\, they stud
ied extensively the deformation rigidity of rational homogeneous spaces of
Picard number one. Inspired by these works\, they conjecture that rationa
l homogeneous spaces of Picard number one can be characterized by their VM
RT's (varieties of minimal rational tangents). In this talk we will discus
s on two related topics\, one is the deformation rigidity of rational homo
geneous spaces of higher Picard numbers\, and the other is the verificatio
n of this characterization conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yongsheng Zhang (Tongji University)
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/59
DESCRIPTION:Title: On the non-existence of solutions to the Dirichlet problem for mi
nimal surface system\nby Yongsheng Zhang (Tongji University) as part o
f ICCM 2020\n\n\nAbstract\nIn this talk，we will show how to generalize t
he non-existence result by Lawson-Osserman.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinkai Li (华南师范大学)
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/60
DESCRIPTION:Title: Well-posedness of entropy-bounded solutions of the compressible N
avier-Stokes equations with vacuum\nby Jinkai Li (华南师范大学)
as part of ICCM 2020\n\n\nAbstract\nThe entropy is one of the fundamental
physical states of a fluid. For the ideal gases\, the entropy can be expre
ssed as some linear combination of the logarithms of the density and tempe
rature in the non-vacuum region\, and\, in the viscous case\, the equation
that it satisfies is highly singular in the region close to the vacuum. D
ue to the singularity of the logarithmic function at zero\, which may lead
to the singularity of the entropy\, and the singularity of the entropy eq
uation near the vacuum region\, in spite of its importance in the gas dyna
mics\, the mathematical analyses on the behavior of the entropy near the v
acuum region\, were rarely carried out\; in particular\, in the presence o
f vacuum\, it was unknown if the entropy remains its boundedness. We will
show in this talk that the ideal gases retain their uniform boundedness of
the entropy\, locally or globally in time\, if the vacuum occurs at the f
ar field only and the density decays slowly enough at the far field. Preci
sely\, we consider the Cauchy problem to the full compressible Navier-Stok
es equations\, with or without heat conductivity\, and establish the local
and global existence and uniqueness of entropy-bounded solutions in the p
resence of vacuum at the far field only. These are joint works with Prof
. Zhouping Xin.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xu Hao
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/61
DESCRIPTION:Title: Bergman kernel and quantization of Kahler manifolds\nby Xu Ha
o as part of ICCM 2020\n\n\nAbstract\nSimilar to the asymptotic expansion
of heat kernel\, the asymptotic expansion of Bergman kernel on Kahler mani
folds have important geometric applications. We will talk about some inter
esting physical interpretation of this expansion (e.g.\, quantum Hall effe
ct) and review recent works on its relations to deformation quantization.\
n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juyong Zhang
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/62
DESCRIPTION:Title: Anderson Acceleration for First-Order Methods in Visual Computing
\nby Juyong Zhang as part of ICCM 2020\n\n\nAbstract\nAlternating opti
mization methods like local-global solver and alternating direction multip
lier method (ADMM) are commonly used in areas like signal processing\, mac
hine learning and computer graphics. These methods converge quickly to an
approximate solution\, but can take a long time to converge to a solution
of high-accuracy. In this talk\, I will present our works about applying A
nderson acceleration to speed up the convergence of these methods by treat
ing them as fixed-point iteration. We also analyze the convergence of the
proposed acceleration method on nonconvex problems\, and verify its effect
iveness on a variety of problems.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhonggen Su (Zhejiang University)
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/63
DESCRIPTION:Title: Fluctuations on Plancherel interger partitions around its limit s
hape\nby Zhonggen Su (Zhejiang University) as part of ICCM 2020\n\n\nA
bstract\nFor s natural number n\, let P_n be the space of all integer part
itions \\lambda of n. Let P_{pl}(\\lambda)=\\frac{d_{\\lambda}^2}{n!}\, wh
ere d_{\\lambda} stands for the numbers of all standard Young tableanux wi
th shape \\lambda. A remarkable result\, almost simultaneously obtained by
Logan and Shepp\, Vershik and Kerov in the seventies\, is that there is a
limit shape w(x) for suitably scale \\lambda under the probability measur
e P_{pl}. In this talk we will report a Gaussian fluctuation result for \\
lambda_{[\\sqrt{n}x]} around the shape curve w(x). The result complements\
, in a striking way\, the well-known theorem of Kerov on the generalized G
aussian convergence. The proofs are based on the poissonization techniques
and the Costin-Lebowitz-Soshnikov central limit theorem for determinantal
point processes.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Wan (Morningside Center of Mathematics\, AMSS)
DTSTART:20201229T060000Z
DTEND:20201229T070000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/64
DESCRIPTION:Title: Iwasawa main conjecture at bad primes\nby Xin Wan (Morningsid
e Center of Mathematics\, AMSS) as part of ICCM 2020\n\n\nAbstract\nI pres
ent an ongoing joint work with Olivier Fouquet to prove the Iwasawa main c
onjecture allowing arbitrary ramification at p. Then we discuss some appli
cations.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lu Wang (Caltech)
DTSTART:20201229T060000Z
DTEND:20201229T070000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/65
DESCRIPTION:Title: Nonuniqueness in Mean Curvature Flow\nby Lu Wang (Caltech) as
part of ICCM 2020\n\n\nAbstract\nMean curvature flow is the gradient flow
of area functional that decreases the area in the steepest way. In genera
l the flow will develop singularities in finite time. It is known that the
re may not be a unique way to continue the flow through singularities. In
this talk\, we will discuss some global features of the space of mean curv
ature flows that emerge from cone-like singularities. This is joint with J
acob Bernstein.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jintai Ding/丁津泰 (Yau Mathematical Sciences Center\, Tsinghua
University)
DTSTART:20201229T060000Z
DTEND:20201229T070000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/66
DESCRIPTION:Title: Multivariate public key cryptosystems - Candidates for the Next
Generation Post-quantum Standards\nby Jintai Ding/丁津泰 (Yau Mathe
matical Sciences Center\, Tsinghua University) as part of ICCM 2020\n\n\nA
bstract\nModern Cryptography\, in particular\, public key cryptography is
the security foundation of our modern communication systems like the Inter
net. In this lecture\, we will first present the basic idea of public key
cryptography and its applications in privacy protection and blockchain. Th
e second half of the the talk will discuss the quantum threat and post-qua
ntum cryptography. The focus will be on the fundamental mathematical chall
enges in post-quantum cryptography.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xu Shen/申旭 (Morningside Center of Mathematics\, AMSS)
DTSTART:20201229T060000Z
DTEND:20201229T070000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/67
DESCRIPTION:Title: Diamonds and p-adic period domains\nby Xu Shen/申旭 (Mornin
gside Center of Mathematics\, AMSS) as part of ICCM 2020\n\n\nAbstract\nTh
e theory of diamonds was introduced by Scholze in his 2014 Berkeley lectur
es\, which provides a powerful tool to study p-adic Hodge theory and the L
anglands program. In this talk\, we will investigate the geometry of some
diamonds\, namely the B_{dR}^+-affine Schubert varieties\, via the Fargues
-Fontaine curve. Along the way\, the theory of p-adic period domains arise
s naturally. We will explain how the de Rham periods and the Hodge-Tate pe
riods are related to each other\, and we will discuss the structure of cer
tain generalized p-adic period domains.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cuibo Jiang/ 姜翠波 (上海交通大学)
DTSTART:20201229T070000Z
DTEND:20201229T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/68
DESCRIPTION:Title: The analogue of classical Schur-Weyl duality in VOAs\nby Cu
ibo Jiang/ 姜翠波 (上海交通大学) as part of ICCM 2020\n\n\nAbstra
ct\nWe will talk about the analogue of classical Schur-Weyl duality in the
theory of vertex operator algebras.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fu-Tsun Wei 魏福村 (National Tsing Hua University)
DTSTART:20201229T070000Z
DTEND:20201229T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/69
DESCRIPTION:Title: On Kronecker terms over function fields\nby Fu-Tsun Wei 魏
福村 (National Tsing Hua University) as part of ICCM 2020\n\n\nAbstract\
nIn this talk\, I shall present a function field analogue of the Kronecker
limit formula (in mixed characteristic)\, which connects a special value
of “non-holomorohic” Ensenstein series on the Drinfeld period domain w
ith the Drinfeld-Siegel units. This leads to analytic means of deriving a
Colmez-type formula for “stable Taguchi height” of CM Drinfeld modules
having arbitrary rank. A Lerch-Type formula for “totally real” functi
on fields is also obtained\, with the Heegner cycle on the Bruhat-Tits bui
ldings intervene. Also\, our limit formula is naturally applied to the spe
cial values of both the Rankin-Selberg L-functions and the Godement-Jacque
t L-functions associated to automorphic cuspidal representations over glob
al function fields.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yueran Sun/孙悦然 (Zhejiang University)
DTSTART:20201229T070000Z
DTEND:20201229T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/70
DESCRIPTION:Title: Big Picard Theorem on moduli spaces of polarized manifolds\nb
y Yueran Sun/孙悦然 (Zhejiang University) as part of ICCM 2020\n\n\nAbs
tract\nIn 1972 Armand Borel obtained a big Picard type extension theorem f
or holomorphic maps from products of punctured unit disc to arithmetic var
ieties\, by using the Baily-Borel compactification. As a consequence\, he
proved that the algebraic structure on an arithmetic variety is unique. In
this talk\, I will present a similar big Picard type extension theorem in
the setting of moduli spaces of polarized manifolds with semi-ample canon
ical divisor\, which is a joint work with Ya Deng\, Steven Lu and Kang Zuo
. The proof uses the Viehweg-Zuo construction for families of varieties an
d some analytic tools from value distribution theory.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Zhou 周鑫 (Cornell University)
DTSTART:20201229T070000Z
DTEND:20201229T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/71
DESCRIPTION:Title: Existence of constant mean curvature hypersurfaces\nby Xin Zh
ou 周鑫 (Cornell University) as part of ICCM 2020\n\n\nAbstract\nWe will
survey some recent progress on the existence of closed CMC hypersurfaces.
\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meng Wang/ 王梦 (Zhejiang University)
DTSTART:20201229T070000Z
DTEND:20201229T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/72
DESCRIPTION:Title: A note on the Asymptotic solutions for MHD systems\nby Meng W
ang/ 王梦 (Zhejiang University) as part of ICCM 2020\n\n\nAbstract\nWe d
erive free boundary problem for the limit values of the magnetic field and
the velocity field of the fluid. We will also construct the 1-order asymp
totic solution.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengyu Hu /胡正宇
DTSTART:20201229T070000Z
DTEND:20201229T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/73
DESCRIPTION:Title: Minimal model theory for log canonical pairs\nby Zhengyu Hu /
胡正宇 as part of ICCM 2020\n\n\nAbstract\nIn this talk\, I will discus
s recent progress on minimal model theory for log canonical pairs. In the
minimal model program(MMP) one can quantify the type of singularities whic
h occur: the simplest MMP-singularities are called “terminal” and the
most complex ones are the so-called "log canonical". There are others in b
etween\, for example\, the "Kawamata log terminal" singularities that are
most widely used. I will give an inductive argument of extending results f
rom the Kawamata log terminal pairs to log canonical pairs. Part of this t
alk is based on joint work with Kenta Hashizume.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingyi Hong 洪明毅 (University of Minnesota)
DTSTART:20201229T070000Z
DTEND:20201229T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/74
DESCRIPTION:Title: Convergence Analysis of Alternating Direction Method of Multiplie
rs for a Family of Nonconvex Problems\nby Mingyi Hong 洪明毅 (Unive
rsity of Minnesota) as part of ICCM 2020\n\n\nAbstract\nThe alternating di
rection method of multipliers (ADMM) is widely used to solve large-scale l
inearly constrained optimization problems\, convex or nonconvex\, in many
engineering fields. However there is a general lack of theoretical underst
anding of the algorithm when the objective function is nonconvex. In this
work we analyze the convergence of the ADMM for solving certain nonconvex
consensus and sharing problems. By using a three-step argument\, we show t
hat the classical ADMM converges to the set of stationary solutions\, prov
ided that the penalty parameter in the augmented Lagrangian is chosen to b
e sufficiently large. For the sharing problems\, we show that the ADMM is
convergent regardless of the number of variable blocks. Our analysis does
not impose any assumptions on the iterates generated by the algorithm\, an
d is broadly applicable to many ADMM variants involving proximal update ru
les and various flexible block selection rules. Finally\, we discuss a few
generalizations of the three-step analysis to a broader class of algorith
ms\, with applications in signal processing and machine learning.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:I-Ping Tu/杜憶萍 (The Institute of Statistical Science\,Academi
a Sinica\,Taiwan)
DTSTART:20201229T070000Z
DTEND:20201229T081500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/75
DESCRIPTION:Title: 2SDR for noisy high-dimensional images and application to Cryogen
ic Electron Microscopy\nby I-Ping Tu/杜憶萍 (The Institute of Stati
stical Science\,Academia Sinica\,Taiwan) as part of ICCM 2020\n\n\nAbstrac
t\nPrincipal component analysis (PCA) is arguably the most widely used dim
ension-reduction method for vector-type data. When applied to a sample of
images\, PCA requires vectorization of the image data\, which in turn enta
ils solving an eigenvalue problem for the sample covariance matrix. We pro
pose herein a two-stage dimension reduction (2SDR) method for image recons
truction from high-dimensional noisy image data. The first stage treats th
e image as a matrix\, which is a tensor of order 2\, and uses multilinear
principal component analysis (MPCA) for matrix rank reduction and image de
noising. The second stage vectorizes the reduced-rank matrix and achieves
further dimension and noise reduction. Simulation studies demonstrate exce
llent performance of 2SDR\, for which we also develop an asymptotic theory
that establishes consistency of its rank selection. Applications to cryo-
EM (cryogenic electronic microscopy)\, which has revolutionized structural
biology\, organic and medical chemistry\, cellular and molecular physiolo
gy in the past decade\, are also provided and illustrated with benchmark c
ryo-EM datasets. Connections to other contemporaneous developments in imag
e reconstruction and high-dimensional statistical inference are also discu
ssed. \nTh
is is a joint work with Szu-Chi Chung\, Po-Yao Niu\, Su-Yun Huang and Wei-
Hau Chang.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yucai Su/苏育才
DTSTART:20201229T081500Z
DTEND:20201229T090000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/76
DESCRIPTION:Title: A key Lemma related to 2-dimensional Jacobian conjecture\nby
Yucai Su/苏育才 as part of ICCM 2020\n\n\nAbstract\nIn a recent paper
entitled "Proof of two-dimensional Jacobian conjecture" (arXiv:1603.01867)
\, we present an attempt to give a proof of two-dimensional Jacobian conje
cture. In this talk\, the speak will report the key Lemma used in the pap
er.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chong Zhang/张翀 (南京大学)
DTSTART:20201229T081500Z
DTEND:20201229T090000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/77
DESCRIPTION:Title: Regular supercuspidal representations and applications\nby Ch
ong Zhang/张翀 (南京大学) as part of ICCM 2020\n\n\nAbstract\nRegula
r supercuspidal representations are recently introduced by Kaletha\, which
are a subclass of tame supercuspidal representations. This new constructi
on has many applications in the representation theory of p-adic reductive
groups. I will discuss the distinction problem for these representations\,
and also its relation with the local theta correspondence.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:JinXin Xu/许金兴 (USTC)
DTSTART:20201229T081500Z
DTEND:20201229T090000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/78
DESCRIPTION:Title: Reduction mod p proofs of some theorems in linear algebraic group
s\nby JinXin Xu/许金兴 (USTC) as part of ICCM 2020\n\n\nAbstract\nM
any algebraic geometry statements involve only finitely many data\, and he
nce their proofs can be reduced to problems over finite fields. I will sho
w how to use this well-known technique to get new proofs of some fundament
al results in linear algebraic groups\, including: structure of unipotent
groups\, Jordan decomposition\, and the connectedness of the normalizer of
a Borel subgroup. This is a joint work with Xiaopeng Xia.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Lei/雷力
DTSTART:20201229T081500Z
DTEND:20201229T090000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/79
DESCRIPTION:Title: Ancient solution of mean curvature flow of arbitrary codimension<
/a>\nby Li Lei/雷力 as part of ICCM 2020\n\n\nAbstract\nIn this talk\, w
e will discuss rigidity problem of ancient solutions of the mean curvature
flow with arbitrary codimension in space forms. We first prove that under
certain sharp pointwise curvature pinching condition the ancient solution
in a sphere is either a shrinking spherical cap or a totally geodesic sph
ere. Then we show that under certain pointwise curvature pinching conditio
n the ancient solution in a hyperbolic space is a family of shrinking sphe
res. We also obtain a rigidity result for ancient solutions in a nonnegati
vely curved space form under an integral curvature pinching condition. Thi
s is joint work with Prof. H. W. Xu and Prof. E. T. Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hexi Ye/叶和溪 (Zhejiang University)
DTSTART:20201229T081500Z
DTEND:20201229T090000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/80
DESCRIPTION:Title: Common prepreodic points and its application\nby Hexi Ye/叶
和溪 (Zhejiang University) as part of ICCM 2020\n\n\nAbstract\nIn this t
alk\, we briefly introduce preperiodic points in dynamics\, and then talk
about the upper bound for the number of common preperiodic points of two q
uadratic polynomials and Lattes maps. As an application\, we use this to b
ound the number of torison points for a family of genus two curves. This i
s a joint work with L. DeMarco and H. Krieger.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yalong Cao/曹亚龙
DTSTART:20201229T081500Z
DTEND:20201229T090000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/81
DESCRIPTION:Title: Gopakumar-Vafa type invariants for Calabi-Yau 4-folds\nby Yal
ong Cao/曹亚龙 as part of ICCM 2020\n\n\nAbstract\nGopakumar-Vafa type
invariants on Calabi-Yau 4-folds (which are non-trivial only for genus zer
o and one) are defined by Klemm-Pandharipande from Gromov-Witten theory\,
and their integrality is conjectured. In this talk\, I will explain how to
give a sheaf theoretical interpretation of them using counting invariants
on moduli spaces of one dimensional stable sheaves. Based on joint works
with D. Maulik and Y. Toda.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yinhua Xia/夏银华 (USTC)
DTSTART:20201229T081500Z
DTEND:20201229T090000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/82
DESCRIPTION:Title: Structure preserving arbitrary Lagrangian-Eulerian discontinuous
Galerkin methods\nby Yinhua Xia/夏银华 (USTC) as part of ICCM 2020\
n\n\nAbstract\nIn this talk\, we will discuss the structure preserving pro
perties of the arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-D
G) methods. Based on the time dependent linear affine mapping\, the ALE-DG
methods presented here maintains almost all mathematical properties of DG
methods on static grids\, such as conservation\, geometric conservation l
aw\, entropy stability and optimal error estimates. Meanwhile the mesh mov
ement function requires only a very mild Lipschitz continuity and without
any remapping. In this talk we will focus on the structure preserving prop
erty of the ALE-DG schemes for hyperbolic conservation laws\, including th
e positivity preserving property for Euler equations and the well-balanced
property for shallow water equations. The numerical stability\, robustnes
s and accuracy of the methods will also be shown by a variety of computati
onal experiments on moving meshes.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenbo Sun (Virginia Tech)
DTSTART:20201229T081500Z
DTEND:20201229T090000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/83
DESCRIPTION:Title: Recurrence theorem for multiplicative systems and applications\nby Wenbo Sun (Virginia Tech) as part of ICCM 2020\n\n\nAbstract\nPoinca
re recurrence theorem is one fundamental result in a dynamical system\, wh
ich says that the orbit of a point on a measure-preserving system can visi
t the neighborhood of another point infinitely many times. Variations and
applications of this theorem have been studied extensively in the literatu
re. In this talk\, we discuss the recurrence properties of a multiplicativ
e system\, i.e. a system admitting a multiplicative group action instead o
f a conventional additive group action. This is a direction that has not b
een studied much in the past\, yet has many interesting applications. We w
ill discuss recent progress on this topic\, and its connections with probl
ems in combinatorics and number theory.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoyi Cui 崔潇易 (Sun Yat-Sen Univ.\, Zhuhai)
DTSTART:20201229T091500Z
DTEND:20201229T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/84
DESCRIPTION:Title: Lie algebroid\, deformation\, and BV theories\nby Xiaoyi Cui
崔潇易 (Sun Yat-Sen Univ.\, Zhuhai) as part of ICCM 2020\n\n\nAbstract\
nFormal geometry has been used to encode geometric data in the algebraic f
ormulation of perturbative quantum field theories. We define a class of de
formation of (curved) L_\\infty algebras with geometric origin\, and show
that those deformations are connected with Lie algebroids. We also study t
he BV quantization of holomorphic and topological quantum field theories b
uilt from such deformed algebras.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daxin Xu/许大昕 (中科院晨兴数学中心)
DTSTART:20201229T091500Z
DTEND:20201229T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/85
DESCRIPTION:Title: Drinfeld's lemma for F-isocrystals\nby Daxin Xu/许大昕 (
中科院晨兴数学中心) as part of ICCM 2020\n\n\nAbstract\nDrinfeld'
s lemma for l-adic local systems is a fundamental result in arithmetic geo
metry. It plays an important role in the Langlands correspondence for a re
ductive group over the function field of a curve over a finite field\, pio
neered by Drinfeld for GL_2 and subsequently extended by L. Lafforgue and
then V. Lafforgue. In this talk\, we will discuss Drinfeld's lemma for p-a
dic local systems: overconvergent F-isocrystals. This is based on a joint
work with Kiran Kedlaya.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yat-Hin Suen (IBS\, Korea)
DTSTART:20201229T091500Z
DTEND:20201229T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/86
DESCRIPTION:Title: Tropical Lagrangian multi-section and smoothing of locally sheave
s over degenerated Calabi-Yau surfaces\nby Yat-Hin Suen (IBS\, Korea)
as part of ICCM 2020\n\n\nAbstract\nHomological mirror symmetry suggests t
hat Lagrangian multi-sections over an integral affine manifold with singul
arities $B$ should mirror to holomorphic vector bundles. In this talk\, I
will introduce the tropical version of Lagrangian multi-sections\, called
tropical Lagrangian multi-sections. I will mainly focus on dimension 2. To
certain tropical Lagrangian multi-sections over $B$\, I will construct a
locally free sheaf $E_0$ on the log Calabi-Yau surface $X_0(B)$ associated
to $B$ and study the smoothability of the pair $(X_0(B)\,E_0)$. This is a
joint work with Kwokwai Chan and Ziming Ma.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Fu/傅鑫 (University of California\,Irvine)
DTSTART:20201229T091500Z
DTEND:20201229T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/87
DESCRIPTION:Title: Geometric Estimates for Complex Monge-Ampere Equations\nby Xi
n Fu/傅鑫 (University of California\,Irvine) as part of ICCM 2020\n\n\nA
bstract\nWe prove uniform gradient and diameter estimates for a family of
geometric complex Monge-Amp`ere equations. Such estimates can be applied t
o study geometric regularity of singular solutions of complex Monge-Amp`er
e equations. We also prove a uniform diameter estimate for collapsing fami
lies of twisted K¨ahler-Einstein metrics on K¨ahler manifolds of nonnega
tive Kodaira dimensions. This is a joint work with Bin Guo and Jian Song.\
n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quoc hung Nguyen (上海科技大学)
DTSTART:20201229T091500Z
DTEND:20201229T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/88
DESCRIPTION:Title: The Muskat equation is well-posed on the critical Sobolev space\nby Quoc hung Nguyen (上海科技大学) as part of ICCM 2020\n\n\nAbs
tract\nThis talk is about a series of papers with Thomas Alazard\, devoted
to the study of solutions with critical regularity for the two-dimensiona
l Muskat equation. I will describe our main result\, which states that the
Cauchy problem is well-posed on the endpoint Sobolev space of L^2 functio
ns with three-half derivative in L^2 (locally in time for large data\, and
globally for small enough data). This result is optimal with respect to t
he scaling of the equation. For the proof\, we introduce weighted fraction
al laplacians and use these operators to estimate the solutions for a norm
which depends on the initial data themselves. Another key ingredient of t
he proof is a null-type structure\, allowing to compensate for the degener
acy of the parabolic behavior for large slopes.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyuan Xu/许智源 (Hangzhou Normal University)
DTSTART:20201229T091500Z
DTEND:20201229T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/89
DESCRIPTION:Title: The Pólya conjecture and Li-Yau inequality for higher eigenvalue
s\nby Zhiyuan Xu/许智源 (Hangzhou Normal University) as part of ICC
M 2020\n\n\nAbstract\nIn this talk\, we will talk about the Pólya conject
ure and Li-Yau inequality for higher eigenvalues. We will first introduce
the background and some results on higher eigenvalue problems for the Lapl
ace operator on bounded domain in the Euclidean space. Then\, we will disc
uss the generalizations for those results on compact minimal submanifolds
with boundary. We will also discuss the estimates on the number of eigenva
lues of the Schrödinger operator on compact minimal submanifolds with bou
ndary. This is joint work with Prof. Hongwei Xu.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kung-Chien Wu 吳恭儉 (National Cheng-Kung University國立成
功大學)
DTSTART:20201229T091500Z
DTEND:20201229T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/90
DESCRIPTION:Title: Space-time behavior of the solution to the Boltzmann equation wit
h soft potentials\nby Kung-Chien Wu 吳恭儉 (National Cheng-Kung Uni
versity國立成功大學) as part of ICCM 2020\n\n\nAbstract\nIn this tal
k\, we will discuss the quantitative space-time behavior of the full Boltz
mann equation with soft potentials in the close to equilibrium setting\, u
nder some velocity decay assumption\, but without any Sobolev regularity a
ssumption on the initial data.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dangzheng Liu/刘党政 (USTC)
DTSTART:20201229T091500Z
DTEND:20201229T100000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/91
DESCRIPTION:Title: Phase transitions for infinite products of large non-Hermitian ra
ndom matrices\nby Dangzheng Liu/刘党政 (USTC) as part of ICCM 2020\
n\n\nAbstract\nProducts of M i.i.d. random matrices of size N relate class
ical limit theorems in Probability Theory (large M and N=1) to Lyapunov ex
ponents in Dynamical Systems (large M and finite N)\, and to universality
in Random Matrix Theory (finite M and large N). Under the two different li
mits of large M and large N\, the eigenvalue statistics for the random ma
trix product display Gaussian and non-Hermitian RMT universality\, respe
ctively. However\, what happens if both M and N go to infinity simultaneou
sly? This problem lies at the heart of understanding two kinds of universa
l limits. In this talk we examine it and investigate possible phase trans
itions and critical phenomena.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziyang Gao (CNRS & IMJ-PRG)
DTSTART:20201229T003000Z
DTEND:20201229T013000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/92
DESCRIPTION:Title: Bounding the number of rational points on curves\nby Ziyang G
ao (CNRS & IMJ-PRG) as part of ICCM 2020\n\n\nAbstract\nMazur conjectured\
, after Faltings’s proof of the Mordell conjecture\, that the number of
rational points on a curve of genus g at least 2 defined over a number fie
ld of degree d is bounded in terms of g\, d and the Mordell-Weil rank. In
particular the height of the curve is not involved. In this talk I will ex
plain how to prove this conjecture and some generalizations. I will focus
on how functional transcendence and unlikely intersections are applied in
the proof. If time permits\, I will talk about how the dependence on d can
be furthermore removed if we moreover assume the relative Bogomolov conje
cture. This is joint work with Vesselin Dimitrov and Philipp Habegger.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Columbia University)
DTSTART:20201229T003000Z
DTEND:20201229T013000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/93
DESCRIPTION:Title: The Beilinson-Bloch conjecture for unitary Shimura varieties\
nby Chao Li (Columbia University) as part of ICCM 2020\n\n\nAbstract\nThe
Beilinson-Bloch conjecture is a vast generalization of the celebrated Birc
h and Swinnerton-Dyer conjecture to higher dimensional varieties. We will
motivate these conjectures and discuss our recent theorems for unitary Shi
mura varieties. This is joint work with Yifeng Liu.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengwei Liu (Tsinghua University)
DTSTART:20201229T003000Z
DTEND:20201229T013000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/94
DESCRIPTION:Title: Subfactors--in Memory of Vaughan Jones\nby Zhengwei Liu (Tsin
ghua University) as part of ICCM 2020\n\n\nAbstract\nJones initiated the m
odern theory of subfactor in early 1980s and investigated this area for hi
s whole academic life. Subfactor theory has both deep and broad connection
s with various areas in mathematics and physics. One well-known peak in th
e development of subfactor theory is the discovery of the Jones polynomial
\, for which Jones won the Fields Metal in 1990. Let us travel back to the
dark room at the beginning of the story\, to appreciate how radically ou
r viewpoint has changed.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ming Yuan (Columbia University)
DTSTART:20201229T003000Z
DTEND:20201229T013000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/95
DESCRIPTION:Title: Complexity of High Dimensional Sparse Functions\nby Ming Yuan
(Columbia University) as part of ICCM 2020\n\n\nAbstract\nWe investigate
optimal algorithms for estimating a general high dimensional smooth and s
parse function from the perspective of information based complexity. Our
algorithms and analyses reveal several interesting characteristics for th
ese tasks. In particular\, our results illustrate the potential value of e
xperiment design for high dimensional problems.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (MIT)
DTSTART:20201229T013000Z
DTEND:20201229T023000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/96
DESCRIPTION:Title: Flag varieties and representations of p-adic groups\nby Charl
otte Chan (MIT) as part of ICCM 2020\n\n\nAbstract\nThe intimate connectio
n between algebraic geometry and representation theory has led to many dee
p and fruitful discoveries over the last century. I will illustrate some h
istorical instances of this relationship. I will then survey recent advanc
es in understanding the role of geometry in the representation theory of
p-adic groups and the Langlands program.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hsian-Hua Tseng (Ohio State University)
DTSTART:20201229T013000Z
DTEND:20201229T023000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/97
DESCRIPTION:Title: Root constructions and Gromov-Witten theory\nby Hsian-Hua Tse
ng (Ohio State University) as part of ICCM 2020\n\n\nAbstract\nRoot constr
uctions are geometric ways to introduce stack structures in codimensions 0
and 1. In this talk we review these constructions and discuss how they af
fect Gromov-Witten theory.\n\n2910349950\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junyi Xie (CNRS Rennes)
DTSTART:20201229T013000Z
DTEND:20201229T023000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/98
DESCRIPTION:Title: On the Zariski dense orbit conjecture\nby Junyi Xie (CNRS Ren
nes) as part of ICCM 2020\n\n\nAbstract\nWe prove the following theorem. L
et f be a dominant endomorphism of a projective surface over an algebraica
lly closed field of characteristic 0. If there is no nonconstant invariant
rational function under f\, then there exists a closed point whose orbit
under f is Zariski dense. This result gives us a positive answer to the Za
riski dense orbit conjecture for endomorphisms of projective surfaces. We
define a new canonical topology on varieties over an algebraically closed
field which has finite transcendence degree over Q. We call it the adelic
topology. This topology is stronger than the Zariski topology and an irred
ucible variety is still irreducible in this topology. Using the adelic top
ology\, we propose an adelic version of the Zariski dense orbit conjecture
\, which is stronger than the original one and quantifies how many such or
bits there are. We also prove this adelic version for endomorphisms of pro
jective surfaces\, for endomorphisms of abelian varieties\, and split poly
nomial maps. This yields new proofs of the original conjecture in the latt
er two cases.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nike Sun (MIT)
DTSTART:20201229T030000Z
DTEND:20201229T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/99
DESCRIPTION:Title: Maximum independent sets on random regular graphs\nby Nike Su
n (MIT) as part of ICCM 2020\n\n\nAbstract\nWe determine the asymptotics o
f the independence number of the random d-regular graph for all d exceedin
g an absolute constant. The independence number is highly concentrated\, w
ith constant-order fluctuations around (a*n-c*log n) for explicit constant
s a(d) and c(d). Our proof rigorously confirms one-step replica symmetry b
reaking heuristics for this problem.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Liu (Yale University)
DTSTART:20201229T030000Z
DTEND:20201229T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/100
DESCRIPTION:Title: Isolation of trace formulae and application to automorphic perio
ds\nby Yifeng Liu (Yale University) as part of ICCM 2020\n\n\nAbstract
\nIn this talk\, we introduce some recent results on the isolation of spec
tra in the trace formulae\, followed by applications in the study of some
automorphic periods\, namely the Gan-Gross-Prasad conjecture. This is a jo
int work with Raphaël Beuzart-Plessis\, Wei Zhang\, and Xinwen Zhu.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenhao Ou (Academy of Mathematics and Systems Sciences\,Chinese Ac
ademy of Sciences)
DTSTART:20201229T030000Z
DTEND:20201229T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/101
DESCRIPTION:Title: Projective manifolds whose tangent bundle contains a strictly ne
f subsheaf\nby Wenhao Ou (Academy of Mathematics and Systems Sciences\
,Chinese Academy of Sciences) as part of ICCM 2020\n\n\nAbstract\nAfter a
theorem of Andreatta and Wisniewski\, if the tangent bundle of a projectiv
e manifold $X$ contains an ample subsheaf\, then $X$ is isomorphic to the
projective space. We show that\, if the tangent bundle contains a strictly
nef subsheaf\, then X is a projective bundle over a hyperbolic manifold.
Moreover\, if the fundamental group of $X$ is virtually abelian\, then $X$
is isomorphic to a projective space. This is joint with Jie Liu and Xiaok
ui Yang.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20201229T030000Z
DTEND:20201229T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/102
DESCRIPTION:Title: Legendrian knots\, Lagrangian fillings\, and Cluster algebras\nby Linhui Shen (Michigan State University) as part of ICCM 2020\n\n\nAb
stract\nClassifications of Legendrian knots and their exact Lagrangian fil
lings are central questions in low-dimensional contact and symplectic topo
logy. Recent development suggests that one can distinguish exact Lagrangia
n fillings by applying tools from cluster algebras. In this talk\, we focu
s on Legendrian links that are obtained as the rainbow closure of positive
braids. We prove that any positive braid Legendrian link not isotopic to
a standard finite type link admits infinitely many exact Lagrangian fillin
gs. The main techniques of its proof include cluster algebras and Chekanov
-Eliashberg differential graded algebras. This is joint work with Honghao
Gao and Daping Weng.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Li (Massachusetts Institute of Technology)
DTSTART:20201229T030000Z
DTEND:20201229T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/103
DESCRIPTION:Title: Exotic Calabi-Yau metrics\nby Yang Li (Massachusetts Institu
te of Technology) as part of ICCM 2020\n\n\nAbstract\nI will survey the pr
oblem of constructing complete Calabi-Yau metrics on noncompact manifolds\
, and trace its history from the foundational work of Tian-Yau to some mor
e recent developments. Some emphasis will be given to a concrete construct
ion of a nontrivial Calabi-Yau metric on C^3 with maximal volume growth\,
which turns out to be also relevant in describing collapsing Calabi-Yau me
trics.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu-Wei Fan (UC Berkeley)
DTSTART:20201229T030000Z
DTEND:20201229T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/104
DESCRIPTION:Title: Stokes matrices\, character varieties\, and points on spheres\nby Yu-Wei Fan (UC Berkeley) as part of ICCM 2020\n\n\nAbstract\nModuli
spaces of points on n-spheres carry natural actions of braid groups. For n
=0\,1\, and 3\, we prove that these symmetries extend to actions of mappin
g class groups of positive genus surfaces\, through exceptional isomorphis
ms with certain character varieties. 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 o
f triangulated categories. Joint work with Junho Peter Whang.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Long Chen (University of California at Irvine)
DTSTART:20201229T030000Z
DTEND:20201229T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/105
DESCRIPTION:Title: Discrete Gradgrad and Divdiv Complex\nby Long Chen (Universi
ty of California at Irvine) as part of ICCM 2020\n\n\nAbstract\nWe present
conforming finite element/virtual element complexes for grad-grad complex
and div-div complex in three dimensions and apply to discretize the linea
rized time-independent Einstein-Bianchi system and biharmonic equation\, r
espectively. This is a joint work with Xuehai Huang from Shanghai Universi
ty of Finance and Economics.\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Runze Li (The Pennsylvania State University at University Park)
DTSTART:20201229T030000Z
DTEND:20201229T034500Z
DTSTAMP:20260404T094700Z
UID:iccm2020/106
DESCRIPTION:Title: A Tuning-free Robust and Efficient Approach to High-dimensional
Regression\nby Runze Li (The Pennsylvania State University at Universi
ty Park) as part of ICCM 2020\n\n\nAbstract\nWe introduce a novel approach
for high-dimensional regression with theoretical guarantees. The new proc
edure overcomes the challenge of tuning parameter selection of Lasso and p
ossesses several appealing properties. It uses an easily simulated tuning
parameter that automatically adapts to both the unknown random error distr
ibution and the correlation structure of the design matrix. It is robust w
ith substantial efficiency gain for heavy-tailed random errors while maint
aining high efficiency for normal random errors. Comparing with other alte
rnative robust regression procedures\, it also enjoys the property of bein
g equivariant when the response variable undergoes a scale transformation.
Computationally\, it can be efficiently solved via linear programming. Th
eoretically\, under weak conditions on the random error distribution\, we
establish a finite-sample error bound with a near-oracle rate for the new
estimator with the simulated tuning parameter. Our results make useful con
tributions to mending the gap between the practice and theory of Lasso and
its variants. We also prove that further improvement in efficiency can be
achieved by a second-stage enhancement with some light tuning. Our simula
tion results demonstrate that the proposed methods often outperform cross-
validated Lasso in various settings."\n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Shing-Tung Yau (Havard University)
DTSTART:20201227T000000Z
DTEND:20201227T013000Z
DTSTAMP:20260404T094700Z
UID:iccm2020/108
DESCRIPTION:Title: Opening Ceremony and Best Paper Award Ceremony\nby Professor
Shing-Tung Yau (Havard University) as part of ICCM 2020\n\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/iccm2020/108/
END:VEVENT
END:VCALENDAR