1
Contents
The General Program of EACDFM 2016....... 2
The Detailed Program of EACDFM 2016.......3
Information about Invited Talks........................7
Information about Oral Presentations...........11
Brief Map...........................................................31
2
The General Program of EACDFM 2016
3
The Detailed Program of EACDFM 2016
4
5
6
Service Guide
1. Accommodation Services
All accommodations will be arranged in Yanyuan Hotel, the Guest House of Fudan
University. Address: No.270, ZhengTong Road.
Hotel name and address in Chinese: “复旦燕园宾馆（政通路 270号）”
2. Catering Services
1) There will be a welcome reception at 18:00 on the registration day, the 8th of January
at Yanyuan Restaurant in Yanyuan Hotel, which is near the gate of hotel.
2) Each participant will be provided with a campus card within deposit of 300 CNY. This
card allows everyone to have meals at DanYuan Canteen as long as other school canteens.
It also allows everyone to have coffee or tea at the coffee lounge on the 15th floor of
GuangHua tower building.
3) Meals are provided at DanYuan Canteen and other school canteens. One can
always has food there as long as it is open but the recommended time duration is listed as
follows:
Breakfast: 7:00 - 8:30 Lunch: 11:30 - 12:30 Dinner: 17:00 - 18:30.
3. Transportation Services
1) There will be a social activity & banquet at 15:30 on January 11th. The rally point will
be the eastern lawn, east of GuangHua east sub-building unless further notice.
2) If you want to go shopping, Wujiaochang is the nearest town center from the campus
within only ten minutes walk.
3) If you need to go some place far from the campus, taking a subway is highly
recommended for its convenience and safety. The nearest subway station is Jiangwan
Stadium of Subway Line No. 10 at Wujiaochang, the east of the campus.
7
Information about Invited Talks
Shuai Lu, Fudan University
Title: Multi-frequency inverse acoustic source problems
Abstract: In this talk, we investigate an interior Helmholtz inverse source problem with
multiple frequencies. By implementing sharp uniqueness of the continuation results and
exact observability bounds for the wave equation, a (nearly Lipschitz) increasing stability
estimate is explicitly obtained for Cauchy measurements in a non-empty wave-number
interval. With a specific geometric domain, an iterative/recursive reconstruction algorithm is
proposed aiming at recovering unknown sources by the multifrequency boundary
measurement. Both convergence and error estimates are derived to guarantee its reliability.
Numerical examples verify the efficiency of our proposed algorithm. It is a joint work with
Gang Bao (Zhejiang University), Jin Cheng, Boxi Xu (Fudan University) and Victor Isakov
(Wichita University).
JianGang Ying, Fudan University
Title: Regular subspaces of Dirichlet spaces
Abstract: A regular Dirichlet form corresponds a symmetric Markov process. We will focus
on the problem that whether a regular Dirichlet form has non-trivial regular subspaces. In
this talk, we would discuss regular subspaces and their structure of Dirichlet form of
Brownian motion.
8
Lin Wang, Tsinghua University
Title: Variational principle for contact Hamiltonian systems and its Applications
Abstract: By establishing a variational principle for contact Tonelli Hamiltonian systems, we
find some dynamical properties of viscosity solutions of certain Hamilton -Jacobi equations
depending on unknown functions. Besides, I will talk about some connections with contact
geometry and thermodynamics. This talk is based on some joint works with Jun Yan.
Guohua Zhang, Fudan University
Title: ENTROPY THEORY OF COUNTABLE GROUP ACTIONS
Abstract: One of central problems in ergodic theory is deciding when two measurable
dynamical systems are measurably conjugate. The usual way to tackle the problem is to
look for measure-isomorphism invariants. Entropy is one of the most important such
invariants. In this talk, I shall give a survey of entropy theory for countable discrete group
actions, including recalling the classical entropy theory for the integer group action and
discussing recent progress about entropy theory for countable amenable group actions and
then for countable sofic group actions.
My talk is based on a series of joint works with A. Dooley (UK), T. Downarowicz & D. Huczek
(Poland), W. Huang & X. D. Ye (China) and N.-P. Chung (Vietnam).
Jongil Park, Seoul University
Title: On knot surgery 4-manifolds
Abstract: (null)
9
Nobu Kishimoto, Kyoto university
Title: Nonlinear dispersive equations with periodic boundary conditions
Abstract: In this talk, we consider the initial boundary value problem with periodic boundary
conditions for nonlinear dispersive partial differential equations such as nonlinear
Schroedinger equations and the Korteweg-de Vries equation. The analysis of nonlinear
interactions between "resonant" frequencies often plays an important role in the study of
nonlinear effects for these equations. We see with some examples that the analysis of the
"resonant" interactions has combinatorial aspects. We also introduce the normal form
method as a tool to deal with the "non-resonant" interactions and apply it to the unconditional
uniqueness problem.
Chung-Jun Tsai, National Taiwan University
Title: Cohomology and Hodge theory on symplectic manifolds
Abstract: In this talk, I will explain the differential cohomologies on symplectic manifolds,
which are analogous to the Dolbeault theory in complex geometry. These symplectic
cohomologies admit certain algebraic structure, which encodes interesting information for
non-Kahler symplectic manifolds. This is a joint work with L.-S. Tseng and S.-T. Yau.
Jiansheng Xie, Fudan University
Title: Range-Renewal Structure in Continued Fractions
Abstract: It is well known that any irrational number in $(0,1)$ can be coded into infinite
continued fraction form. In this talk we focus on the growth rate of the number of disctinct
partial quotients (and alikes) in the first $n$ "digits". It is proved that, for Lebesgue almost
10
every (irrational) fractions, the leading term of the growth rate is $\sqrt{\frac{\pi n}{\log 2}}$.
The Hausdorff dimensions of the related level sets are also discussed. This work is done
jointly with Prof. Jun Wu.
11
Information about Oral Presentations
Chih-Wei Chang, National Taiwan University
Title: The Moving Intersection Numbers and The Newton-Okounkov Bodies
Abstract: The classical Bernstein-Kushnirenko theorem relates the number of non-zero
solutions of a general system of Laurent polynomial equations to the mixed volume of their
Newton polytopes. In their work, A.G. Khovanskii and Kiumars Kaveh introduced the notion
of Newton-Okounkov bodies and established a relation among the followings: the moving
intersection number of a linear system, the volume of the Newton-Okounkov body associate
to the (closure of) algebra generated by the linear system, and the asymptotic growth of this
algebra. In this report, I will briefly introduce their work and discuss possible generalizations.
Hsin-Ku Chen, National Taiwan University
Title: On the estimate of the topology of varieties
Abstract: On the estimate of the topology of varieties we prove that, given an algebraic set
which is a intersection of k hypersurfaces of degree less or equal to d in an n-dimensional
affine/projective space, the topological Euler characteristic of the given one can be bounded
by a fixed number depends only on n, d and k.
Xi Chen, Fudan University
Title: Microlocal Analysis on Asymptotically Hyperbolic Manifolds and its Interactions with
Harmonic Analysis and Dispersive PDEs.
Abstract: The asymptotically hyperbolic manifold is a class of conformally compact
Riemannian manifolds with the sectional curvature approaching -1 at boundary. It attracts
considerable attentions due to the internal interests in mathematics (conformal geometry,
spectral and scattering theories) as well as the external applications to physics (for example
12
anti-de Sitter spaces from AdF/CFT correspondence and de Sitter-Schwarzschild models in
general relativity). The microlocal analysis on such manifolds plays a crucial role in these
fields. It has been flourishing from the pioneering work of Mazzeo-Melrose. The bulk of the
analysis are built up in a series of remarkable works: meromorphic resolvent
(Mazzeo-Melrose), spectrum and eigenvalues (Mazzeo, Guillarmou), scattering matrix
(Graham-Zworski, Joshi-Sa Barreto), semiclassical resolvent (Vasy, Melrose-Sa
Barreto-Vasy). We are interested in not only developing these works but also drawing the
links with other areas such as harmonic analysis (spectral multipliers and restriction
theorem), dispersive PDEs (dispersive estimates and Strichartz estimates) and index
theorem (heat kernel asymptotic and renormalized heat trace). In this talk we will introduce
our advances and compare the results with other manifolds, including Euclidean and
hyperbolic spaces, asymptotically conic (Euclidean) manifolds.
Yan Cui, Fudan University
Title: Stability and Controllability of Wave Equations Coupled by Velocities
Abstract: The first part of this topic will analyzes the longtime behavior of a system of two
wave equations that are coupled by velocities.Only one wave equation is supposed to be
damped with a damping function d(x). If the union set of coupling term d(x) and damping
term c(x) is not null. We show that smooth solutions of the system decay logarithmically at
infinity without any geometric conditions. The second part of this topic will give a sufficient
and necessary condition of the coupled matrix such that the system is controllable by only
one boundary control.
13
Yiwei Dong, Fudan University
Title: Ergodic Properties of Systems with Asymptotic Average Shadowing Property
Abstract: In this paper, we explore a topological system MMf : with asymptotic
average shadowing property and extend Sigmund's results from Bowen's speci cation case.
We show that every non-empty, compact and connected subset fMV inv coincides with
some yV f . Moreover, we show that the set VyVMyM fV : is dense in
fMv inv maxsupp v . In particular, if fMv inv max
supp v coincides with M , then
fMyVyM invf :max is residual in M .
As consequences, we have several corollaries. One is that every invariant measure has
generic points. Another is that the set consisting of those points for which the Birkho ergodic
average does not exist (called irregular set) is either dense in max (residual provided that
M max ) or empty.
SooKyung Eom, Ewha Womans University
Title: Efficient pairing computation on elliptic curves
Abstract: Cryptographic pairing computations are required for a wide variety of new
cryptographic protocols and applications. Many results have been focused on speeding up
the pairing computations based on Tate pairing and Weil pairing. In other words, the efficient
pairing is reducing the number of iterations in the Miller’s algorithm. Some variants based on
the Tate pairing are suggested as the eta pairing, the ate pairing and the R-ate pairing.
Vecauteren gives an efficient method to find an optimal pairing and Hess provides a
convenient mathematical framework that essentially encompasses all known pairing
functions based on the Tate pairing and Weil pairing. A classical optimization in pairing
based cryptography is to consider elliptic curve with even embedding degree. Such curve
14
admit a twist and it is possible to eliminate the computation of denominators. Another
advantage is the use of tower extension of fields in order to improve the computation.
In this talk, we describe and improve efficient methods for computing the pairings over
elliptic curves with prime or composite order.
Minjung Gim, Seoul National University
Title: Recurrence criteria for generalized Dirichlet forms
Abstract: We develop sufficient analytic conditions for recurrence and transience of
non-sectorial perturbations of possibly non-symmetric Dirichlet forms on a general state
space. These form an important subclass of generalized Dirichlet forms which were
introduced in [St1]. In case there exists an associated process, we show how the analytic
conditions imply recurrence and transience in the classical probabilistic sense. As an
application, we consider a generalized Dirichlet form given on a closed or open subset of Rd
which is given as a divergence free first order perturbation of a non-symmetric energy form.
Then using volume growth conditions of the sectorial and non-sectorial first order part, we
derive an explicit criterion for recurrence. This is joint work with Professor Gerald Trutnau.
Weiqiang He, Tsinghua University
Title: Landau-Ginzburg mirror symmetry conjecture
Abstract: I will a brief introduction to our work on Landau-Ginzburg mirror symmetry
conjecture,which is an important conjecture in cohomological field theory. The conjecture
implies the relation between Fan-Jarvis-Ruan-Witten theory and Saito-Givental theory.
These two theories come from the intersection theory of moduli space and the theory of
singularities respectively. We hope our result can show the deep correspondence between
the two different mathematical fields. This is a joint work with Si Li, Yefeng shen and Rachel
15
Webb.
Han En Hsieh, National Taiwan University
Title: The Eigen-Decomposition and Singular Value Decomposition of Curl Operators and
Its Application for Maxwell's Equations
Abstract: In this talk, we focus on introducing the eigen-decomposition and singular value
decomposition of curl type operators and solving the generalized eigenvalue problems (GEP)
arising in the source-free Maxwell equation with magnetoelectric coupling effects. One of the
important breakthrough in our research is that we found the explicit eigen-decomposition of
discrete double curl operator, and this consequence can further derive the singular value
decomposition of discrete single curl operator. Due to the finding of
these decompositions, we can derive a null space free algorithm for Maxwell's equations
which can remove the null space of the original problem and transform the GEP into a Null
Space Free GEP (NFGEP) whose coefficient matrices are Hermitian and Hermitian positive
definite. Hence this NFGEP can be solved by using the invert Lanczos method without
shifting. Furthermore, the embedded linear system can be solved efficiently by using the
conjugate gradient method without preconditioning, and the FFT-based matrix vector
multiplications can be applied to accelerate the computations.
Shih-Hsuan Hsu, National Chiao Tung University
Title: Coupling Closest Point and Grid Based Particle methods for Interfacial Flows with
Insoluble Surfactant
Abstract: Many physical problems arising in biological or material sciences involve solving
partial differential equations in deformable interfaces. For instance, the surfactant adheres to
the fluid interface and it affects the interface surface tension. In this situation, the
16
concentration of surfactant can be described as convection-diffusion equations on a moving
interface. Thus, it is important to accurately solve convection-diffusion equations especially
when the interface is moving. In this talk, we first propose a numerical scheme coupling
closest point and grid based particle methods for solving convection-diffusion equations on a
moving interface. In the scheme, we only solve equation on underlying uniform Eulerian
mesh by standard finite difference scheme and the interface is represented by meshless
particles. Coupling the Navier-Stokes solver, we propose a numerical scheme for simulation
of 3D interfacial flows problem with insoluble surfactant. The effect of surfactant on drop
deformation in a shear flow is investigated by studying the influences of different physical
parameters.
Jihyun Hwang, Sungkyunkwan University
Title: Recurrence relations for Fourier coefficients of meromorphic modular forms on certain
genus zero groups
Abstract: Let zf be a meromorphic function on the upper half-plane with Fourier
expansion of the form
hn
nqnazf )()( , where izeq 2 . We define an operator , which is
called Ramanujan's theta operator, by
hn
nqnnazfzi
zf )(dd
21:)(
. Ramanujan's theta
operator plays an important role in the theory of modular forms.
Let N0 be the group generated by the Hecke subgroup )(0 N and Fricke involution
010
:N
WN . In this talk, by using Ramanujan's theta operator, we will find recurrence
relations for Fourier coefficients of meromorphic modular forms on the groups N0 of
17
genus zero, that is, on the groups N0 where N lies in
71,59,50,49,47,41,39,36,35,32,,29,27,,23,21,,1 .
Motoko Kato, Tokyo University
Title: On Serre's property FA of higher dimensional Thompson's groups
Abstract: Thompson’s group V was defined by Richard Thompson in 1965. This group was
one of the earliest examples of finitely presented infinite simple groups. In 2004, Brin defined
a family of infinite simple groups nV of which 1V is Thompson’s group V . nV , n-dimensional
Thompson’s group, is a group which consists of partially affine, partially orientation
preserving bijections between n-dimensional cubes. In this talk we prove that every action of
nV on a tree has a global fixed point, that is, nV has Serre’s property FA. This is a
generalization of the corresponding result of Farley, who studied Thompson’s group V .
Daisuke Kawagoe, Kyoto University
Title: Regularity of solutions to the stationary transport equation and its application to DOT
Abstract: Recently, Diffused Optical Tomography (DOT) has been expected as a new
medical technique for noninvasive measuring of the brain function. Our goal is to realize
DOT based on a mathematical theory and an accurate numerical computation. We require
regularity of the exact solution to the STE to guarantee that we can compute the STE with
some accuracy. In this talk, we discuss regularity of solutions to the STE in a very simple
case.
Koei Kawamura, Kyoto University
Title: q-Hypergeometric polynomials as zonal spherical functions over a finite or local field
Abstract : We consider the situation that a compact group G acts on a locally compact
abelian group M preserving structures of group, measure and topology of M. Then Fourier
18
transformation of G-invariant functions on M is related to zonal spherical functions of
Gelfand-pair (M ⋊G, G). Especially when M and G are concerned with a finite field, it is
known that these functions can be written by certain orthogonal functions of hypergeometric
type like Krawtchouk polynomials or its q-analogues. Now we take M and G concerned with
a non-Archimedean local field, where we see a new orthogonal functions which may be
regarded as 'infinite-variable' Krawtchouk polynomials.
Boran Kim, Ewha Womans UniversityTitle: Self-dual codes over Z8 or Z16
Abstract: There have been active development on self-dual codes over finite fields or finite
rings. We prove that every extremal free self-dual code over Z2m can be found from a binary
extremal Type II code. Moreover, we provide a explicit construction method to find extremal
free self-dual codes over Z8 or Z16. This construction idea is from a lifting method basically.
We present algorithms to find extremal free self-dual codes over Z8 or Z16. By using this
algorithm, we find extremal free self-dual codes over Z8 or Z16 up to lengths 40. For
implementation, we use Magma.
Byoung-IL Kim, Seoul National University
Title: Analysis of the Perfect Table Fuzzy Rainbow Tradeoff
Abstract: Cryptanalytic time memory tradeoff algorithms are tools for inverting one-way
functions. We provides an accurate complexity analysis of the perfect table fuzzy rainbow
tradeoff. We also show that the perfect fuzzy rainbow tradeoff outperforms the original
rainbow tradeoff, which is widely believed to be the best tradeoff algorithm among
implementers. The perfect fuzzy rainbow tradeoff can achieve higher online efficiency at
lower pre-computation cost than the original rainbow tradeoff.
19
Daejun Kim, Seoul National University
Title: Generalized Cullen numbers with the Lehmer property
Abstract: We say a positive integer n satisfies the Lehmer property if φ(n) divides n-1,
where φ(n) is the Euler's totient function. Clearly, every prime satisfies the Lehmer property.
No composite integer satisfying the Lehmer property is known. In this talk, we show that
every composite integer of the form Dp,n=npn+1, for a prime p and a positive integer n, or of
the form α2β+1 for α β does not satisfy the Lehmer property.
Takahiro Kosugi, Tohoku University
Title: Comparison principle for fully nonlinear equations involving the p-Laplace equation
Abstract: We discuss a comparison principle for viscosity solutions of second-order
quasilinear and fully nonlinear elliptic PDEs with no zeroth order terms
in ⑴
where is a bounded domain. In 2001, G. Barles and J. Busca showed that the
comparison principle holds for ⑴ such as the minimal surface equation, the ∞-Laplace
equation and the p-Laplace equation avoided a singularity for by transforming
unknown functions. We adapt a different transformation to enable us to deal with more
general equations. This is joint work with Prof. S. Koike in Tohoku University.
Sushma Kumari, Kyoto University
Title: Measuring Concentration of Distances : An Efficient, Effective and Empirical index
Abstract: High dimensional data analysis gives rise to many challenges. One such that has
come to gain a lot of attention recently is the Concentration of Distances (CoD) phenomenon,
which is the inability of distances to distinguish points well in high dimensions. CoD affects
almost every machine learning and data analysis algorithm in high dimensions. In this talk, I
20
will present a novel efficient and effective empirical measure that not only illustrates whether
a distance function tends to concentrate for a given data set, but also enables us to measure
the rate of concentration and allows us to compare different distance functions vis-à-vis their
rate of concentration. As opposed to existing empirical indices, the proposed empirical
measure uses only the internal characteristics of a given data set and hence is applicable on
real data sets, which was hitherto not possible.
Mikyoung Lee, Seoul National University
Title:W2,p-regularity for elliptic equations in nondivergence form with BMO coefficients
Abstract: In this talk, we discuss the global W2,p-estimates to the Dirichlet problem for
nondivergence elliptic equations with discontinuous coefficients on a C1,1 bounded domain
for every variable exponent p with log-Hölder continuity.
Yi-Hsuan Lin, National Taiwan University
Title: Strong unique continuation for a residual stress system with Gevrey coefficients
Abstract:We consider the problem of the strong unique continuation for an elasticity system
with general residual stress. Due to the known counterexamples, we assume the coefficients
of the elasticity system are in the Gevrey class of appropriate indices. The main tools are
Carleman estimates for product of two second order elliptic operators.
Yijie Lin, Tsinghua University
Title: Topological recursion relations from Pixton relations
Abstract: Pixton relations in ngM , are extensions of Faber-Zagier relations in gM . We
propose an algorithm to derive tautological relations from Pixton relations. We carry out this
algorithm to derive some results in genus 0,1,2,3 from Pixton relations and analyze the
possibility to generalize in higher genera. As an application, some results about
21
reconstruction of Gromov-Witten invariants can be derived. This is a joint work with Jian
Zhou.
Qi Lou, Fudan University
Title: Co-Poisson structures on polynomial coalgebra
Abstract: In this talk we concern co-Poisson structures on a coalgebra C. We characterise
all co-Poisson structures on polynomial coalgebra. Poisson Hopf structures and co-Poisson
Hopf structures on polynomial Hopf algebra are also studied.
Xing Lu, Fudan University
Title: A constructive method in controllability
Abstract: In this talk, a constructive method,which is used to reach the controllability of
quasilinear hyperbolic systems, its recent progress and applications are presented. This is a
direct and simple method in contol theory.
Hironobu Naoe, Tohoku University
Title: Infinitely many corks with special shadow comlexity one
Abstract: A cork is a compact Stein surface which gives rise to exotic pairs of 4-manifolds.
We find infinitely many corks with special shadow complexity one among the 4-manifolds
constructed from contractible special polyhedra having one true vertex by using the notion of
Turaev’s shadow.
Ken-ichi Okubo, Kyoto University
Title: Exact Lyapunov exponents of the generalized Boole transformations
Abstract: The generalized Boole transformations have rich behavior ranging from the
standard ergodic region with the Cauchy measure to the distinct ergodic region with the
infinite Lebesgue measure. In this forum, I show an analytical formula of the Lyapunov
22
exponents of the generalized Boole transformations bridging those behavior smoothly in
which the Lyapunov exponents are explicitly parameterized in terms of the parameter of
the generalized Boole transformations in the range of 2log,0 . Using this formula, we then
prove an existence of extremely sensitive dependency of Lyapunov exponents with the
parameter, where the absolute values of the derivative of Lyapunov exponents with respect
to the parameter goes to infinity in the limit of 0 , and 1 . This result shows the
computational complexity on the numerical simulations of the Lyapunov exponentsnear
1,0 .
Genki Ouchi, Tokyo University
Title: Lagrangian embeddings of cubic fourfolds containing a plane
Abstract: In this talk, I would like to talk about some application of derived categories to
geometry of algebraic varieties, especially cubic fourfolds. For a cubic fourfold X not
containing a plane, Lehn et al constructed examples of irreducible holomorphic symplectic
eightfolds containing X as a Lagrangian submanifold via Hilbert scheme of twisted cubic
curves on X. I will construct similar example of irreducible holomorphic symplectic eightfolds
via derived categories of cubic fourfolds containing a plane.
Gunjan Sapra, Kyoto University
Title: Tensor Stable Positivity of Linear maps
Abstract: This talk focuses on a conjecture called tensor stable positivity of linear maps. It
deals with the existence of non-trivial tensor stable positive linear maps that is linear maps
(other than completely positive and co completely positive) which are tensor stable positive.
Non trivial tensor stable positive maps give an upper bound on the quantum capacity of a
quantum channel. We study that the existence of infinite locally entanglement annihilating
23
channels which is not entanglement breaking channel leads to the existence of Non trivial
tensor stable positive maps. I will talk about entanglement breaking and infinite locally
entanglement annihilating channels. We need to find an infinite locally quantum annihilating
channel which is not entanglement breaking. To answer this question, we investigate about
Random unitary channels and EPOSIC channels.
Wonmin Shin, Sungkyunkwan University
Title: A generalization of contact metric manifolds and its applications
Abstract: We give a characterization of a contact metric manifold as a special almost
contact metric manifold. Furthermore, we study curvature identities on quasi contact metric
manifolds based on the geometry of the corresponding quasi Keahler cones and we provide
several results derived from the obtained curvature identities.
Masato Shinjo, Kyoto University
Title: Asymptotic analysis for the discrete hungry Lotka-Volterra system and an associated
Fibonacci sequence
Abstract: The Casorati determinant appears in representation of the solution to the discrete
hungry Lotka-Volterra (dhLV) system, which is an integrable variant of the famous
predator-prey model in mathematical biology. In this talk, first, an asymptotic expansion
formula of a certain Casorati determinant is presented. Next, an asymptotic behavior of the
solution to the dhLV system is clarified by an asymptotic expansion of the Casorati
determinant. Finally, we show that, if the entries of the Casorati determinant are given by an
extended Fibonacci sequence at the initial discrete-time, then one of the dhLV variable
converges to the limit of the ratio of two successive extended Fibonacci numbers as the
discrete-time goes to infinity.
24
Cheng-Fang Su, National Chiao Tung University
Title: 3-dimensional incompressible Navier-Stokes equations interacting with a nonlinear
elastic shell
Abstract: We study the Navier-Stokes equations interacting with a nonlinear elastic biofluid
shell which can be used to describe the dynamics of the membrane of blood cells. To solve
this problem, we introduce the sign-distance function which measures the distance between
the moving boundary and the initial boundary. Using this sign-distance function, we can
transform the equations given on the moving domain to equations on a fixed reference
domain, and apply fixed point arguments to construct a solution to the corresponding
equations. To explain how we close estimates, I will take a linear case to demonstrate the
difficulties and technicality that requires to solve the nonlinear problem.
Ren-He Su, Kyoto University
Title: Kohnen plus space and Jacobi forms
Abstract: The Kohnen plus space is a space consisting of some modular forms of
half-integral weight characterized by some properties of whose Fourier coefficients. For
example, in the classic case, if a modular form of weight k+1/2 with Fourier coefficients a(n)
is in the space, then a(n) vanishes unless (-1)^kn is congruent to 0 or 1 mod 4. The
concept was initially brought up by Kohnen and generalized to the Hilbert-Siegel case later.
It is known that the plus space is isomorphic to the space of Jacobi forms. In this talk, I look
forward to explain how this isomorphism works.
Uhi Rinn Suh, Seoul National University
Title: classical affine W-(super)algebras
Abstract: There are four types of W-algebras : quantum affine, classical affine, quantum
25
finite, classical finite W-algebras. Hence we can consider two possible constructions of
classical affine W-algebras. One is via classical limits of quantum affine W-algebras and the
other one is via affinizations of classical finite W-algebras. In this talk, I will show the two
constructions give rise to equivalent definitions of classical affine W-algebras. Also, I will
introduce the superalgebraic analogues of these arguments.
Wei Sun, Fudan University
Title: The complex Monge-Ampere type equations on closed Hermitian manifolds
Abstract: The complex Monge-Ampere type equations include some of the most important
differential equations in complex geometry, e.g. the complex Monge-Ampere equation and
Donaldson's equation. In this talk, I will report on a priori estimates, and the existence of the
admissible solution under the cone condition.
Doman Takata, Kyoto University
Title: "Dirac operators" on compact Lie groups and Loop groups
Abstract: Dirac operator D on a Riemannian manifold M is an important object of differential
geometry. It acts on the space of L2 sections of a vector bundle S, L2(S). If M has a structure
of a compact Lie group G, Peteer-Weyl theorem enables us to describe Dirac operator in
terms of only representation theory. Although the Loop group LG of compact Lie group G
does not have a good measure, Freed, Hopkins and Teleman “defined” a space of “L2
sections” and “Dirac operator” on LG. Moreover, they defined the isomorphism from the
representation group of LG to twisted equivariant K-theory by use of the family of “Dirac
operator” and I studied their work from the view point of functoriality. In this talk, I will present
the construction of Dirac operator on compact Lie groups and Loop groups in terms of
representation theory. If possible, I will also explain the works of Freed, Hopkins and
26
Teleman.
Hejie Wei, Fudan University
Title: A Riemannian subspace limited-memory SR1 trust region method
Abstract: In this paper, we present a new trust region algorithm on any compact
Rieman-nian manifolds using subspace techniques. The global convergence of the method
is proved and local d+1-step superlinear convergence of the algorithm is presented, where d
is the dimension of the Riemannian manifold. Our numerical results show that the proposed
sub- space algorithm is competitive to some recent developed methods, such as the
LRTR-SR1 method, the LRTR-BFGS method, the Riemannian CG method.
Qing Xu, Fudan University
Title: Some Results on the Controllability of Stochastic Schrödinger Equations
Abstract: This talk is concerned with the controllability of stochastic
Schrödinger equations in a bounded domain D in R^N. When N=1, we prove the exact
controllability when the control is imposed on an interval. We also show that the equation is
not null controllable by using pointwise controls or finite rank controls, while the equation is
approximately controllable for a large class of pointwise controls and finite rank controls.
When N≥2, we prove the approximate controllability when the control is imposed on an
nonempty open set. We also prove the exact controllability when D is a square. Such a
result implies that geometric control condition, which is a sufficient and necessary condition
in the exact controllability of wave equations, is unnecessary for the exact controllability of
stochastic Schrödinger equations.
Anming Yang, Fudan University
Title: Duality of martingale Hardy-Lorentz space and John-Nirenberg inequality
27
Abstract: In this paper we defined a generalized BMO martingale space by stopping time
sequences which enables us to characterize the dual space of martingale Hardy-Lorentz
space when 0<p ≤ 1. We prove the duality theorems by improving the previous atomic
decomposition results of martingale Hardy-Lorentz spaces. Then under the condition of
regularity, we prove the John-Nirenberg theorem of the generalized BMO martingale spaces.
It is an extension of the John-Nirenberg theorem of the Lipschitz spaces. Finally, we extend
the boundedness of fractional integrals from martingale Hardy spaces to martingale
Hardy-Lorentz spaces.
Silu Yin, Fudan University
Title: Global existence for a model of inhomogeneous incompressible elastodynamics in 2D
Abstract: In this talk, we investigate a model of incompressible, isotropic, inhomogeneous
elastodynamics in two space dimensions. We prove the global existence for this Cauchy
problem with sufficiently small initial displacement and small density disturbance around
constant.
Fuetaro Yobuko, Tohoku University
Title: Quasi-Frobenius-splitting and lift of Calabi-Yau varieties
Abstract: In this talk, we consider whether a Calabi-Yau variety over an algebraically closed
field of positive characteristic admits a lift to characteristic zero or not. It is well known that,
for K3 surfaces, the answer is yes. But Hirokado and Schr¨oer constructed non liftable
Calabi-Yau threefolds. Their varieties have infinite Artin-Mazur height, so there is a hope for
affirmative answer for finite height varieties. In this talk, we introduce
quasi-Frobenius-splitting varieties and show that a Calabi-Yau variety of finite height admits
a lift to the ring of Witt vectors of length two.
28
Jun Yoshida, Tokyo University
Title: Morse-Cerf theory in some relative situations
Abstract: The Morse-Cerf theory is a very important tool for the study of oriented manifolds.
It relates the topology of a manifold with analysis around singular points. In this talk, we
introduce analogous results for “relative manifolds”. More precisely, we consider finite
lattices S and functors S → Emb which preserve and reflect limits, where Emb is the category
of manifolds with corners and embedding maps. Such functors are called arrangements. If
an arrangement is locally diffeomorphic to an “Euclidean” arrangement, it is said to be
excellent. Some arguments for usual oriented manifolds extends to excellent arrangements.
For example, we can define jet bundles and multi-jet bundles for excellent arrangements,
and we obtain an analogue of Thom’s transversality theorem. We also give some simple
examples and, as an application, a complete list of generators for “(1+1)-dimensional
oriented cobordisms with defect lines”, which gives a geometric description for planar
algebras.
Lei Yu, Fudan University
Title: Controllability of Traffic flow
Abstract: First I will give an introduction to mathematical study of controllability for traffic
models which are described by solutions to system of hyperbolic partial differential
equations on a network. Then I will talk about my recent work with Prof. Daqian Li [2] on the
study of boundary controllability for entropy solutions to a class of hyperbolic conservation
laws and its application to traffic flow control for the Aw-Rascle model[1].
29
Mei-Heng Yueh, National Chiao Tung University
Title: Computational Conformal Mapping for Genus Zero Surface with Applications
Abstract: The celebrated uniformization theorem states that a closed simply connected
Riemann surface of genus zero is conformally equivalent to a unit sphere. In this talk, I will
introduce the numerical methods for computing conformal mappings for genus zeros
surfaces, and then demonstrate some applications.
Kaili Zhuang, Fudan University
Title: Exact controllability for nonautonomous first order quasilinear hyperbolic systems with
internal controls
Abstract: Based on the theory of the local exact boundary controllability for nonautonomous
first order quasilinear hyperbolic systems, using an extension method, the authors establish
the exact controllability in a shorter time by means of internal controls acting on suitable
domains.
Kyeong-Dong Park, Seoul National University
Title: Deformation rigidity of odd Lagrangian Grassmannians
Abstract: Let $V$ be a complex vector space endowed with a skew-symmetric bilinear form
$\omega$ of maximal rank. When $\dim V$ is odd, say, $2n+1$, we call the variety
$\Gr_{\omega}(k, 2n+1)$ of all $k$-dimensional isotropic subspaces of $V$ as the odd
symplectic Grassmannian, which is not homogeneous and has two orbits under the action of
its automorphism group if $2 \leq k \leq n$.
We prove the rigidity under K\"{a}hler deformation of the complex structure of odd
Lagrangian Grassmannians, i.e., the Lagrangian case $\Gr_{\omega}(n, 2n+1)$ of odd
symplectic Grassmannians.
30
To obtain the global deformation rigidity of the odd Lagrangian Grassmannian, we use
results about the automorphism group of this manifold, the Lie algebra of infinitesimal
automorphisms of the affine cone of the variety of minimal rational tangents and its
prolongations.
31
Brief Map
