学术报告
报告1
报 告 人：白朝芳 （厦门大学）
报告题目：Coherence measure
报告时间：10月29日（星期日）下午3:00-3:25
报告地点：香洲大饭店7楼B厅会议室
报告摘要：Quantum coherence provides an important resource for quantum information processing. There arises naturally the question of how it can be quantified, i.e., measuring coherence. In this talk, we will review several coherence measures and give a new one.
报告2
报 告 人：曹广福（华南农业大学）
报告题目：Spectral Theory of Multiplication Operators on Hardy-Sobolev Spaces
报告时间：10月29日（星期日）上午9:20-10:00
报告地点：香洲大饭店7楼A厅会议室
报告摘要：For a pointwise multiplier $\varphi$ of the Hardy-Sobolev space $H^2_\beta$ on the open unit ball $bn$ in $cn$, we study spectral properties of the multiplication operator $M_\varphi: H^2_\beta\to H^2_\beta$. In particular, we compute the spectrum and essential spectrum of $M_\varphi$ and develop the Fredholm theory for these operators.
报告3
报 告 人：陈晓漫（复旦大学）
报告题目：Coarse geometry at infinity
报告时间：10月28日（星期六）上午8:20-9:00
报告地点：香洲大饭店7楼A厅会议室
报告4
报 告 人：陈艳妮（陕西师范大学）
报告题目：Commutative and Noncommutative Hardy spaces based on unitarily invariant norms
报告时间：10月28日（星期六）下午3:35-4:00
报告地点：香洲大饭店7楼B厅会议室
报告摘要：The theory of Hardy spaces originated with discoveries made sixty years ago by famous mathematicians: Hardy, Littlewood, Riesz, Smirnov, which plays a central role in many parts of applied mathematics, e.g., systems theory, control theory, signal and image processing. As a more general $\|\|_p-$norm on the Hardy space, the unitarily invariant norms are very important in the study of function spaces, group representations and in obtaining certain bounds of importance in quantum field theory. Now it is natural to ask: \begin{enumerate}\item What does one get if one combines the classical Hardy spaces and unitarily invariant norms?
\item What does one get if one combines the theory of Arveson's noncommutative Hardy's spaces and unitarily invariant norms?\end{enumerate}
In this talk, replacing the $\|\|_p-$norms with unitarily invariant norms, we are going to introduce the generalized Hardy spaces and extend many classical results in the commutative and noncommutative Hardy spaces.
报告5
报 告 人：陈泽乾 （中国科学院武汉物理与数学研究所）
报告题目：The geometric phase of quantum systems
报告时间：10月29日（星期日）上午10:50-11:30
报告地点：香洲大饭店7楼A厅会议室
报告摘要：In this talk, we will report that the geometric phase is introduced associated with quantal observable space. The phase is determined by the Heisenberg equation, contrary to the usual one by the Schrödinger equation. Geometrical interpretation of the phase over the quantal observable space is also presented.
报告6
报 告 人：程国正 （温州大学）
报告题目：Random Weighted Shift
报告时间：10月29日（星期日）下午2:30-3:00
报告地点：香洲大饭店7楼A厅会议室
报告摘要：In this taking, we firstly shall briefly review the past of Two projections theory. The subject is not only an old topic, but also a new topic in operator theory and operator algebra. More recently, the two projections theory has attracting attentions of a variety of mathematicians (see: A gentle guide to the basics of two projections theory, Linear Algebra Appl. 432 (2010) 1412-1459 ). After that we will present our recent researching results involving the two projections.
报告7
报 告 人：杜鸿科 （陕西师范大学）
报告题目：Two projections theory and applications
报告时间：10月29日（星期日）上午8:40-9:20
报告地点：香洲大饭店7楼A厅会议室
报告摘要：In this taking, we firstly shall briefly review the past of Two projections theory. The subject is not only an old topic, but also a new topic in operator theory and operator algebra. More recently, the two projections theory has attracting attentions of a variety of mathematicians (see: A gentle guide to the basics of two projections theory, Linear Algebra Appl. 432 (2010) 1412-1459 ). After that we will present our recent researching results involving the two projections.
报告8
报 告 人：段周波 （太原理工大学）
报告题目：Contractive freedom for infinite-dimensional
报告时间：10月28日（星期六）下午3:10-3:35
报告地点：香洲大饭店7楼A厅会议室
报告摘要：The unitary freedom in ensemble of pure states with a given state and the
unitary in freedom operator-sumrepresentation for a given channel are no longer valid for infinite dimensional systems. Instead, what we can establish are the contractive freedom in ensemble and the contractive freedom in operator-sum representation. Namely, we show that,
(1) two ensembles
and
determine the same state if and only if there exists some contractive matrix
such that
for each
;
(2) two sequences
and
of Kraus operators in operator-sum representations determine the same channel if and only if there exists some contractive matrix
such that
for each
.
报告9
报 告 人：房军生 河北师范大学
报告题目：On a class of operators in the hyperfinite type II1 factor
报告时间：10月28日（星期六）下午2:30-3:10
报告地点：香洲大饭店7楼A厅会议室
报告摘要： In this talk, we introduce a class of operators in the hyperfinite type II1 factor. We will discuss the spectrum, Brown spectrum, invariant subspaces of the operators. We also characterize the von Neumann algebras and C*-algebras generated by the class of operators.
报告10
报 告 人：郭坤宇（复旦大学）
报告题目：Dirichlet series and Hilbert modules in infinitely many variables
报告时间：10月29日（星期日）上午8:00-8:40
报告地点：香洲大饭店7楼A厅会议室
报告摘要：The Hardy module $H^2(\mathbb{D}_2^{\infty})$ in infinitely many variables is closely related to some classical problems, such as the completeness problem and the Riesz basis problem of $L^2(0,1)$ concerning systems of dilated functions; and the problem of zero points of Dirichlet series. This inspires us to focuses on polynomial generated submodules of the Hardy module $H^2(\mathbb{D}_2^{\infty})$ in infinitely many variables. Since the polynomial ring $\mathcal{P}_{\infty}$ in infinitely many variables is not Noetherian, some standard tricks for finitely many variables fail to work. Therefore, we need to introduce new techniques to the situation of infinitely many variables. It is shown that some classical results of $H^2(\mathbb{D}^n)$ remain valid for infinitely many variables. However, some new phenomena indicate that the Hardy module $H^2(\mathbb{D}_2^{\infty})$ diverges considerably from the case in finitely many variables. This is a joint work with Hui Dan and Hansong Huang.
报告11
报 告 人：侯晋川 （太原理工大学）
报告题目：Characterizing the Gaussian coherence breaking channel and its property with assistant entanglement inputs
报告时间：10月28日（星期六）上午9:00-9:40
报告地点：香洲大饭店7楼A厅会议室
报告摘要：We give a characterization of arbitrary
-mode Gaussian coherence breaking channels (GCBCs) and show that the tensor product of a GCBC with an arbitrary Gaussian channel maps all input states into product states. The inclusion relations between the sets of GCBCs, Gaussian positive partial transpose channels (GPPTCs), entanglement breaking channels (GEBCs), Gaussian classical-quantumchannels (GCQCs) and Gaussian quantum-classical channels (GQCCs) are displayed.
报告12
报 告 人：黄寒松 （华东理工大学）
报告题目：Cyclic vectors in Fock-type spaces
报告时间：10月28日（星期六）下午4:00-4:25
报告地点：香洲大饭店7楼B厅会议室
报告摘要：In this talk, we study cyclic vectors in Fock-type spaces and completely characterize them.
报告13
报 告 人：黄辉斥 （重庆大学）
报告题目：The discrete quantum group fixing a sequence of finite sets
报告时间：10月29日（星期日）下午4:00-4:25
报告地点：香洲大饭店7楼A厅会议室
报告摘要：Motivated by a generalization of Szemeredi's theorem, we consider the discrete quantum subgroup fixing a sequence of finite subsets. Then we prove a generalized mean ergodic theorem for discrete quantum groups.
报告14
报 告 人：刘浏（大连理工大学）
报告题目：The stability analysis of causal systems on the Hilbert resolution space
报告时间：10月28日（星期日）下午4:00-4:25
报告地点：香洲大饭店7楼A厅会议室
报告摘要：The stability theory of causal linear systems on Hilbert resolution space is an important application of operator theory and non-self adjoint operator algebra theory to the control theory. Within the context of operator theory and operator algebra, some results on the factorization, stable rank, gap metric and time-varying (TV) gap of causal linear systems are introduced in this talk. It is shown that the TV gap has no advantage over gap metric in stability and robustness analysis on the Hilbert resolution space $(\ell^2(\mathbb{Z}_+):\{P_n\}_{n\in\mathbb{Z}_+})$, while it stands out on $(\ell^2(\mathbb{Z}):\{P_n\}_{n\in\mathbb{Z}})$.
报告15
报 告 人：吉国兴 陕西师范大学
报告题目：Pencils of Pairs of Projections
报告时间：10月29日（星期日）上午11:30-12:00
报告地点：香洲大饭店7楼A厅会议室
报告摘要：Let
be a self-adjoint operator on a complex Hilbert space
. We give a sufficient and necessary condition for
to be the pencil
of a pair
of projections at some point
Then we represent all pairs
of projections such that
for a fixed
and find that all such pairs are connected if
. Afterwards, the von Neumann algebra generated by such pairs
is characterized. Moreover, we prove that there are at most two real numbers such that
is the pencils at these real numbers for some pairs of projections. Finally, we determine when the real number is unique.
报告16
报 告 人：江永乐 （韩国skku大学)
报告题目：On calculating the second cohomology group of Bernoulli shifts
报告时间：10月29日（星期日）下午4:25-4:50
报告地点：香洲大饭店7楼A厅会议室
报告摘要：In the early 2000, Popa initiated his powerful deformation/rigidity techniques in von Neumann algebras. In the past decades, many old questions in von Neumann algebras and related areas have been settled using these techniques. One of the early success is calculating the first cohomology group with the unit circle $\mathbb{T}$ as the target group for Bernoulli actions $G\curvearrowright (X_0, \mu)^G$ of property (T) groups (e.g. $G=SL_3(\mathbb{Z})$), i.e. it is shown that $H^1(G\curvearrowright X_0^G; \mathbb{T})=H^1(G, \mathbb{T})$. Motivated by this result, Popa asked whether the same result holds for the second cohomology group. We discuss the negative answer we get by using the idea of algebraic actions.
报告17
报 告 人：李辉（华东师范大学）
报告题目：Boundary Quotient C*-algebras of Products of Two Odometers
报告时间：10月28日（星期六）下午3:10-3:35
报告地点：香洲大饭店7楼A厅会议室
报告摘要：The semigroups of products of 2 odometers, constructed by Brownlowe-Ram agge-Robertson-Whittaker, are generalizations of odometers. However, the boundary quotient C*-algebra of a product of 2 odometers was not well understood. In this talk I will firstly write down the explicit relations of the generators for the boundary quotient C*-algebra of a product of 2 odometers. Then for any product of 2 odometers I will construct a regular topological 2-graph associated to it, such that the boundary quotient C*-algebra of the product of 2 odometers is isomorphic to the topological 2-graph C*-algebra. This identification allows us to provide conditions under which the boundary quotient C*-algebra of the product of 2 odometers is amenable, simple, and purely infinite. This is joint work with Dilian Yang.
报告18
报 告 人：李启慧 （华东理工大学）
报告题目：Wave operators and Kato-Rosenblum Theorem insemifinite von Neumann algebras
报告时间：10月28日（星期六）下午5:30-5:55
报告地点：香洲大饭店7楼A厅会议室
报告摘要：The wave operator is the basic object of scattering theory. In this talk, we will extend this concept to the setting of semifinite von Neumann algebras. By showing the existence of wave operators, we will provide a version of the Kato-Rosenblum theorem in a semifinite von Neumann algebras.
报告19
报 告 人：麻振华 （河北建筑工程学院）
报告题目：非交换Orlicz空间中若干拓扑性质和几何性质的研究
报告时间：10月28日（星期六）下午5:25-5:50
报告地点：香洲大饭店7楼A厅会议室
报告摘要：主要对非交换 Orlicz 空间
中的一些几何及拓扑性质进行了研究. 主要包括以下内容:
1 该空间中的一类重要子空间及相关性质;
2依测度收敛下的Kadec-Klee 性质及自反性;
3装球常数的下界估计;
4 非交换 Orlicz 序列空间及若干几何性质.
报告20
报 告 人：马攀（中南大学）
报告题目：Semicommutator and commutator of truncated Toeplitz operators
报告时间：10月29日（星期日）下午3:25-3:50
报告地点：香洲大饭店7楼B厅会议室
报告摘要：A necessary and sufficient condition is found on the semi-commutator of truncated Toeplitz operators with bounded symbol in model spaces which the corresponding inner function
. Also, a uniform way to characterize the semicommutator and commutator of truncated Toeplitz operators is presented by the techniques of Toeplitz operators and Hankel operators on Hardy space.
报告21
报 告 人：孟庆（曲阜师范大学）
报告题目：Weak Haagerup property of
crossed products
报告时间：10月29日（星期日）下午4:50-5:15
报告地点：香洲大饭店7楼A厅会议室
报告摘要：We show that if $M\bar{\rtimes}_\alpha \Gamma$ has the weak Haagerup property, then both $M$ and $\Gamma$ have the weak Haagerup property. Let $\Gamma$ be an amenable group, then the weak Haagerup property of $M$ implies that of $M\bar{\rtimes}_\alpha \Gamma$. Moreover, we give a condition under which the weak Haagerup property of $M$ and $\Gamma$ imply that of $M\bar{\rtimes}_\alpha \Gamma$.
报告22
报 告 人：彭双阶 （华中师范大学）
报告题目：Local uniqueness reduced by concentration
报告时间：10月28日（星期六）上午11:10-11:50
报告地点：香洲大饭店7楼A厅会议室
报告摘要：We will talk about a type of elliptic equations with critical exponents and scalar curvature K(y), K(y) is positive and periodic in its first k variables (y_1,..., y_k). Under some conditions on K(y) near its critical point, we prove not only that this problem admits solutions with infinitely many bubbles, but also that the bubbling solutions obtained in our existence result are locally unique. This local uniqueness result implies that some bubbling solutions preserve the symmetry of K(y).
报告23
报 告 人：齐宵霏 （山西大学）
报告题目：Strong 3-skew commutativity preserving maps on operator algebras
报告时间：10月28日（星期六）下午4:35-5:05
报告地点：香洲大饭店7楼A厅会议室
报告摘要：Let
be a unital prime *-ring containing a nontrivial symmetric idempotent. For
, the 3-skew commutator is defined by
Let
be a surjective map. It is shown that
satisfies
for all
if and only if there exists
with
such that
for all
. Where
is the unit of
and
is the symmetric center of
This result then is applied to matrix algebras and operator algebras such as prime C*-algebras, factor von Neumann algebras, the indefinite self-adjoint standard operator algebras and symmetric standard operator algebras.
报告24
报 告 人：乔雨 （山西师范大学）
报告题目：Fredholm Groupoids and Exhaustive Families of Representations of Groupoid Algebras
报告时间：10月28日（星期六）下午5:05-5:30
报告地点：香洲大饭店7楼A厅会议室
报告摘要：In this talk, we first review the primitive ideal space of a C*-algebra, exhaustive families of representations of C*-algebras (defined by Nistor and Prudhon), and groupoid C*-algebras (via representation theory of C*-algebras). Then we introduce the notions of Fredholm groupoids and Exel's strong property for groupoids.
We show that under suitable assumptions, a groupod with Exel's strong property is Fredholm. Finally we obtain the following theorem: if $\mathcal{G}$ is a locally compact, second countable, and Hausdorff groupoid with the unit space
, such that all isotropy groups $\mathcal{G}^x_x, x\in M$，
are amenable，then $\mathcal{G}$ is metrically amenable and has Exel's strong property. Hence, combining these two results, we obtain a sufficient condition for a groupoid to be Fredholm. This is joint work with Catarina Carvalho and Victor Nistor.
报告25
报 告 人：石洛宜 （天津工业大学）
报告题目：Amenability, similarity and approximation
报告时间：10月28日（星期六）下午3:35-4:00
报告地点：香洲大饭店7楼A厅会议室
报告摘要：The concept of amenability is fundamental in the study of operator algebras. Farenick, Forrest, Marcoux and Popov investigated the amenability of Banach algebras singly generated by Hilbert space operators. It is proved that the Banach algebra generated by
is amenable if and only if
is similar to a normal operator whose spectrum has a connected complement and an empty interior. The amenability of C*-algebras is closely related to another important notion called nuclearity, by the work of Connes and Haagerup, a C*-algebra is amenable if and only if it is nuclear. Inspired by the above mentioned works, we are interested in determining when a singly generated C*a-algebra is amenable. We say that an operator
is *-amenable if the C*-algebra
generated by
is amenable. In this talk, we will show that the *-amenability of operators is unstable under similarity and each operator similar to
is C*-amenable if and only if
is a polynomially compact operator of order at most two. Moreover, we will show that the set of C*-amenable operators is not closed and nowhere dense in
, when
. At last, we will discuss the *-amenability of special classes of operators.
报告26
报 告 人：王航 （华东师范大学）
报告题目：Character identity: A point of view from index theory
报告时间：10月29日（星期日）下午3:00-3:25
报告地点：香洲大饭店7楼A厅会议室
报告摘要：In this talk, we reconstruct Shelstad's character identities using index theory of elliptic operators in the framework of
-theory, for a pair of real (semisimple, linear, algebraic) groups sharing the same
-group. This geometric interpretation of the character identity reveals that index theory could serve as a new geometric perspective for the algebraic constructions in the Endoscopic transfer appeared in the local Langlands correspondence.
报告27
报 告 人：王凯 （复旦大学）
报告题目：Dixmier trace of quotient module on bounded symmetric domain
报告时间：10月28日（星期六）下午2:30-3:10
报告地点：香洲大饭店7楼B厅会议室
报告摘要：In this talk, we mainly concern the essential normality of Toeplitz operators on bounded symmetric domains. We define a Hilbert quotient module corresponding to partitions of length 1 and prove that it belongs to the Macaev class Ln,∞. We next obtain an explicit formula for the Dixmier trace of Toeplitz commutators in terms of the underlying boundary geometry. This is a joint work with Prof. Harald Upmeier.
报告28
报 告 人：王茂发 （武汉大学）
报告题目：Joint Carleson measure and difference of composition operators over the half-plane
报告时间：10月29日（星期日）下午2:30-3:00
报告地点：香洲大饭店7楼B厅会议室
报告摘要：As is well known joint Carleson measure now is a basic tool to characterize the boundness and compactness of the differences of two composition operators on the weighted Bergman spaces over the unit disk. In this talk, we use Khinchine's inequality and atomic decomposition techniques to introduce similar joint Carleson measure char-acterizations of when the difference of composition operators is bounded or compact from standard weighted Bergman spaces to Lebesgue spaces over the half-plane for all choices of the indexes. As applications, we obtain direct analytic characterizations of the bounded and compact difference of composition operators on such spaces. This talk closes with a joint Carleson measure characterization of when the difference of composition operators is Hilbert-Schmidt. This is a joint work with C. Pang.
报告29
报 告 人：王勤，(华东师范大学)
报告题目：Higher index problems associated with coarse geometry and Banach space geometry
报告时间：10月28日（星期六）上午11:50-12:30
报告地点：香洲大饭店7楼A厅会议室
报告摘要：Higher index theory associated with coarse geometry is a program to compute K-theory of the Roe C*-algebras of various spaces. There are beautiful links between higher index theory, metric geometry, dynamical systems and Banach space geometry. In this talk, we will discuss these links and some of recent progress in this direction.
报告30
报 告 人：王子鹏 （陕西师范大学）
报告题目：The Doubling Measure Property and Operators on Function Spaces
报告时间：10月29日（星期六）下午4:00-4:25
报告地点：香洲大饭店7楼B厅会议室
报告摘要：Doubling measures arise naturally in various ways in analysis and geometry and there is an industry building on them. In this talk, we will explain their three applications to operators on function spaces.
(1) Carleson measures on the Bergman and Dirichle space
(2) Weighted inequalities for the Bergman projection
(3) Toeplitz Operators on the weighted harmonic Bergman space.
These are based on my joint works with Cheng Guozheng, Fang Xiang, Guo Kunyu, Yu Jiayang and Zhao Xianfeng.
报告31
报 告 人：乌兰哈斯 （汕头大学）
报告题目：Composition Operators on BMOA and related function spaces
报告时间：10月28日（星期六）上午10:30-11:10
报告地点：香洲大饭店7楼A厅会议室
报告摘要：I will talk some results on composition operators on BMOA and related function spaces. Also, I will mention some open problems in this area.
报告32
报 告 人：武俊德 (浙江大学)
报告题目：浅议量子网络理论
报告时间：10月29日（星期日）上午12:00-12:30
报告地点：香洲大饭店7楼A厅会议室
报告摘要：基于著名的Choi-Jamiolkowski 同构而建立的量子网络理论是近年来发展起来的一个重要研究方向。该理论在量子信息处理、量子层析技术、量子变换的学习等方面有巨大的应用潜力。群表示论、Schur-Weyl 对偶、局部紧群上的积分是研究该理论的重要工具。我们将浅议该理论的研究进展和可能的发展趋势。
报告33
报 告 人：杨容伟 （纽约州立大学奥尔巴尼分）
报告题目：算子预解集上的Hermitian度量
报告时间：10月29日（星期日）上午10:10-10:50
报告地点：香洲大饭店7楼A厅会议室
报告摘要：作为复平面内的开集，算子预解集上有传统的欧氏度量。但欧氏度量不能反映该算子的性质。我们尝试在预解集上定义和算子相关的度量，并研究在该度量下预解集几何性质和算子的关系。一个重要的应用是对拟幂零算子的研究。
报告34
报 告 人：姚兴兴 （武汉工程大学）
报告题目：Dirichlet 级数空间上复合算子的一些性质
报告时间：10月29日（星期日）下午4:25-4:50
报告地点：香洲大饭店7楼B厅会议室
报告摘要：在本报告中, 我们考虑系数平方可和的Dirichlet 级数构成的Hilbert 空间上复合算子的不变子空间, 复对称性和 Toeplitz 性等.
:
报告35
报 告 人：余佳洋 （四川大学）
报告题目：Cauchy-Kowalevski And Holmgren Type Theorems with Infinite Number of Variables
报告时间：10月29日（星期日）下午4:50-5:15
报告地点：香洲大饭店7楼B厅会议室
报告摘要：Firstly, we establish a family of
induced topologies on
and corresponding topologies on
with infinity point which will be used to describe analyticity. Secondly, we adapt the definition of analyticity of functions on
by Hilbert as monomial expansions and by the method of majorants we get a Cauchy-Kowalevski type theorem with infinite number of variables. Thirdly, based on the Cauchy-Kowalevski type theorem we have established, the tools of abstract Wiener spaces, Malliavin analysis and a divergence theorem for Hilbert space, we obtain a Holmgren type theorem with infinite number of variables.
报告36
报 告 人：张钧 （太原理工大学）
报告题目：Stronger uncertainty relations with tight bounds
报告时间：10月28日（星期六）下午4:35-5:00
报告地点：香洲大饭店7楼B厅会议室
报告摘要：The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. In order to improve the bounds, we utilize quantum superposition principle to establish the upper and lower bounds on the stronger uncertainty relation [Phys. Rev. Lett. 113, 260401 (2014)], i.e., the ``weighted-like” sum of the variances of observables. Our bounds include some free parameters which not only guarantee the nontrivial bounds but also can effectively control the bounds as tightly as one expects. Especially, these parameters don't obviously depend on the state and observables. It also implies one advantage of our method that any nontrivial bound can always be tight enough. In addition, we generalize both bounds to the uncertainty relation with multiple observables, but the perfect tightness is not changed. In addition, we also present tighter bounds on entropic uncertainty relation for multiple measurements in the presence of quantum memory.
报告37
报 告 人：张远航 （吉林大学）
报告题目：Blackadar的一个问题
报告时间：10月29日（星期日）下午3:25-3:50
报告地点：香洲大饭店7楼A厅会议室
报告摘要：在其专著《K-theory for operator algebras》中,Blackadar提出了如下问题: AF代数A的K_0群上的有限阶自同构是否均可以提升为A的同样阶自同构? 我们将首先回顾一下这个问题的背景及意义，而后，就一些典型的情形对此问题给出肯定的回答。
报告38
报 告 人：张志涛 （中国科学学院）
报告题目：Existence of solutions for Schrodinger systems with linear and nonlinear couplings
报告时间：10月28日（星期六）上午9:40-10:20
报告地点：香洲大饭店7楼A厅会议室
报告摘要：We are concerned with the important system of nonlinear Schrodinger equations with linear and nonlinear couplings which arises from Bose-Einstein condensates, we prove phase segregation results of the limit competition case, which covers S. Terracini's conjecture; we use variational methods to prove the existence of ground state and bound state solutions of the systems, and use bifurcation theory to get structure of positive solutions. We give some partial symmetry results of positive solutions by Morse index and obtain existence and uniqueness of positive solution via synchronized solution techniques etc.
报告39
报 告 人：赵显锋 （重庆大学）
报告题目：The spectrum of Toeplitz operators with some analytic polynomial symbols on the harmonic Bergman space
报告时间：10月28日（星期六）下午5:00-5:25
报告地点：香洲大饭店7楼B厅会议室
报告摘要： Let
be an analytic polynomial on the unit disk and
be the corresponding Toeplitz operator on the harmonic Bergman space. A fundamental but nontrivial problem is to compute the spectrum of a Toeplitz operator. In this talk, we will discuss the structure of the spectrum of
via some techniques used in the study of Toeplitz operators on the Bergman space.
