Volume 23, Horticultural Reviews

Education 2 PBS Kids Writers Contest (Grades K-3) TIME for Kids, a non- fiction weekly news magazine for classrooms, is a child-oriented categories: Dramatic Script, Flash Fiction, Humor, Journalism, Personal Essay.

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The Lie group of automorphisms of a principle bundle. JOP - Vol. A convenient structure of Lie group to the entire group Aut P of G- automorphisms of a principal G-bundle without any assumption of compactness on the structure group G or on the base manifold. Its Lie algebra and the expo. Some relevant principal bundles are discussed having A ut P or its subgroup Gau P of gauge transformations as structure group. The group DiffM of diffeomorphisms of a manifold M is quite familiar since long time to people working in General Relativity. More recently the group Gau P of the gauge transformations of a principal bundle P, p, M, G gained a similar popularity among people working in Yang-Mills theories.

Convenient smoothness structure for these groups have been proposed along with realizations of their Lie algebras and properties of the exponential map have been investigated [1,2, 3]and references therein, [4,5,6,7,8]. An automorphism of P induces a diffeomorphism on the base manifold and, in the case of a trivial P or of the bundle LM of linear frames, the group Aut P is an extension of DiffM by Gau P. Although the group AutP is a subgroup of Diff P from algebraic point of view, the inherited topology is discrete, hence the Lie structure trivial, in the case of non compact structure group.

This difficulty appears already in the group Gau P when considered as a subgroup of Diff P [9]. This pathology cannot be avoided in the relevant case of frame bundles. As in the case of Gau P the way out of the difficulty is to interprete the entire Aut P as a space of sections of a suitable fiber bundle. More generally, homomorphisms of principal bundles must be conveniently considered as sections of a naturally constructed fiber bundle.

Universal anomalies are generated by pulling back coho- mology classes of classifying spaces via Eu. The Lie structure of the group Aut P, its Lie algebras and the exponential map are illustrated in Sec. Gau Pis proved to be a splitting subgroup ofAutP. In the last section we discuss some principal bundles. Such an identification is already known. Using 8. Here we prefer to look at this bundle in a slightly different way. The resulting identification is closer to the one well known in the case of morphisms of vector bundles, so we first illustrate our procedure with a short discussion of this latter case.

Actually, F is a natural equivalence of the functor Horn , , with the functor FL1 ,. Using We denote it by GauF. We can state the following theorem. As a consequence of these arguments we can state. The map F gives a natural equivalence ofthefunctorHom , with the functor F Eq1 ,. It was proved in In dealing with G-homomorphisms of G-principal bundles the same difficulty arises. So we obtain the following theorem. We can factorize these canonical maps as follows. By By Lemma 2. Then we give a natural realization of its Lie algebra and its exponential map.

By Theorem 2. Since GauP is the kernel of the homomorphism , it is a closed normal sub- group of AutP. By direct inspection one easily checks that is injective. Recall that TP is turn a principal bundle with structure group TG. I will talk about extensions of their results to probability measures on groves that are periodic in appropriate coordinates. Based on joint work with F. Camia, A. Gandolfi and G. We consider the collection of near maxima of the discrete log-correlated Gaussian field in the interior of a box. We provide a rough description of the geometry of the set of near maxima.

We show that two near maxima can other either simultaneously either at microscopic or at macroscopic level, but not at mesoscopic level. In , Elon Lindenstrauss and Akshay Venkatesh gave a proof of this law for quite general quotients of semisimple Lie groups. The proof crucially uses the fact that solutions of the corresponding wave equation propagate with finite speed.

I will try to explain what they did in the simplest setting of the upper half plane. I will also try to explain why such eigenfunctions, also known as automorphic forms, are of central importance in number theory. The first 45 minutes of the talk should be accessible to students who have a knowledge of some basic complex analysis and calculus.

In this talk I will briefly describe the idea of a proof of the Mordell-Weil Theorem and introduce the n-Selmer group and Tate-Shafarevitch group associated to Elliptic Curves. I will define the L-function and some other arithmetic invariants attached to the Elliptic Curves and state the celebrated Birch-Swinnerton-Dyer Conjecture.

Elliptic curves are important objects of study in various areas of research in modern mathematics. In this talk I will develop some algebraic and geometric tools to understand the group structures on elliptic curves and their Isogenies certain kind of homomorphisms. I will specialise the general study of Elliptic Curves over finite fields, define zeta functions of associated Elliptic Curve and state the Weil Conjectures.

The main aim of this thesis is to explain the behaviour of some conformal metrics and invariants near a smooth boundary point of a domain in the complex plane. To estimate the higher order curvatures using scaling, we generalize an old theorem of Suita on the real analyticity of the Caratheodory metric on planar domains and in the process, we show convergence of the Szego and Garabedian kernels as well. Let G be a finite-dimensional complex simple Lie algebra and G[t] be its current algebra. The degree grading on the polynomial ring gives a natural grading on G[t] and makes it a graded Lie algebra.

Local Weyl modules introduced by Chari and Pressley are interesting finite-dimensional graded G[t]-modules. Corresponding to a dominant integral weight x of G there is a local Weyl module denoted by W x. The zeroth graded piece of W x is the irreducible G-module V x. In this talk, we discuss how to obtain a basis for W x from the basis of V x given by Gelfand-Tsetlin patterns, when G is of type A and C. In this talk we shall see three very different areas of applications of combinatorics in mathematics and computer science, illustrating four different flavours of combinatorial reasoning.

The first problem is on the decomposition, into irreducible representations, of the Weil representation of the full symplectic group associated to a finite module of odd order over a Dedekind domain. We shall discuss how a poset structure defined on the orbits of finite abelian p-groups under automorphisms can be used to show the decomposition of the Weil representation is multiplicity-free, as well as parametrize the irreducible subrepresentations, compute their dimensions in terms of p, etc.

Next, we consider lower bounds on the maximum size of an independent set, as well as the number of independent sets, in k-uniform hypergraphs, together with an extension to the maximum size of a subgraph of bounded degeneracy in a hypergraph. Joint works with C. We shall go through its generalisation to the Shallow Packing Lemma for systems of shallow cell complexity, and see how it can be used to prove the existence of small representations of set systems, such as epsilon nets, M-nets, etc. Let G be a central product of two groups H and K. In this talk, I shall discuss about the second cohomology group of G, having coefficients in a divisible abelian group D with trivial G-action, in terms of the second cohomology groups of certain quotients of H and K.

The talk will discuss the non-CM case and focus on obtaining upper bounds. This is joint work with C. David, A. Gafni, A. Malik and C. The aim of this talk is to answer the Nielsen Realisation problem: Can every finite subgroup of the mapping class group can be realised as a subgroup of the isometry group of some hyperbolic surface? Shear coordinates on the other hand, instead of using pair of pants, use ideal triangles as the basic pieces.

As ideal triangles are unique up to isometry, only the gluing data needs to be tracked in this case. We shall see a convexity result concerning the length of simple closed curves with respect to these coordinates. This result leads to a positive answer for the Nielsen Realisation problem. Some technical results will be assumed. Familiarity with Fenchel-Nielsen coordinates will be helpful. Since its introduction, the class of entanglement breaking maps played a crucial role in the study of quantum information science and also in the theory of completely positive maps.

In this talk, I will present a certain class of linear maps on matrix algebras that have the property that they become entanglement breaking after composing finite or infinite number of times with themselves. These maps are called eventually entanglement breaking maps. This means that the Choi matrix of the iterated linear map becomes separable in the tensor product space. It turns out that the set of eventually entanglement breaking maps forms a rich class within the set of all unital completely positive maps.

I will relate these maps with irreducible positive linear maps which have been studied a lot in the non-commutative Perron-Frobenius theory. Christandl that says that every PPT channel, when composed with itself, becomes entanglement breaking. In this work, it is proved that every unital PPT-channel becomes entanglement breaking after finite number of iterations. This is a joint work with Sam Jaques and Vern Paulsen.

A hyperplane arrangement cuts up a vector space into several pieces. The combinatorics and topology of this subdivision is encoded in the associated abelian category of perverse sheaves. This category has an alternate algebraic description due to Kapranov and Schechtman, in terms of representations of a quiver with relations. I will first explain the background and setup.

The aim of the talk is to describe how recollement on the above category of perverse sheaves translates to the category of quiver representations. A Riemann surface appears in many different guises in mathematics, for example, as a branched cover of the Riemann sphere, an algebraic subset of a projective space, or a complex analytic 1-manifold.

What is the relationship between various representations of the same Riemann surface? In the first part of my talk, I will describe a conjectural answer to one aspect of this question, due to Mark Green. In the second part, I will talk about ribbons. In this talk I will outline a proof of the classical Gauss-Bonnet theorem. The proof uses Chern-Weil theory which is standard but more interestingly, Morse theory. Algebraic identities play a pivotal role in the study of many mathematical structures although once understood, they are subconsciously regarded as being obvious or even tautological.

In this talk, the main goal is to discuss a systematic approach towards developing a theory of rank identities and determinant identities. By taking a universal approach, we will see how these methods translate to the world of finite von Neumann algebras specifically II1 factors where there is a natural notion of center-valued rank which measures the degree of non-degeneracy of an operator, and a notion of determinant known as the Fuglede-Kadison determinant.

We will also see some applications to the non-self-adjoint algebraic structure of finite von Neumann algebras and to certain operator inequalities. In this talk we will describe connections between second order partial differential equations and Markov processes associated with them. This connection had been an active area of research for several decades. The talk is aimed at Analysts and does not assume familiarity with probability theory.

We consider a finite version of the one-dimensional Toom model with closed boundaries. The dynamics are as follows: the leftmost particle in a block can exchange its position with the leftmost particle of the block to its right. In this thesis, we have shown the following. Secondly, we have made progress on a conjecture for the nonequilibrium partition function.

We discuss some properties of the holomorphic functions and see the condition under which these two notions coincide. We will survey recent progress of birational geometry in positive characteristic fields. As well, we will introduce subadditiviy of Kodaira dimension and canonical bundle formula in positive characteristics. Given a system of a fixed number of linearly independent homogeneous polynomial equations of a fixed degree with coefficients in a finite field F, what is the maximum number of common solutions they can have in the corresponding protective space over F?

The case of a single homogeneous polynomial i. For the general case, an elaborate conjecture was made by Tsfasman and Boguslavsky, which was open for almost two decades. We will outline these developments and report on some recent progress. An attempt will be made to keep the prerequisites at a minimum. If there is time and interest, connections to coding theory or to the problem of counting points of sections of Veronese varieties by linear subvarieties of a fixed dimension will also be outlined. In this talk we will review this theory, discuss some applications of this theory to the local Langlands correspondence, and some ingredients in generalizing the work of Kazhdan and some variants of it to non-split groups.

We give examples of two inequivalent smooth structures on the complex projective 9-space such that one admits a metric of nonnegative scalar curvature and the other does not. Following this example and the work of Thomas Farrell and Lowell Jones, we also construct examples of closed negatively curved Riemannian manifolds, which are homeomorphic but not diffeomorphic to complex hyperbolic manifolds. Joint work with Samik Basu. In this talk, we present our new results on the numerical analysis of nonlocal fracture models.


We begin by giving a brief introduction to the Peridynamic theory and the nonlocal potentials considered in our work. We consider a force interaction characterized by a double well potential. Here, one well, near zero strain, corresponds to the linear response of a material, and the other well, for large strain, corresponds to the softening of a material.

We show that the error converges to zero, uniformly in time, in the mean square norm. We consider piecewise linear continuous elements. Theoretical claims are supported by numerical results. This is a joint work with Dr. We show, by construction, given any metric graph, its metric can be rescaled so that it can be essentially and isometrically embedded on a closed hyperbolic surface. Obtaining a sparse representation of high dimensional data is often the first step towards its further analysis. Conventional Vector Autoregressive VAR modelling methods applied to such data results in noisy, non-sparse solutions with a too many spurious coefficients.

Computing auxiliary quantities such as the Power Spectrum, Coherence and Granger Causality GC from such non-sparse models is slow and gives wrong results. Thresholding the distorted values of these quantities as per some criterion, statistical or otherwise, does not alleviate the problem. We propose two sparse Vector Autoregressive VAR modelling methods that work well for high dimensional time series data, even when the number of time points is relatively low, by incorporating only statistically significant coefficients.

In numerical experiments using simulated data, our methods show consistently higher accuracy compared to other contemporary methods in recovering the true sparse model. The relative absence of spurious coefficients in our models permits more accurate, stable and efficient evaluation of auxiliary quantities.

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Our VAR modelling methods are capable of computing Conditional Granger Causality CGC in datasets consisting of tens of thousands of variables with a speed and accuracy that far exceeds the capabilities of existing methods. Using the Conditional Granger Causality computed from our models as a proxy for the weight of the edges in a network, we use community detection algorithms to simultaneously obtain both local and global functional connectivity patterns and community structures in large networks. We also use our VAR modelling methods to predict time delays in many-variable systems.

Using simulated data from non-linear delay differential equations, we compare our methods with commonly used delay prediction techniques and show that our methods yield more accurate results. Application to the Hela gene interaction dataset: The network obtained by applying our methods to this dataset yields results that are at least as good as those from a specialized method for analysing gene interaction.

This demonstrates that our methods can be applied to any time series data for which VAR modelling is valid. In addition to the above methods, we apply non-parametric Granger Causality analysis originally developed by A. Nedungadi, G. Rangarajan et al to mixed point-process and real time-series data. Extending the computations to Conditional GC and by increasing the efficiency of the original computer code, we can compute the Conditional GC spectrum in systems consisting of hundreds of variables in a relatively short period.

Further, combining this with VAR modelling provides an alternate faster route to compute the significance level of each element of the GC and CGC matrices. Interpretation of the results of the analysis is an ongoing collaboration. Classical geometric notion of the Yang-Mills functional has been generalized to the noncommutative context by A.

An instance of additivity will be discussed for the case of noncommutative torus. The main emphasis of this thesis is on developing and implementing linear and quadratic finite element methods for 3-dimensional 3D elliptic obstacle problems. The study consists of a priori and a posteriori error analysis of conforming as well as discontinuous Galerkin methods on a 3D domain. The work in the thesis also focuses on constructing reliable and efficient error estimator for elliptic obstacle problem with inhomogenous boundary data on a 2D domain. In this talk, we first present a quadratic finite element method for three dimensional ellipticobstacle problem which is optimally convergent with respect to the regularity.

We derive a priori error estimates to show the optimal convergence of the method with respect to the regularity, for this we have enriched the finite element space with element-wise bubble functions. Further, aposteriori error estimates are derived to design an adaptive mesh refinement algorithm. The result on a priori estimate will be illustrated by a numerical experiment.

Next, we discuss on two newly proposed discontinuous Galerkin DG finite element methods for the elliptic obstacle problem. Using the localized behavior of DG methods, we derive a priori and a posteriori error estimates forlinear and quadratic DG methods in dimension 2 and 3 without the addition of bubble functions. We consider two discrete sets, one with integral constraints motivated as in the previous work and another with point constraints at quadrature points.

The analysis is carried out in a unified setting which holds for several DG methods with variable polynomial degree. We then proposea new and simpler residual based a posteriori error estimator for finite element approximation of the elliptic obstacle problem. The results here are two fold. Firstly, we address the influence of the inhomogeneous Dirichlet boundary condition in a posteriori error control of the elliptic obstacle problem. We propose two post processing methods and analyse them.

We remark that the results known in the literature are either for the homogeneous Dirichlet boundary condition or that the estimator is only weakly reliable in the case of inhomogeneous Dirichlet boundary condition. Finally, we discuss a uniform mesh refinement algorithm for a 3D domain. Starting with orientation of a face of the tetrahedron and orientation of the tetrahedron, we discuss the ideas for nodes to element connectivity and red-refinement of a tetrahedron. We present conclusions and possible extensions for the future works.

We also intend to indicate progress made towards a new proof of the Helgason conjecture in symmetric spaces of higher rank. A geodesic conjugacy between two closed manifolds is a homeomorphism between their unit tangent bundles that takes geodesic flow orbits of one to that of the other in a time-preserving manner.

One of the central problems in Riemannian geometry is to understand the extent to which a geodesic conjugacy determines a closed Riemannian manifold itself. While an answer to the question in this generality has yet remained elusive, we give an overeview of results on closed surfaces — the most important illustrative case where a complete picture about questions of geodesic conjugacy rigidity is available.

We begin with a introduction to the notion of a resolution of a module over a Noetherian ring, leading to Betti numbers over local or graded rings, and some problems related to them. Most of the talk will focus on the graded case. One of the recent developments in this area is the resolution of the Boij-Soderberg conjectures by Eisenbud-Schreyer We discuss the motivation behind the conjectures, with a quick word on the techniques used in their resolution.

If time permits, we will see other scenarios where parts of the Boij-Soderberg conjectures hold, and discuss obstacles in extending the Eisenbud-Schreyer techniques in general. This last part is joint work with Rajiv Kumar. Let G be a group and H a subgroup of G. In the nineties, B. Gross and D. Prasad started a systemic investigations into the study of branching laws for the groups of interest to Langlands program, and their predictions are known as Gross-Prasad conjectures.

We discuss two basic examples of these predictions. A covering group of a reductive groups is a certain central extensions. In a topological space, a point x is said to be a specialization of another point y if x is in the closure of y. We will define them and show their classical use in classifying certain subcategories. This will allow us to give a characterization of Cohen-Macaulay local rings. Time permitting, we will also discuss some reductions of K-theoretic invariants of derived categories with support. In this talk I will give a brief introduction to Liouville first-passage percolation LFPP which is a model for random metric on a finite planar grid graph.

It was studied primarily as a way to understand the random metric associated with Liouville quantum gravity LQG , one of the major open problems in contemporary probability theory. I will discuss some recent results on this metric and the main focus will be on estimates of the typical distance between two points.

I will highlight the apparent disagreement of these estimates with a prediction made in the physics literature about the LQG metric. I will also mention some of many future problems in this program. Based on a joint work with Jian Ding. We will begin by providing a brief introduction to self-normalizing concentration inequalities for scalar and finite-dimensional martingales, which are very useful in measuring the size of a stochastic process in terms of another, growing, process the book of de la Pena et al is a good reference.

We will then present a self-normalizing concentration inequality for martingales that live in the potentially infinite-dimensional Reproducing Kernel Hilbert Space RKHS of a p. We will conclude by illustrating applications to online kernel least-squares regression and multi-armed bandits with infinite action spaces, a. This is joint work with Jim Borger. In this talk, we will discuss various analytic and geometric aspects of Martin functions, namely how fast they grow at infinity, maximum on a slice, and convexity properties of their level lines.

If time permits, we will also present a inverse balayage problem from Potential theory. In recent years, the theory of complex valued analytic functions defined on multiply connected domains has been recognized to have several applications in applied mathematics. In this talk, we will review the theory of Schottky-Klein prime functions and other allied special functions defined on multiply connected circular domains, and discuss the numerical computation of these special functions.

We will also briefly present applications to selected problems in fluid dynamics through conformal mapping methods. The conjecture states a precise relation between this leading term and p-adic regulator of p-units in an abelian extension. I will then sketch proof of this conjecture of Gross. This is a joint work with Samit Dasgupta and Kevin Ventullo. I will present work done with students and colleagues on the collective behaviour of motile organisms, viewed as interacting particles with an autonomous velocity and noise.

The talk will include a bit of stochastic processes, some statistical mechanics, and some hydrodynamics. I will discuss experiments, analytical theory and some computation. Edelman and Greene constructed a bijective correspondence between the reduced words of the reverse permutation n, n - 1, …, 2, 1 and standard Young tableaux of the staircase shape n - 1, …, 1.

Recently, motivated by random sorting networks, we studied this bijection and discovered some new properties in joint work with Svante Linusson. In this talk, I will discuss them and, if time permits, also a related project with Linusson and Robin Sulzgruber on random sorting networks where the intermediate permutations avoid the pattern The classification of homogeneous scalar weighted shifts is known.

Recently, Koranyi obtained a large class of inequivalent irreducible homogeneous bi-lateral 2-by-2 block shifts. We construct two distinct classes of examples not in the list of Koranyi. It is then shown that these new examples of irreducible homogeneous bi-lateral 2-by-2 block shifts, together with the ones found earlier by Koranyi, account for every unitarily inequivalent irreducible homogeneous bi-lateral 2-by-2 block shift.

In this talk we will discuss an analytic model theory for pure hyper-contractions introduced by J. Agler which is analogous to Sz. Nagy-Foias model theory for contractions. We then proceed to study analytic model theory for doubly commuting n-tuples of operators and analyze the structure of joint shift co-invariant subspaces of reproducing kernel Hilbert spaces over polydisc.

In particular, we completely characterize the doubly commuting quotient modules of a large class of reproducing kernel Hilbert Modules, in the sense of Arazy and Englis, over the unit polydisc. Inspired by Halmos, in the second half of the talk, we will focus on the wandering subspace property of commuting tuples of bounded operators on Hilbert spaces. Along the way we also prove a refinement of a result of Arveson on the uniqueness of the minimal dilations of pure row contractions.

Given the recent successfully concluded Polymath project — and the next Polymath that has already started over the weekend — I will present the origins of Polymath and discuss its workings, using slides of myself and of a Polymath collaborator. Mirror symmetry is a phenomenon predicted by string theory. It allows one to translate questions in symplectic geometry to questions in complex geometry, and vice versa. The homological mirror symmetry program interprets mirror symmetry within the unifying categorical framework of derived noncommutative geometry.

We will see how this leads to i a non-Archimedean categorical analogue of the Donaldson-Uhlenbeck-Yau theorem, inspired by symplectic geometry, and ii the discovery of a refinement of the Harder-Narasimhan filtration which controls the asymptotic behavior of certain geometric flows.

Let X1 , X2 , X3, … Xn be iid random variables. Laws of large numbers roughly state that the average of these variables converges to the expectation value of each of them when n is large. Various forms of these laws have many applications. The strong and weak laws along with the following three applications will be discussed: a Coin-tossing.

In joint work with Steve Lalley and Jenya Sapir, we study the tessellation of a compact, hyperbolic surface induced by a typical long geodesic segment. We show, that when properly scaled, the local behavior of a typical geodesic is that of a Poisson line process. This implies that the global statistics of the tessellation — for instance, the fraction of triangles — approach those of the limiting Poisson line process.

They have strong chaotic properties: for example, the sine-process has the Kolmogorov property and satisfies the Central Limit Theorem. A Functional Limit Theorem for the sine-process has been established in joint work with A. A delicate aspect of the behaviour of a determinantal point process is that particles interact at infinite radius. For instance, Ghosh and Peres showed that, under the sine-process, the number of particles in a bounded interval is determined by the configuration in the outside of the interval. For determinantal point processes with so-called integrable kernels, an explicit description is given of conditional measures of the process in a bounded interval with respect to the fixed exterior.

These conditional measures are given by orthogonal polynomial ensembles with explicitly found weights. A key step in the argument is that projections inducing our processes satisfy a weaker analogue of the division axiom of de Branges: in fact, this weak division property, as shown in joint work with Roman Romanov, characterizes integrable kernels.

Similar results for determinantal point processes governed by orthogonal projections onto Hilbert spaces of holomorphic functions are obtained in joint work with Y. The talk is based on the preprints. Dymov , and the paper. Alexander I. I will discuss the proof of this result and also the process of discovery in which I had a minor role. Gorenstein rings are very common and significant in many areas of mathematics. The following are two important and widely open problems in commutative algebra and algebraic geometry:. Recently, in a joint work with M. Rossi, we obtained partial results to these problems in some cases K-algebras of socle degree 4.

In this talk, we will discuss these new developments. We derive a priorierror estimates to show the optimal convergence of the method with respect to the regularity, forthis we have enriched the finite element space with element-wise bubble functions. We then proposea new and simpler residual based a posteriori error estimator for finite element approximationof the elliptic obstacle problem.

Firstly, we address the influenceof the inhomogeneous Dirichlet boundary condition in a posteriori error control of the elliptic obstacle problem. This talk will focus on the rooted Galton-Watson GW tree. First order properties on rooted trees capture the local, finite structures inside the tree. We analyze the probabilities of first order properties under the GW measure, and obtain these probabilities as fixed points of contracting distributional maps. Moreover, we come up with nice functions that express these probabilities conditioned on survival of the GW tree.

This is joint work with Joel Spencer. A version of the uniformization theorem states that any compact Riemann surface admits a metric of constant curvature. A deep and important problem in complex geometry is to characterize Kahler manifolds admitting constant scalar curvature Kahler cscK metrics or extremal Kahler metrics.

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Their main results says that a Fano manifold admits a Kahler-Einstein metric if and only if it is K-stable. I will survey some of these recent developments, and then focus on a refinement obtained in collaboration with Gabor Szekelyhidi. This has led to the discovery of new Kahler-Einstein manifolds. If time permits, I will also talk about some open problems on constructing cscK and extremal metrics on blow-ups of extremal manifolds, and mention some recent progress. Homogenization of boundary value problems posed on rough domains has paramount importance in real life problems.

Materials with oscillating rough boundary are used in many industrial applications like micro strip radiator and nano technologies, biological systems, fractal-type constructions, etc. In this talk, we will be focusing on homogenization of optimal control problems. We will begin with homogenization of a boundary control problem on an oscillating pillar type domain. Then, we will consider a time-dependent control problem posed on a little more general domain called branched structure domain.

Asymptotic analysis of this interior control problem will be explained. Next, we will present a generalized unfolding operator that we have developed for a general oscillatory domain. Using this unfolding operator, we study the homogenization of a non-linear elliptic problem on this general highly oscillatory domain.

Also, we analyse an optimal control problem on a circular oscillating domain with the assistance of this operator. Finally, we consider a non-linear optimal control problem on the above mentioned general oscillatory domain and study the asymptotic behaviour. Of course, this problem is intractable at the above level of generality. However, two special cases of the problem — which we shall study in this thesis — have been of lasting interest:. McCullough later refined their result by identifying a smaller family of matrices.

The interest in this arises from problems in Control Theory. Later, Agler—Young established a relation between the interpolation problem in the spectral unit ball and that in the symmetrized polydisc — leading to a necessary condition for the existence of an interpolant. Derived category is an important tool in homological algebra invented by Grothendieck and Verdier.

In these days derived categories play important roles in many areas of algebraic geometry. In this talk, I will discuss derived categories and their applications to study Ulrich bundles on some Fano manifolds. In this talk, I will tell you about the Borel-de-Sibenthal theorem which gives the classification of all maximal closed subroot systems of finite crystallographic root systems.

The concept of root system is very fundamental in the theory of Lie groups and Lie algebras. Especially they play a vital role in the classification of finite dimensional semi-simple Lie algebras. Closed subroot systems of finite root systems naturally appear in the Borel-de-Sibenthal theory which describes the closed connected subgroups of a compact Lie group that have maximal rank.

The classification of closed subroot systems is essential in the classification of semi-simple subalgebras of semi-simple Lie algebras. Through out this talk, we will try to stay within the theory of root systems and reflection groups. No knowledge of Lie algebras or Lie groups will be assumed. If time permits I will discuss about my joint work with R. Venkatesh which gives explicit descriptions of the maximal closed subroot systems of affine root systems. We will present results obtained in collaboration with J. Burgos and M.

These extend the well known dictionary between the geometric properties of toric varieties and convex geometry. In particular, we give combinatorial descriptions of classical invariants of arithmetic geometry, such as metric, height or essential minimum. In this talk, we prove the unique factorization property of Schur functions. This fundamental property of Schur functions was first observed and proved by C.

Rajan in I give a different proof of this beautiful fact which I jointly obtained with my adviser S. I begin my talk with introducing the Schur functions and their connections with representation theory of general linear groups.

ISBN 13: 9780906812013

Basic knowledge of elementary algebra will be assumed like group theory and linear algebra. If time permits, I will tell you about the possible generalizations of this result. It is a well-known result from Hermann Weyl that if alpha is an irrational number in [0,1 then the number of visits of successive multiples of alpha modulo one in an interval contained in [0,1 is proportional to the size of the interval. In this talk we will revisit this problem, now looking at finer joint asymptotics of visits to several intervals with rational end points.

We observe that the visit distribution can be modelled using random affine transformations; in the case when the irrational is quadratic we obtain a central limit theorem as well. Not much background in probability will be assumed. This is in joint work with Jon Aaronson and Michael Bromberg. We consider the computation of n-variate polynomials over a field F via a sequence of arithmetic operations such as additions, subtractions, multiplications, divisions, etc. It has been known for at five decades now that a random n-variate polynomial of degree n is hard to compute. Yet not a single explicit polynomial is provably known to be hard to compute although we have a lot of good candidates.

Regularity of the p -harmonic maps with potential. Strong solutions to the compressible liquid crystal system.

Books by Christopher Dodson

Pacific Journal of Mathematics 37— The Landau—Lifshitz—Maxwell equation in dimension three. Bloch functions of several complex variables. Curves with prescribed intersection with boundary divisors in moduli spaces of curves. Long-time existence of mean curvature flow with external force fields. Boundary Schwarz lemma for non-equidimensional holomorphic mappings and its application.

Positive solutions for nonlinear third-order multi-point. On slope genera of knotted tori in the 4-space. Symmetry and monotonicity of positive solutions for an integral system with negative exponents. Extremal pairs of Young's inequality for Kac algebras. Addition formulas for Jacobi theta functions, Dedekind's eta function, and Ramanujan's congruences. An extension of the quintuple product identity and its applications.

Pacific Journal of Mathematics 53— Some Eisenstein series identitiesrelated to modular equations of the seventh order. Generalization of the Hilbert metric to the space of positive definite matrices. A coefficient inequality for functions of positive real part with an application to multivalent functions. On the integral means of univalent, meromorphic functions. A generalization of an inequality due to Beurling.

Some Hausdorff means which exhibit the Gibbs' phenomenon. Knot 4-genus and the rank of classes in W Q t. Knot invariants in 3-manifolds and essential tori. Pacific Journal of Mathematics 73— Knot mutation: 4-genus of knots and algebraic concordance. Nonsplittability of the rational homology cobordism group of 3-manifolds.

Observations on Lickorish knotting of contractible 4-manifolds. On surgery curves for genus-one slice knots. Pacific Journal of Mathematics 77— Classification of algebraic surfaces with sectional genus less than or equal to six. Rational surfaces. On the deformation quantization of coadjoint orbits of semisimple groups. A note on the set of periods for Klein bottle maps. Hopf bifurcation in higher dimensional differential systems via the averaging method.

Minimal sets of periods for torus maps via Nielsen numbers. Multiplicity of invariant algebraic curves in polynomial vector. Pacific Journal of Mathematics 63— Automorphisms of the semigroup of finite complexes of a periodic locally cyclic group. Pacific Journal of Mathematics 72 27— On the group of permutations with countable support. Pacific Journal of Mathematics 58 — On the retractability of some one-relator groups.

Representations of lattice-ordered groups having a basis. Feller boundary induced by a transition operator. On certain projections in spaces of continuous functions. Banach-Buck measure, density, and uniform distribution in rings of algebraic integers. Pacific Journal of Mathematics 39— Almost rigid Hopfian and dual Hopfian atomic Boolean algebras. Monotone operators and nonlinear biharmonic boundary value problems.

Pacific Journal of Mathematics 60 39— Self-adjointness for multi-point differential operators. Relations between the maximum modulus and maximum term of entire functions. On topologically induced generalized proximity relations. Characterizing the divided difference weights for extended complete Tchebycheff systems. Pacific Journal of Mathematics 1—9. On the continuity of the nonlinear Tschebyscheff operator. On generation of solutions of the biharmonic equation in the plane by conformal mappings. Subspaces of symmetric matrices containing matrices with a multiple first eigenvalue.

On spaces of matrices containing a nonzero matrix of bounded rank. A geometric function determined by extreme points of the unit ball of a normed space. Brownian motion and the heat semigroup on the path space of a compact Lie group. Quaternionicrepresentations of exceptional Lie groups. Double affine Lie algebras and finite groups. A general solution of Tonelli's problem of the calculus of variations. The semicontinuity of the most general integral of the calculus of variations in non-parametric form.

The homotopy groups of knots. Pacific Journal of Mathematics 95 — Monotonicity of permanents of certain doubly stochastic matrices. Rearrangement inequalities involving convex functions. Two inequalities in nonnegative symmetric matrices. Hypergeometric evaluation identities and supercongruences. Bott formula of the Maslov-type index theory. On generalizations of alternative algebras. Scalar dependent algebras in the alternative sense. Pacific Journal of Mathematics 76 — A simple proof of the existence of modular automorphisms in approximately finite-dimensional von Neumann algebras.

A spectral mapping theorem for locally compact groups of operators. The maximal right quotient semigroup of a strong semilattice of semigroups. A note on the Gauss map of complete nonorientable minimal surfaces. Pacific Journal of Mathematics 1 — Stable relations.

The noncommutative topology of one-dimensional spaces. Counter-examples to some conjectures about doubly stochastic measures. Pacific Journal of Mathematics 99 — Biharmonic surfaces of constant mean curvature. Calcul du nombre de classes des corps de nombres. Pacific Journal of Mathematics 27 —c. Self-adjoint multi-point boundary value problems. Maximal quotient rings of ring extensions. Roots of Toeplitz operators on the Bergman space. Cohomology over Banach crossed products.

Application to bounded derivations and crossed homomorphisms.

Comparison of Topological space

Pacific Journal of Mathematics 84 — Analysis of the module determining the properties of regular functions of several quaternionic variables. Algebraic structure for a set of nonlinear integral operations. An asymptotic analysis of an odd order linear differential equation. Product integrals for an ordinary differential equation in a Banach space.

Vertically countable spheres and their wild sets. Techniques for approaching the dual Ramsey property in the projective hierarchy. The simulation technique and its applications to infinitary combinatorics under the axiom of Blackwell determinacy. Completeness properties for convergence spaces. On the convergence of closed and compact sets. On generating subgroups of the Moebius group by pairs of infinitesimal transformations. Uniform finite generation of the affine group. Some dual series equations involving Laguerre polynomials. Triple series equations involving Laguerre polynomials.

Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant. Regularity of the heat operator on a manifold with cylindrical ends. Relative formulae for the sprectral invariants of the b -calculus and generalized APS boundary problems of Dirac operators. Geodesic flows on hyperbolic orbifolds, and universal orbifolds. Formal groups of elliptic curves with potential good supersingular reduction. Modules satisfying ACC on a certain type of colons. The axial symmetry and regularity of solutions to an integral equation in a half space.

Pacific Journal of Mathematics 65— Theta correspondence and the Prasad conjecture for SL 2. Eigenvalue estimates on domains in complete noncompact Riemannian manifolds. The maximum principle for systems of parabolic equations subject to an avoidance set. Some characterizations of Campanato spaces via commutators on Morrey spaces. A direct method of moving planes for the system of the fractional Laplacian. Some maximum properties for a family of singular hyperbolic operators.

On a class of contractive perturbations of restricted shifts. Divergence of complex rational approximations. Games with unique solutions that are nonconvex. On the probability of generating finite groups with a unique minimal normal subgroup. Some properties of the probabilistic zeta function of finite simple groups.

Pacific Journal of Mathematics 3— On radicals and continuity of homomorphisms into Banach algebras. Singularities of superpositions of distributions. A note on quasidiagonal and quasitriangular operators. Closed ranged restriction operators on weighted Bergman spaces. The generalized translational hull of a semigroup.

A commutativity theorem for non-associative algebras over a principal ideal domain. A note on the group structure of unit regular ring elements. Pacific Journal of Mathematics 80 77— Derivations and commutativity of rings. Pacific Journal of Mathematics 85 19— Derivations of higher order and commutativity of rings. Pacific Journal of Mathematics 69 73— On the associativity and commutativity of algebras over commutative rings. Some extensions of a theorem of Marcinkiewicz. A quasi order characterization of smooth continua.

Multiplicative perturbation of semigroup generators. A functional calculus for Banach PI-algebras. Subdifferentials of convex functions on Banach spaces. Subalgebras of finite codimension in the algebra of analytic functions on a Riemann surface. An overdetermined problem in potential theory. Actions of finite groups on knot complements.

Determination of modular elliptic curves by Heegner points. Monic representations and Gorenstein-projective modules. Energy identity and removable of singularities of maps from a Riemann surface to a closed Riemannian manifold with unbounded tension field in L 2. A combinatorial characterization of tight fusion frames.

A theorem on holomorphic extension of CR-functions. Holomorphic continuation in several complex variables. Continuous families of nonnegative divisors. An obstruction to extending isotopies of piecewise linear manifolds. Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for outer space. Action of longest element on a Hecke algebra cell module. Weak denseness of nonatomic measures on perfect, locally compact spaces. A perturbation theorem for spectral operators.

On the reduction of rank of linear differential systems. Dugundji extension theorems for linearly ordered spaces. Generalized ordered spaces with capacities. Pseudo-completeness and the product of Baire spaces. Pacific Journal of Mathematics 48 1— On compact metric spaces with noncoinciding transfinite dimensions. On compactifications of metric spaces with transfinite dimensions.

Symmetry and non-existence of solutions for a fully nonlinear nonlocal system. An interpolation theorem in the predicate calculus. Properties preserved in subdirect products. Maximal subgroups and automorphisms of Chevalley groups. The local structure of some measure-algebra homomorphisms.

Semilattices having bialgebraic congruence lattices. The boundary behaviour of harmonic univalent maps. Covering theorems for open continuous mappings having two valences between orientable surfaces. Quasihomeomorphisms and univalent harmonic mappings ontopunctured bounded convex domains. Volume Number 1. Download current issue. For Screen. For Printing. Recent Issues.

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Cell-like mappings. I Pacific Journal of Mathematics 30 — Cell-like mappings. Lachlan, Alistair Initial segments of one-one degrees Pacific Journal of Mathematics 29 — The transcendental rank of a theory Pacific Journal of Mathematics 37 — Theories with a finite number of models in an uncountable power are categorical Pacific Journal of Mathematics 61 — Lackenby, Marc Exceptional surgery curves intriangulated 3-manifolds Pacific Journal of Mathematics — Ladas, Gerasimos Nonoscillatory functional-differential equations Pacific Journal of Mathematics — Ladde, Gangaram On flow-invariant sets Pacific Journal of Mathematics 51 — Systems of functional differential inequalities and functional differential systems Pacific Journal of Mathematics 66 — Laffer, Walter Decomposition of sets of group elements Pacific Journal of Mathematics 14 — Laffey, Thomas On the structure of algebraic algebras Pacific Journal of Mathematics 62 — Lafontaine, Jacques On a nonlinear equation related to the geometry of the diffeomorphism group Pacific Journal of Mathematics — Lagarias, Jeffrey Best simultaneous Diophantine approximations.

Laghi, Norberto Strongly singular integrals along curves Pacific Journal of Mathematics — Lagnese, John Existence, uniqueness and limiting behavior of solutions of a class of differential equations in Banach space Pacific Journal of Mathematics 53 — Laha, Radha On a linear form whose distribution is identical with that of a monomial Pacific Journal of Mathematics 15 — Lahiri, D. Lahr, Charles Approximate identities for convolution measure algebras Pacific Journal of Mathematics 47 — Weak and norm approximate identities are different Pacific Journal of Mathematics 72 99— Lai, King Fai Asymptotic behaviour of eigenfunctions on semi-homogeneous tree Pacific Journal of Mathematics — Integer points on elliptic curves Pacific Journal of Mathematics — Lai, Yuan Y.

Laird, Philip G. On characterizations of exponential polynomials Pacific Journal of Mathematics 80 — Lakien, Eric Nonfactorization in commutative, weakly selfadjoint Banach algebras Pacific Journal of Mathematics 80 — Lakser, H. The amalgamation property in equational classes of modular lattices Pacific Journal of Mathematics 45 — Lakshmibai, Venkatramani Free resolutions of some Schubert singularities Pacific Journal of Mathematics — Free resolutions of some Schubert singularities in the Lagrangian Grassmannian Pacific Journal of Mathematics — Lakshmikantham, V.

On flow-invariant sets Pacific Journal of Mathematics 51 — Laksov, Dan An elementary, explicit, proof of the existence of Quot schemes of points Pacific Journal of Mathematics — Determinantal criteria for transversality of morphisms Pacific Journal of Mathematics — Lakzian, Sajjad Differential Harnack estimates for positive solutions to heat equation under Finsler-Ricci flow Pacific Journal of Mathematics — Lal, Shiva Narain On a theorem of M.

Izumi and S. Lam, K. Composition properties of projective homotopy classes Pacific Journal of Mathematics 68 47— Lam, Ping-Fun Homeomorphisms of manifolds with zero-dimensional sets of nonwandering points Pacific Journal of Mathematics 50 — Lambek, Joachim Completions and classical localizations of right Noetherian rings Pacific Journal of Mathematics 48 — On the distribution of Pythagorean triangles Pacific Journal of Mathematics 5 73— Lambert, Alan Strictly cyclic operator algebras Pacific Journal of Mathematics 39 — The structure of a special class of weighted translation semigroups Pacific Journal of Mathematics 75 — Lambert, Howard Differential mappings on a vector space Pacific Journal of Mathematics 35 — Lamel, Bernhard Holomorphic maps of real submanifolds in complex spaces of different dimensions Pacific Journal of Mathematics — Lami Dozo, Enrique Some geometric properties related to the fixed point theory for nonexpansive mappings Pacific Journal of Mathematics 40 — Lamm, Tobias Compactness results for sequences of approximate biharmonic maps Pacific Journal of Mathematics 59— Lamoreaux, Jack Continua in the plane with limit directions Pacific Journal of Mathematics 74 37— Lampe, William A.

I Pacific Journal of Mathematics 82 59—68 Congruence lattices of algebras of fixed similarity type. Lamperti, John Chains of infinite order and their application to learning theory Pacific Journal of Mathematics 9 — Correction to: Chains of infinite order and their application to learning theory Pacific Journal of Mathematics 15 — On the isometries of certain function-spaces Pacific Journal of Mathematics 8 — Stationary measures for certain stochastic processes Pacific Journal of Mathematics 8 — Lance, E.

Lance, Timothy L. Submodules of the Hardy space over polynomial algebras Pacific Journal of Mathematics — Landau, Lawrence Periodic Gaussian Osterwalder-Schrader positive processes and the two-sided Markov property on the circle Pacific Journal of Mathematics 94 — Landau, Zeph Fuss--Catalan algebras and chains of intermediate subfactors Pacific Journal of Mathematics — Landers, Dieter Relations between convergence of series and convergence of sequences Pacific Journal of Mathematics 64 — Landes, Thomas Normal structure and the sum-property Pacific Journal of Mathematics — Permanence properties of normal structure Pacific Journal of Mathematics — Landesman, Edward Hilbert-space methods in elliptic partial differential equations Pacific Journal of Mathematics 21 — Linear eigenvalues and a nonlinear boundary value problem Pacific Journal of Mathematics 33 — Lane, Ernest Insertion of a continuous function Pacific Journal of Mathematics 66 — PM-normality and the insertion of a continuous function Pacific Journal of Mathematics 82 — Lange, Christian On the existence of closed geodesics on 2-orbifolds Pacific Journal of Mathematics — Lange, Ridgley Automatic continuity for weakly decomposable operators Pacific Journal of Mathematics — Duality and asymptotic spectral decompositions Pacific Journal of Mathematics 93— Lanini, Martina Categorification of a parabolic Hecke module via sheaves on moment graphs Pacific Journal of Mathematics — Degenerate flag varieties and Schubert varieties: a characteristic free approach Pacific Journal of Mathematics — Lansky, Joshua M.

Lanteri, Antonio Elliptic surfaces and ample vector bundles Pacific Journal of Mathematics — Polarized surfaces with hyperelliptic sections Pacific Journal of Mathematics 9— Lantz, David Integral domains that lose ideals in overrings Pacific Journal of Mathematics — Preservation of local properties and chain conditions in commutative group rings Pacific Journal of Mathematics 63 — Lapid, Erez On the degrees of matrix coefficients of intertwining operators Pacific Journal of Mathematics — Truncation of Eisenstein series Pacific Journal of Mathematics — Lappan, Peter Identity and uniqueness theorems for automorphic functions Pacific Journal of Mathematics 14 — Laquer, H.

Generalized immersions and the rank of the second fundamental form Pacific Journal of Mathematics — Larcher, Gerhard Base change problems for generalized Walsh series and multivariate numerical integration Pacific Journal of Mathematics 75— Larcher, Heinrich A geometric characterization for a class of discontinuous groups of linear fractional transformations Pacific Journal of Mathematics 13 — Lardy, Lawrence Some ring extensions with matrix representations Pacific Journal of Mathematics 26 — Larguier, Everett Homology bases with applications to local connectedness Pacific Journal of Mathematics 2 — Larman, D.

On the inner aperture and intersections of convex sets Pacific Journal of Mathematics 55 — On the union of two starshaped sets Pacific Journal of Mathematics 21 — On visual hulls Pacific Journal of Mathematics 32 — Larmore, Lawrence Enumerating immersions and embeddings of projective spaces Pacific Journal of Mathematics 64 — Enumerating normal bundles of immersions and embeddings of projective spaces Pacific Journal of Mathematics 70 — Twisted cohomology and enumeration of vector bundles Pacific Journal of Mathematics 30 — Twisted cohomology theories and the single obstruction to lifting Pacific Journal of Mathematics 41 — Larotonda, Angel A spectral theory for solvable Lie algebras of operators Pacific Journal of Mathematics 15—22 Homogeneous spectral sets and local-global methods in Banach algebras Pacific Journal of Mathematics — Sheaves and functional calculus Pacific Journal of Mathematics — Spectral sets as Banach manifolds Pacific Journal of Mathematics — Larson, David The carrier space of a reflexive operator algebra Pacific Journal of Mathematics 81 — Larson, Jean A solution for scattered order types of a problem of Hagendorf Pacific Journal of Mathematics 74 — Square-free and cube-free colorings of the ordinals Pacific Journal of Mathematics 89 — Lascarides, Constantine G.

Lashof, Richard Lie algebras of locally compact groups Pacific Journal of Mathematics 7 — Laskar, Renu Eigenvalues of the adjacency matrix of cubic lattice graphs Pacific Journal of Mathematics 29 — Lassak, Marek Covering a convex body by its negative homothetic copies Pacific Journal of Mathematics 43— Lasser, Rupert Convolution semigroups on hypergroups Pacific Journal of Mathematics — Lassueur, Caroline Endo-trivial modules: a reduction to p'-central extensions Pacific Journal of Mathematics — LaTorre, Donald A construction of the idempotent-separating congruences on a bisimple orthodox semigroup Pacific Journal of Mathematics 60 — LaTorre, J.

A characterization of uniquely divisible commutative semigroups Pacific Journal of Mathematics 18 57— Lattarulo, Michele Anisotropic real curves and bordered line arrangements Pacific Journal of Mathematics — Lau, A. Laurent-Gengoux, Camille Foliations on super-manifolds and characteristic classes Pacific Journal of Mathematics — Hierarchies and compatibility on Courant algebroids Pacific Journal of Mathematics 1— Laurie, Cecelia Invariant subspace lattices and compact operators Pacific Journal of Mathematics 89 — Lavallee, Lorraine Mosaics of metric continua and of quasi-Peano spaces Pacific Journal of Mathematics 14 — Laver, Richard Square-free and cube-free colorings of the ordinals Pacific Journal of Mathematics 89 — Lavie, Meira Disconjugacy of linear differential equations in the complex domain Pacific Journal of Mathematics 32 — Lavrov, Mikhail Generalized normal rulings and invariants of Legendrian solid torus links Pacific Journal of Mathematics — Lawlor, Gary Area-minimizing minimal graphs overnonconvex domains Pacific Journal of Mathematics — Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms Pacific Journal of Mathematics 55— Lawrence, James Lopsided sets and orthant-intersection by convex sets Pacific Journal of Mathematics — Lawson, Jimmie Embeddings of compact convex sets and locally compact cones Pacific Journal of Mathematics 66 — Intrinsic topologies in topological lattices and semilattices Pacific Journal of Mathematics 44 — Lattices with no interval homomorphisms Pacific Journal of Mathematics 32 — Lie semigroups with triple decompositions Pacific Journal of Mathematics — Measure algebras of semilattices with finite breadth Pacific Journal of Mathematics 69 — Lawther, Ross Correction to: Fixed point spaces in actions of exceptional algebraic groups Pacific Journal of Mathematics — Fixed point ratios in actions of finiteexceptional groups of Lie type Pacific Journal of Mathematics — Fixed point spaces in actions ofexceptional algebraic groups Pacific Journal of Mathematics — Lax, Robert Gap sequences at a singularity Pacific Journal of Mathematics — Independence of normal Weierstrass points under deformation Pacific Journal of Mathematics — The local rigidity of the moduli scheme for curves Pacific Journal of Mathematics 56 — Weierstrass points of products of Riemann surfaces Pacific Journal of Mathematics 66 — Weierstrass points on Gorenstein curves Pacific Journal of Mathematics — Laxton, R.

Elements of finite order Pacific Journal of Mathematics 32 — Le, Nam Remarks on curvature behavior at the first singular time of the Ricci flow Pacific Journal of Mathematics — Lea, Jim The peripherality of irreducible elements of lattice Pacific Journal of Mathematics 45 — Leach, Ronald Coefficient estimates for certain multivalent functions Pacific Journal of Mathematics 74 — Leader, Solomon A topological characterization of Banach contractions Pacific Journal of Mathematics 69 — Convergence topologies for measures and the existence of transition probabilities Pacific Journal of Mathematics 6 — Measures on semilattices Pacific Journal of Mathematics 39 — Leaf, G.

A spectral theory for a class of linear operators Pacific Journal of Mathematics 13 — Leahy, John An analogue of Oka's theorem for weakly normal complex spaces Pacific Journal of Mathematics 68 — Leal, G. On rings which are sumsof two PI-subrings: a combinatorial approach Pacific Journal of Mathematics 17— Leavitt, William A radical coinciding with the lower radical in associative and alternative rings Pacific Journal of Mathematics 30 — Lechicki, Alois Compactoid and compact filters Pacific Journal of Mathematics 69—98 On bounded and subcontinuous multifunctions Pacific Journal of Mathematics 75 — Lediaev, J.

Representable distributive Noether lattices Pacific Journal of Mathematics 28 — Structure of Noether lattices with join-principal maximal elements Pacific Journal of Mathematics 37 — Lee, Eunjeong Grossberg-Karshon twisted cubes and hesitant walk avoidance Pacific Journal of Mathematics — Lee, Hojoo Solitons for the inverse mean curvature flow Pacific Journal of Mathematics — Lee, Jeffrey Domains in Riemannian manifolds and inverse spectral geometry Pacific Journal of Mathematics 43— Lee, John A note on flux integrals over smooth regular domains Pacific Journal of Mathematics — Lee, John Applications of topological transversality to differential equations.

Bernstein Pacific Journal of Mathematics 74 67—82 Topological transversality. Lee, Jung Bridge spheres for the unknot are topologically minimal Pacific Journal of Mathematics — Lee, Kyu-Hwan Quantum affine algebras and q-deformation of arithmetical functions Pacific Journal of Mathematics — Lee, Tim Weng Fundamental domains of arithmetic quotients of reductive groups over number fields with appendix by Takao Watanabe Pacific Journal of Mathematics — Lee, Lina Asymptotic behavior of the Kobayashi metric on convex domains Pacific Journal of Mathematics — Lee, Min Conjugates of equivariant holomorphic maps of symmetric domains Pacific Journal of Mathematics — Mixed automorphic vector bundles on Shimura varieties Pacific Journal of Mathematics — Mixed cusp forms and holomorphic forms on elliptic varieties Pacific Journal of Mathematics — Lee, Ronnie Quotients of the complex ball by discrete groups Pacific Journal of Mathematics — Lee, Tsiu-Kwen Generalized skew derivations characterized by acting on zero products Pacific Journal of Mathematics — Lee, Y.

A Witt's theorem for unimodular lattices Pacific Journal of Mathematics 80 — Leela, S. Stability of measure differential equations Pacific Journal of Mathematics 55 — Leeman, George A local estimate for typically real functions Pacific Journal of Mathematics 52 — Lees, Milton Asymptotic decay of solutions of differential inequalities Pacific Journal of Mathematics 11 — von Newmann difference approximation to hyperbolic equations Pacific Journal of Mathematics 10 — Legg, D.

Discrete logarithmic energy on the sphere Pacific Journal of Mathematics — Lehman, R. Sherman Algebraic properties of the composition of solutions of partial differential equations Pacific Journal of Mathematics 13 — Approximation of improper integrals by sums over multiples of irrational numbers Pacific Journal of Mathematics 5 93— Development of the mapping function at an analytic corner Pacific Journal of Mathematics 7 — Lehmer, D.

On certain character matrices Pacific Journal of Mathematics 6 — Power character matrices Pacific Journal of Mathematics 10 — The chromatic polynomial of a graph Pacific Journal of Mathematics — The sextic period polynomial Pacific Journal of Mathematics — Lehner, Joseph A diophantine property of the Fuchsian groups Pacific Journal of Mathematics 2 — Note on the Schwarz triangle functions Pacific Journal of Mathematics 4 — On the generation of discontinuous groups Pacific Journal of Mathematics 13 — Lehrer, Gustav Cellularity of certain quantum endomorphism algebras Pacific Journal of Mathematics 11— Lei, Yutian Asymptotic estimation for a p-Ginzburg-Landau type minimizer in higher dimensions Pacific Journal of Mathematics — Leinert, Michael Convolution and limit theorems for conditionally free random variables Pacific Journal of Mathematics — Leingang, Matthew Symmetric space valued moment maps Pacific Journal of Mathematics — Leininger, Christopher Exhausting curve complexes by finite rigid sets Pacific Journal of Mathematics — Leistner, Thomas The ambient obstruction tensor and conformal holonomy Pacific Journal of Mathematics — Leland, Kenneth Maximum modulus theorems for algebras of operator valued functions Pacific Journal of Mathematics 40 — Lelek, Andrew An example of a simple triod with surjective span smaller than span Pacific Journal of Mathematics 64 — Continua of constant distances in span theory Pacific Journal of Mathematics — Lemmermeyer, F.

Lemmermeyer, Franz On the unit group of some multiquadratic number fields Pacific Journal of Mathematics 27— Leng, Yan Notes on the extension of the mean curvature flow Pacific Journal of Mathematics — Leonard, Philip Note on the quadratic character of a quadratic unit Pacific Journal of Mathematics 92 35—38 Sequencings and Howell designs Pacific Journal of Mathematics 92 — The quadratic and quartic character of certain quadratic units.

Leptin, Horst A new kind of eigenfunction expansions on groups Pacific Journal of Mathematics 45—67 On symmetry of some Banach algebras Pacific Journal of Mathematics 53 — Lequain, Yves Differential simplicity and complete integral closure Pacific Journal of Mathematics 36 — Differential simplicity and extensions of a derivation Pacific Journal of Mathematics 46 —