

Abstract: Logistic regression is an important and widely used regression model for binary responses and is extensively used in many applied fields.
Abstract: High dimension, low sample size data pose great challenges for the existing statistical methods. For instance, several popular methods for cluster analysis based on the Euclidean distance often fail to yield satisfactory results for high dimensional data. In this talk, we will discuss a new measure of dissimilarity, called MADD and see how it can be used to achieve perfect clustering in high dimensions. Another important problem in cluster analysis is to find the number of clusters in a data set. We will see that many existing methods for this problem can be modified using MADD to achieve superior performance. A new method for estimating the number of clusters will also be discussed. We will present some theoretical and numerical results in this connection.
Abstract: Most of todays experimentally verifiable scientific research, not only requires us to resolve the physical features over several spatial and temporal scales but also demand suitable techniques to bridge the information over these scales. In this talk I will provide two examples in mathematical biology to describe these systems at two levels: the micro level and the macro (continuum) level. I will then detail suitable tools in homogenization theory to link these different scales.
Abstract: In this talk, I shall consider the highdimensional moving average (MA) and autoregressive (AR) processes. My goal will be to explore the asymptotics for eigenvalues of the sample autocovariance matrices. This asymptotics will help in the estimation of unknown order of the highdimensional MA and AR processes. Our results will also provide tests of different hypotheses on coefficient matrices. This talk will be based on joint works with Prof. Arup
Abstract: McKay correspondence relates orbifold cohomology with the cohomology of a crepant resolution. This is a phenomenon in algebraic geometry. It was proved for toric orbifolds by Batyrev and Dais in the nineties. In this talk we present a similar correspondence for omnioriented quasitoric orbifolds. The interesting feature is how we deal with the absence of an algebraic or analytic structure. In a suitable sense, our correspondence is a generalization of the algebraic one.
Abstract: We show that if a modular cuspidal eigenform f of weight 2k is 2adically close to an elliptic curve E over the field of rational numbers Q, which has a cyclic rational 4isogeny, then the nth Fourier coefficient of f is nonzero in the short interval (X, X + cX^{1/4}) for all X >> 0 and for some c > 0. We use this fact to produce nonCM cuspidal eigenforms f of level N>1 and weight k > 2 such that i_f(n) << n^{1/4} for all n >> 0$.
Abstract: Given an irreducible polynomial f(x) with integer coefficients and a prime number p, one wishes to determine whether f(x) is a product of distinct linear factors modulo p. When f(x) is a solvable polynomial, this question is satisfactorily answered by the Class Field Theory. Attempts to find a nonabelian Class Field Theory lead to the development of an area of mathematics called the Langlands program.
Abstract: Affine KacMoody algebras are infinite dimensional analogs of semisimple Lie algebras and have a central role both in Mathematics and Mathematical Physics. Representation theory of these algebras has grown tremendously since their independent introduction by R.V. Moody and V.G.
Abstract: Given an irreducible polynomial f(x) with integer coefficients and a prime number p, one wishes to determine whether f(x) is a product of distinct linear factors modulo p. When f(x) is a solvable polynomial, this question is satisfactorily answered by the Class Field Theory. Attempts to find a nonabelian Class Field Theory lead to the development of an area of mathematics called the Langlands program.
Abstract: The aim of this lecture is to consider a singularly perturbed semilinear elliptic problem with power nonlinearity in Annular Domains of R^{2n} and show the existence of two orthogonal S^{n−1} concentrating solutions. We will discuss some issues involved in the proof in the context of S^1 concentrating solutions of similar nature.
Abstract: Let E1 and E2 be elliptic curves defined over the field of rational numbers with good and ordinary reduction at an odd prime p, and have irreducible, equivalent mod p Galois representations. In this talk, we shall discuss the variation in the parity of ranks of E1 and E2 over certain number fields.
Abstract: The curvature of a contraction T in the CowenDouglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this talk we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E corresponding to the operator T in the CowenDouglas class which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the CowenDouglas class.
Abstract: In this talk we will introduce the theory of padic families of modular forms and more generally padic family of automorphic forms. Notion of padic family of modular forms was introduced by Serre and later it was generalized in various directions by the work of Hida, ColemanMazur, Buzzard and various other mathematicians. Study of padic families play a crucial role in modern number theory and in recent years many classical long standing problems in number theory has been solved using padic families. I'll state some of the problems in padic families of automorphic forms that I worked on in the past and plan to work on in the future.
Abstract: Fractal Interpolation Function (FIF)  a notion introduced by Michael Barnsley  forms a basis of a constructive approximation theory for nondifferentiable functions. In view of their diverse applications, there has been steadily increasing interest in the particular flavors of FIF such as Ḧolder continuity, convergence, stability, and differentiability. Apart from these properties, a good interpolant/approximant should reflect geometrical shape properties that are described mathematically in terms of positivity, monotonicity, and convexity. These properties act as constraints on the approximation problem.
Abstract: A Subordinated stochastic process X(T(t)) is obtained by timechanging a process X(t) with a positive nondecreasing stochastic process T(t). The process X(T(t)) is said to be subordinated to the driving process X(t) and the process T(t) is called the directing process.
Abstract: Many physical phenomena can be modeled using partial differential equations. In this talk, applications of PDEs, in particular hyperbolic conservation laws will be shown to granular matter theory and crowd dynamics.
Abstract: Moduli of vector bundles on a curve was constructed and studied by Mumford, Seshadri and many others. Simpson simplified and gave general construction of moduli of pure sheaves on higher dimensional projective varieties in characteristic zero. Langer extended it to the positive characteristics. AlvarezConsul and King gave another construction by using moduli of representations of Kronecker quiver.
Abstract: Homogenization is a branch of science where we try to understand microscopic structures via a macroscopic medium. Hence, it has applications in various branches of science and engineering. This study is basically developed from material science in the creation of composite materials though the contemporary applications are much far and wide. It is a process of understanding the microscopic behavior of an inhomogeneous medium via a homogenized medium. Mathematically, it is a kind of asymptotic analysis.
Abstract: In this talk we will discuss certain aspects of vector bundles over complex projective spaces and projective hypersurfaces. Our focus will be to find conditions under which a vector bundle can be written as a direct sum of smaller rank bundles or when it can be extended to a larger space.
Abstract: Enumerative geometry is a branch of mathematics that deals with the following question: "How many geometric objects are there that satisfy certain constraints?" The simplest example of such a question is "How many lines pass through two points?". A more interesting question is "How many lines are there in three dimensional space that intersect four generic lines?". An extremely important class of enumerative question is to ask "How many rational (genus 0) degree d curves are there in CP^2 that pass through 3d1 generic points?" Although this question was investigated in the nineteenth century, a complete solution to this problem was unknown until the early 90's, when KontsevichManin and RuanTian announced a formula. In this talk we will discuss some natural generalizations of the above question; in particular we will be looking at rational curves on delPezzo surfaces that have a cuspidal singularity. We will describe a topological method to approach such questions. If time permits, we will also explain the idea of how to enumerate genus g curves with a fixed complex structure by comparing it with the Symplectic Invariant of a manifold (which are essentially the number of curves that are solutions to the perturbed dbar equation) .
Abstract: For Gaussian process models, likelihood based methods are often difficult to use with large irregularly spaced spatial datasets due to the prohibitive computational burden and substantial storage requirements. Although various approximation methods have been developed to address the computational difficulties, retaining the statistical efficiency remains an issue. This talk focuses on statistical methods for approximating likelihoods and score equations. The proposed new unbiased estimating equations are both computationally and statistically efficient, where the covariance matrix inverse is approximated by a sparse inverse Cholesky approach. A unified framework based on composite likelihood methods is also introduced, which allows for constructing different types of hierarchical low rank approximations. The performance of the proposed methods is investigated by numerical and simulation studies, and parallel computing techniques are explored for very large datasets. Our methods are applied to nearly 90,000 satellitebased measurements of water vapor levels over a region in the Southeast Pacific Ocean, and nearly 1 million numerical model generated soil moisture data in the area of Mississippi River basin. The fitted models facilitate a better understanding of the spatial variability of the climate variables. About the Speaker: Ying Sun is an Assistant Professor of Statistics in the Division of Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) at KAUST. She joined KAUST after oneyear service as an Assistant Professor in the Department of Statistics at the Ohio State University (OSU). Before joining OSU, she was a postdoctorate researcher at the University of Chicago in the research network for Statistical Methods for Atmospheric and Oceanic Sciences (STATMOS), and at the Statistical and Applied Mathematical Sciences Institute (SAMSI) in the Uncertainty Quantification program.
Abstract: In this talk, the LAD estimation procedure and related issues will be discussed in the nonparametric convex regression problem. In addition, based on the concordance and the discordance of the observations, a test will be proposed to check whether the unknown nonparametric regression function is convex or not. Some preliminary ideas to formulate the test statistics of the test along with their properties will also be investigated.
Abstract: The general philosophy of Langlands' functoriality predicts that given two groups H and G, if there exists a 'nice' map between the respective Lgroups of H and G then using the map we can transfer automorphic representations of H to that of G. Few examples of such transfers are JacquetLanglands' transfer, endoscopic transfer and base change. On the other hand, by the work of Serre, Hida, Coleman, Mazur and many other mathematicians, we can now construct padic families of automorphic forms for various groups. In this talk, we will discuss some examples of Langlands' transfers which can be padically interpolated to give rise to maps between appropriate padic families of automorphic forms.
Abstract: Over the last few years, Ominimal structures have emerged as a nice framework for studying geometry and topology of singular spaces. They originated in model theory and provide an axiomatic approach of characterizing spaces with tame topology. In this talk, we will first briefly introduce the notion of Ominimal structures and present some of their main properties. Then, we will consider flat currents on pseudomanifolds that are definable in polynomially bounded ominimal structures. Flat currents induce cohomology restrictions on the pseudomanifolds and we will show that this cohomology is related to their intersection cohomology.
Abstract: The Grothendieck ring, K0(M), of a modeltheoretic structure M was defined by Krajicˇek and Scanlon as a generalization of the Grothendieck ring of varieties used in motivic integration. I will introduce this concept with some examples and then proceed to define the Ktheory of M via a symmetric monoidal category. Prest conjectured that the Grothendieck ring of a nonzero right module, MR, is nontrivial when thought of as a structure in the language of right Rmodules. The proof that such a Grothendieck ring is in fact a nonzero quotient of a monoid ring relies on techniques from simplicial homology, combinatorics, lattice theory as well as algebra. I will also discuss this result that settled Prest’s conjecture in the affirmative..
Abstract: We know how to multiply two real numbers or two complex numbers. In both cases it is bilinear and norm preserving. It is natural to ask which of the other R^n admits a such multiplication. We will discuss how this question is related to vector fields on sphere and the answer given by famous theorem of J. F. Adams.
Abstract: Euler system is a powerful machinery in Number theory to bound the size of Selmer groups. We start from introducing a brief history and we will explain the necessity of generalizing this machinery for the framework of deformations as well as the technical difficulty of commutative algebra which happens for such generalizations. If time permits, we talk about ongoing joint work on generalized Euler system with Shimomoto.
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Abstract: Monodromy group of a hypergeometric differential equation is defined as image of the fundamental group G of Riemann sphere minus three points, namely 0, 1, and the point at infinity, under some certain representation of G inside the general linear group GL_n. By a theorem of Levelt, the monodromy groups are the subgroups of GL_n generated by the companion matrices of two monic polynomials f and g of degree n. If we start with f, g, two integer coefficient monic polynomials of degree n, which satisfy some "conditions" with f(0)=g(0)=1 (resp. f(0)=1, g(0)=1), then the associated monodromy group preserves a nondegenerate integral symplectic form (resp. quadratic form), that is, the monodromy group is a subgroup of the integral symplectic group (resp. orthogonal group) of the associated symplectic form (resp. quadratic form). In this talk, we will describe a sufficient condition on a pair of the polynomials that the associated monodromy group is an arithmetic subgroup (a subgroup of finite index) of the integral symplectic group, and show some examples of arithmetic orthogonal monodromy groups.
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Abstract: Systems of Conservation laws which are not strictly hyperbolic appear in many physical applications. Generally for these systems the solution space is larger than the usual BVloc space and classical GlimmLax Theory does not apply. We start with the nonstrictly hyperbolic system For n = 1, the above system is the celebrated Bugers equation which is well studied by E. Hopf. For n = 2, the above system describes one dimensional model for large scale structure formation of universe. We study (n = 4) case of the above system, using vanishing viscosity approach for Riemann type initial and boundary data and possible integral formulation, when the solution has nice structure. For certain class of general initial data we construct weak asymptotic solution developed by Panov and Shelkovich. As an application we study zero pressure gas dynamics system, namely, where _ and u are density and velocity components respectively.
Abstract: I will recall basic definitions and facts of algebraic geometry and geometry of quadrics and then i will explain the relation of vector bundles and Hitchin map with these geometric facts.
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Product of eigenforms on March 19, 2015 at 4:00 pm in FB567 by Dr. Jaban Meher
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Abstract: I will discuss about all the cases in which product of two eigenforms is again an eigenform. This talk is based on one of my works together with my recent work with Soumya Das.
Abstract: In this talk, we will discuss injectivity sets for the twisted spherical means on $\mathbb C^n.$ Specially, I will explain the following recent result. A complex cone is a set of injectivity for the twisted spherical means for the class of all continuous functions on $\mathbb C^n$ as long as it does not completely lay on the level surface of any bigraded homogeneous harmonic polynomial on $\mathbb C^n.$
Abstract: In this talk we will survey recent developments in the analysis of partial differential equations arising out of image processing area with particular emphasis on a forwardbackward regularization. We prove a series of existence, uniqueness and regularity results for viscosity, weak and dissipative solutions for general forwardbackward diffusion flows.
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Abstract: In this talk we will survey recent developments in the analysis of partial differential equations arising out of image processing area with particular emphasis on a forwardbackward regularization. We prove a series of existence, uniqueness and regularity results for viscosity, weak and dissipative solutions for general forwardbackward diffusion flows.
Abstract: Fuzzy logic is one of the many generalizations of Classical logic, where the truth values are allowed to lie in the entire unit interval [0, 1], as against just the set {0, 1}. Fuzzy implications are a generalization of classical mplication from twovalued logic to the multivalued setting. In this presentation, we will talk about a novel generative method called the composition, of fuzzy implications that we have proposed. Denoting the set of all fuzzy implications defined on [0, 1], by I, the composition on I can be looked in two different ways, viz., (i) a generating method of fuzzy implications, and (ii) a binary operation on the set I. The rest of the talk will be a discussion of the composition on I along these two aspects. Firstly, we will discuss the closures of fuzzy implications with respect to some desirable properties. Then the effect of the composition on fuzzy implications that can be obtained from other generating methods of fuzzy implications, namely, (S,N), R, f, g implications will also be discussed. Secondly, looking at the composition as a binary operation on the set I, we will show that it forms I a lattice ordered monoid. Since it cannot be made a group, we determine the largest subgroup, denoted by S, obtained in I and we propose some group actions on I employing S. Finally, we demonstrate that, using one such group action, we have obtained, for the first time, representations of the Yager’s families of fuzzy implications.
Abstract: Fuzzy logic is one of the many generalizations of Classical logic, where the truth values are allowed to lie in the entire unit interval [0, 1], as against just the set {0, 1}. Fuzzy implications are a generalization of classical implication from twovalued logic to the multivalued setting. In this presentation, we will talk about a novel generative method called the composition, of fuzzy implications that we have proposed. Denoting the set of all fuzzy implications defined on [0, 1], by , the composition on can be looked in two different ways, viz., (i) a generating method of fuzzy implications, and (ii) a binary operation on the set . The rest of the talk will be a discussion of the composition on along these two aspects. Firstly, we will discuss the closures of fuzzy implications with respect to some desirable properties. Then the effect of the composition on fuzzy implications that can be obtained from other generating methods of fuzzy implications, namely, (S, N) , R, f , g implications will also be discussed. Secondly, looking at the composition as a binary operation on the set , we will show that it forms a lattice ordered monoid. Since it cannot be made a group, we determine the largest subgroup, denoted by , contained in and we propose some group actions on employing . Finally, we demonstrate that, using one such group action, we have obtained, for the first time, representations of the Yager’s families of fuzzy implications.
Abstract: In the first part of the talk, we study infection spread in random geometric graphs where n nodes are distributed uniformly in the unit square W centred at the origin and two nodes are joined by an edge if the Euclidean distance between them is less than . Assuming edge passage times are exponentially distributed with unit mean, we obtain upper and lower bounds for speed of infection spread in the subconnectivity regime, In the second part of the talk, we discuss convergence rate of sums of locally determinable functionals of Poisson processes. Denoting the Poisson process as N, the functional as f and Lebesgue measure as , we establish corresponding bounds for
in terms of the decay rate of the radius of determinability.
About the speaker: J. Michael Dunn is Oscar Ewing Professor Emeritus of Philosophy, Professor Emeritus of Computer Science and of Informatics, at the Indiana UniversityBloomington. Dunn's research focuses on information based logics and relations between logic and computer science. He is particularly interested in socalled "substructural logics" including intuitionistic logic, relevance logic, linear logic, BCKlogic, and the Lambek Calculus. He has developed an algebraic approach to these and many other logics under the heading of "gaggle theory" (for generalized galois logics). He has done recent work on the relationship of quantum logic to quantum computation and on subjective probability in the context of incomplete and conflicting information. He has a general interest in cognitive science and the philosophy of mind. Abstract: I will begin by discussing the history of quantum logic, dividing it into three eras or lives. The first life has to do with Birkhoff and von Neumann's algebraic approach in the 1930's. The second life has to do with the attempt to understand quantum logic as logic that began in the late 1950's and blossomed in the 1970's. And the third life has to do with recent developments in quantum logic coming from its connections to quantum computation. I shall review the structure and potential advantages of quantum computing and then discuss my own recent work with Lawrence Moss, Obias Hagge, and Zhenghan Wang connecting quantum logic to quantum computation by viewing quantum logic as the logic of quantum registers storing qubits, i.e., "quantum bits.". A qubit is a quantum bit, and unlike classical bits, the two values 0 and 1 are just two of infinitely many possible states of a qubit. Given sufficient time I will mention some earlier work of mine about mathematics based on quantum logic.
