# University of Iowa Department of Mathematics

Overview
Works: 79 works in 80 publications in 1 language and 84 library holdings Academic theses QA171,
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Most widely held works about University of Iowa

Most widely held works by University of Iowa
Decision problems in group theory by Andrzej Mostowski( Book )

1 edition published in 1969 in English and held by 3 WorldCat member libraries worldwide

The report is primarily an exposition of current material on the presentation of groups with particular attention given to the word problem and to algorithms for effective computations. (Author)
Springer varieties from a topological perspective by Heather Michelle Russell( )

1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide

Generalizations of GCD-domains and related topics by Rebecca Lynn Lewin( )

2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide

GCD-domains are an important class of integral domains from classical ideal theory. In a GCD-domain, the intersection of any two principal ideals is principal. This property can be generalized in several different ways. A domain for which the intersection of any two invertible ideals is invertible is called a generalized GCD-domain (GGCD-domain). If for elements $a, b \in R - \{0\}$, there is an $n$ = $n(a, b)$ with $a\sp n R\ \cap\ b\sp n R$ principal, we say $R$ is an almost GCD-domain (AGCD-domain). Combining these two definitions, we get an almost generalized GCD-domain (AGGCD-domain)--for $a, b \in R - \{0\}$, there is an $n$ = $n(a, b)$ with $a\sp n R \cap b\sp n R$ invertible. Anderson and Zafrullah began the study of the first two of these generalizations. They showed that the integral closure of an AGCD-domain is also an AGCD-domain. We show that, in general, an overring of an AGCD-domain need not be an AGCD-domain. Certain special types of overrings do, however, inherit the property. Among these, it is shown, are localizations and LCM-stable overrings. A similar result holds for the AGGCD-domains. Relationships between these classes of domains and the classical domains of ring theory are investigated. Wealso investigate how adding the property that $R$ is Noetherian affects an AGCD- or AGGCD-domain. It is shown that a Noetherian AGCD-domain is almost weakly factorial, that is, $R$ = $\cap R\sb P$, where $P$ ranges over all rank one primes of $R$, has finite character and $R$ has torsion t-class group. Similarly, it is shown that a Noetherian AGGCD-domain is weakly Krull, that is, $R$ = $\cap R\sb P$, where $P$ ranges over all rank one primes of $R$, has finite character. Finally, we consider two additional generalizations defined using the ideal $I\sb n$, where $I\sb n$ = $\{i\sp n\ \vert\ i \in I\}$. A domain $R$ is called a nearly GCD-domain or NGCD-domain (respectively nearly generalized GCD-domain or NGGCD-domain) if for $a, b \in R - \{0\}$, there is an $n$ = $n(a, b)$ with $\lbrack (a, b)\sb n\rbrack \sb t$ principal (respectively invertible)
Geometry in motion in the manuscripts of Leonardo da Vinci by Matilde Macagno( Book )

1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide

Factorization in integral domains without identity by Jonathan Preisser( )

1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide

On radio labeling of diameter n-2 and caterpillar graphs by Katherine Forcelle Benson( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

The Hessenberg representation by Nicholas James Teff( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

The Hessenberg representation is a representation of the symmetric group afforded on the cohomology ring of a regular semisimple Hessenberg variety. We study this representation via a combinatorial presentation called GKM Theory. This presentation allows for the study of the representation entirely from a graph. The thesis derives a combinatorial construction of a basis of the equivariant cohomology as a free module over a polynomial ring. This generalizes classical constructions of Schubert classes and divided difference operators for the equivariant cohomology of the flag variety
Fully nonlinear flows and Hessian equations on compact Kähler manifolds by Mijia Lai( )

1 edition published in 2011 in English and held by 1 WorldCat member library worldwide

In this thesis, we will study a class of fully nonlinear flows on Kähler manifolds. This family of flows generalizes the previously studied J-flow. We use the quotients of elementary symmetric polynomials or log of them to construct the flow. We obtain a necessary and sufficient condition in terms of positivity of certain cohomology class to guarantee the convergence of the flow. The corresponding limit metric gives rise to a critical metric satisfying a Hessian type equation on the manifold. We shall also discuss several geometric applications of our main result
Extension of positive definite functions by Robert Niedzialomski( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

Positive denite functions play an important role in many aspects of pure and applied mathematics. They are of interest in probability theory, stochastic processes, representation theory, harmonic analysis, complex analysis, approximation theory, information theory, and machine learning. We will give many examples of positive denite functions and positive denite kernels to, at least partially, validate the above statement. The approach to introduce positive defnite functions, that we take here, is to look at them as a subcollection of the collection of positive definite kernels. In this way, we naturally arrive at the notion of a reproducing kernel Hilbert space. The study and the construction of the reproducing kernel Hilbert space associated to a positive defnite kernel will be of great importance for us
Extensions of Hilbert modules over tensor algebras by Andrew Koichi Greene( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

This dissertation explores aspects of the representation theory for tensor algebras, which are non-selfadjoint operator algebras Muhly and Solel introduced in 1998, by developing a cohomology theory for completely bounded Hilbert modules. Similar theories have been developed for Banach modules by Johnson in 1970, for operator modules by Paulsen in 1997, and for Hilbert modules over the disc algebra by Carlson and Clark in 1995. The framework presented here was motivated by a desire to further understand the completely bounded representation theory for tensor algebras on Hilbert spaces. The focal point of this thesis is the first Ext group, Ext<superscript>1</superscript>, which is defined as equivalence classes of short exact sequences of completely bounded Hilbert modules. Alternate descriptions of this group are presented. For general operator algebras, Ext<superscript>1</superscript> can be realized as the collection completely bounded derivations equivalent up to an inner derivation. When the operator algebra is a tensor algebra, Ext<superscript>1</superscript> can be described as a quotient space of intertwining operators, a description analogous to a result of Ferguson in 1996 in the case of the classical disc algebra. A theorem of Sz.-Nagy and Foias from 1967, concerning contractions in triangular form, is applied to analyze derivations that are off-diagonal corners of completely contractive representations. It is proved that, in some cases, this analysis determines when all derivations must be inner or suggests ways to construct non-inner derivations. In the third chapter, a characterization is given of completely bounded representations of a tensor algebra in terms of similarities of contractive intertwiners. Also proven is that for a Csup*;-correspondence X over a Csup*;-algebra A and the Toeplitz algebra T(X), M<subscript>n</subscript>(T(X))= T(M<subscript>n</subscript>(X))
Localized Skein Algebras as Frobenius extensions by Nelson Abdiel Colón( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

There is an algebra defined on a two dimensional manifold, known as the Skein algebra, which has as elements the simple closed curves of the manifold. Just like with numbers, there's a way to add, subtract and multiply elements. Unfortunately division is not allowed in the Skein algebra, which is why we introduced the notion of the Localized Skein Algebra, where we define a way to invert elements so that dividing is possible. These algebras have infinitely many elements, may not be commutative and in fact may have torsion, which makes them a hard object to study. This work is mainly centered in reducing these algebras to something more manageable. We have shown that for any space, its Localized Skein Algebra is a Frobenius extension of its Localized Character Ring, which means that any element of the algebra can be rewritten as a finite linear combination of a finite subset of basis elements, multiplied by elements that do commute. The importance of this result is that it solves this problem of noncommutativity, by rewriting anything that doesn't commute, as elements of a small set which can be controlled, along with elements that commute and behave nicely, making the Skein algebra far more manageable
Operations on infinite x infinite matrices and their use in dynamics and spectral theory by Corissa Marie Goertzen( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

Some representation theory of the group Sl*(2,A) where A=M(2,O/p^2) and * equals transpose by C Wright( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

Let A be a ring with involution *. The group Sl*(2,A), defined by Pantoja and Soto-Andrade, is a noncommutative version of Sl(2,F) where F is a field. In the case of A being artinian, they determined when Sl*(2,A) admitted a Bruhat presentation, and with Gutiérrez, constructed a representation for Sl*(2,A) from its generators. In particular, if A=Mn(F) and * is transposition, then Sl*(2,A) = Sp(2n, F). In this paper, we are interested in the representation theory of G=Sp4(O/p2) where A=M2(O/p2) and O is a local ring with prime ideal p. It has a normal, abelian subgroup K, and by Clifford's theorem we can find distinct irreducible representations of G starting with one-dimensional representations of K. The outline of our strategy will be demonstrated in the example of finding irreducible representations of SL2, (O/p2)
Universal deformation rings of modules over self -injective algebras by José Alberto Vélez Marulanda( )

1 edition published in 2010 in English and held by 1 WorldCat member library worldwide

Reduced [tau]n-factorizations in Z and [tau]n-factorizations in N by Alina Anca Florescu( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

In this dissertation we expand on the study of [tau]n-factorizations or generalized integer factorizations introduced by D.D. Anderson and A. Frazier and examined by S. Hamon. ... This work serves to compare the [tau]n-factorizations of the integers with the reduced [tau]n-factorizations in Z and the [tau]n-factorizations in N. One of the main goals is to explore how the Fundamental Theorem of Arithmetic extends to these generalized factorizations. Results regarding the [tau]n-factorizations in Z have been discussed by S. Hamon. Using different methods based on group theory we explore similar results about the reduced [tau]n-factorizations in Z and the [tau]n-factorizations in N. In other words, we identify the few values of n for which every integer can be expressed as a product of the irreducible elements related to these factorizations and indicate when one can do so uniquely
Extremal sextic truncated moment problems by Seonguk Yoo( )

1 edition published in 2011 in English and held by 1 WorldCat member library worldwide

Inverse problems naturally occur in many branches of science and mathematics. An inverse problem entails finding the values of one or more parameters using the values obtained from observed data. A typical example of an inverse problem is the inversion of the Radon transform. Here a function (for example of two variables) is deduced from its integrals along all possible lines. This problem is intimately connected with image reconstruction for X-ray computerized tomography. Moment problems are a special class of inverse problems. While the classical theory of moments dates back to the beginning of the 20th century, the systematic study of truncated moment problems began only a few years ago. In this dissertation we will first survey the elementary theory of truncated moment problems, and then focus on those problems with cubic column relations
Split covers for certain representations of classical groups by Luke Samuel Wassink( )

1 edition published in 2015 in English and held by 1 WorldCat member library worldwide

Let R(G) denote the category of smooth representations of a p-adic group. Bernstein has constructed an indexing set B(G) such that R(G) decomposes into a direct sum over s ⁸́⁸ B(G) of full subcategories Rs(G) known as Bernstein subcategories. Bushnell and Kutzko have developed a method to study the representations contained in a given subcategory. One attempts to associate to that subcategory a smooth irreducible representation (Ï⁴, W) of a compact open subgroup J <G. If the functor V ⁶́Œ HomJ(W, V) is an equivalence of categories from Rs(G) ⁶́₂ H(G, Ï⁴)mod we call (J, Ï⁴) a type. Given a Levi subgroup L <G and a type (JL, Ï⁴L) for a subcategory of representations on L, Bushnell and Kutzko further show that one can construct a type on G that ⁰́lies over⁰́₊ (JL, Ï⁴L) by constructing an object known as a cover. In particular, a cover implements induction of H(L, Ï⁴L)-modules in a manner compatible with parabolic induction of L-representations. In this thesis I construct a cover for certain representations of the Siegel Levi subgroup of Sp(2k) over an archimedean local field of characteristic zero. In particular, the representations I consider are twisted by highly ramified characters. This compliments work of Bushnell, Goldberg, and Stevens on covers in the self-dual case. My construction is quite concrete, and I also show that the cover I construct has a useful property known as splitness. In fact, I prove a fairly general theorem characterizing when covers are split
Equivariant cohomology and local invariants of Hessenberg varieties by Erik Andrew Insko( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

Nilpotent Hessenberg varieties are a family of subvarieties of the flag variety, which include the Springer varieties, the Peterson variety, and the whole flag variety. In this thesis I give a geometric proof that the cohomology of the flag variety surjects onto the cohomology of the Peterson variety; I provide a combinatorial criterion for determing the singular loci of a large family of regular nilpotent Hessenberg varieties; and I describe the equivariant cohomology of any regular nilpotent Hessenberg variety whose cohomology is generated by its degree two classes
Continuous families of representations of mapping class groups by Michael Colin Fitzpatrick( )

1 edition published in 2014 in English and held by 1 WorldCat member library worldwide

The study of mapping class groups began in the 1920s with Max Dehn and Jakob Nielsen. It was about this time that topology was just being developed, so mapping class groups were of immediate interest, being invariants of topological spaces. The works of Dehn and Nielsen were continued by William Harvey in the 1960s and 70s leading to the development of the curve complex, an important construction still very relevant to mathematics today. William Thurston is another important name in this area since he was able to completely classify homeomorphisms of surfaces in 1976, leading to the famous "Nielsen-Thurston Classification Theorem". Representations were first studied by Carl Gauss in the early 1800s and then explored more thoroughly by Ferdinand Frobenius and Richard Dedekind, among others, at the end of that century. Representation theory has since grown into an extremely important and active area of mathematics today because of its widespread applications to other areas of mathematics and even to other subject areas like physics. Quantum group theory is the youngest area in which this thesis has its roots. This area was formalized and studied extensively for the first time in the 1980s by such mathematicians as Vladimir Drinfeld, Michio Jimbo, and Nicolai Reshetikhin, and immediately found applications in mathematics and theoretical physics. Like representation theory, the study of quantum groups is currently a highly active area of mathematics due to its widespread applications across the mathematical spectrum. In this paper I will present two different methods of constructing projective representations of mapping class groups of surfaces. I will then prove some interesting results concerning each of these methods
Resonance for Maass forms in the spectral aspect by Nathan Salazar( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

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University of Iowa. Dept. of Mathematics

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English (25)