176 research outputs found
Letter from Harrison A. Gerhardt, Lt. Col., General Staff Corp, Office of the Assistant Secretary of War, to Mr. Saburo Nakashima, Chairman, Heart Mountain Community Council, March 13, 1944
No full textCorrespondence from Harrison Gerhardt to Saburo Nakashima in response to Nakashima's questions regarding the draft and racial discrimination, exclusion from the west coast military zone, and discrimination against Japanese American soldiers. Also includes a letter dated March 4, 1944 regarding racial discrimination against Japanese Americans by the military.The Japanese American Archival Collection documents the people, places, and daily life of Japanese Americans, primarily those who lived in the once thriving community of pre-war Florin in the Sacramento region, as well as the conditions in American incarceration camps during World War II. The approximately 7,000 original items include personal and official letters, photographs, diaries, arts and crafts, newsletters, textiles, camps artifacts, yearbooks and other publications
The Ro (S¹)-graded equivariant homotopy of THH(Fp)
No full textThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.Includes bibliographical references (p. 77-78).The main result of this thesis is the computation of ... for ... These RO(S¹)-graded TR-groups are the equivariant homotopy groups naturally associated to the S¹-spectrum THH(Fp), the topological Hochschild S¹-spectrum. This computation, which extends a partial result of Hesselholt and Madsen, provides the first example of the RO(S¹)-graded TR-groups of a ring. In particular, we compute the groups ... for all even dimensional representations a, and the order of these groups for odd dimensional [alpha]. These groups arise in algebraic K-theory computations, and are particularly important to the understanding of the algebraic K-theory of non-regular schemes. We also study RO(S¹)-graded TR-theory as an RO(S¹)-graded Mackey functor. Using Lewis and Mandell's homological algebra tools for graded Mackey functors, we provide examples of how Kunneth spectral sequences can be used to understand RO(S¹)-graded TR.by Teena Meredith Gerhardt.Ph.D
Computations in topological cohochschild homology
No full textIn recent work, Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology (coTHH). In 2018, Bohmann-Gerhardt-Hogenhaven-Shipley-Ziegenhagen developed a coBokstedt spectral sequence to compute the homology of coTHH for coalgebras over the sphere spectrum. However, examples of coalgebras over the sphere spectrum are limited, and one would like to have computational tools to study coalgebras over other ring spectra. In this thesis, we construct a relative coBokstedt spectral sequence to study the topological coHochschild homology of more general coalgebra spectra. We consider H\uD835\uDD3D\uD835\uDC5D 2227HZ H\uD835\uDD3D\uD835\uDC5D and H\uD835\uDD3D\uD835\uDC5D 2227BP H\uD835\uDD3D\uD835\uDC5D for certain values of \uD835\uDC5B as H\uD835\uDD3D\uD835\uDC5D-coalgebras and compute the E2-term of the spectral sequence in these cases. Further, we show that this spectral sequence has additional algebraic structure, and exploit this structure to complete coTHH calculations. Finally, we show that coHochschild homology is a bicategorical shadow, in the sense of Ponto.Thesis (Ph. D.)--Michigan State University. Mathematics, 2020Includes bibliographical reference
RO(S1)-graded TR-groups of Fp, Z and ℓ
No full textAbstractWe give an algorithm for calculating the RO(S1)-graded TR-groups of Fp, completing the calculation started by the second author. We also calculate the RO(S1)-graded TR-groups of Z with mod p coefficients and of the Adams summand ℓ of connective complex K-theory with V(1)-coefficients. These calculations are used elsewhere to compute the algebraic K-theory of certain Z-algebras
Computational tools for twisted topological Hochschild homology of equivariant spectra
No full textTwisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we introduce tools for computing twisted THH, which we apply to computations for Thom spectra, Eilenberg-MacLane spectra, and the real bordism spectrum MUR. In particular, we construct an equivariant version of the Bokstedt spectral sequence, the formulation of which requires further development of the Hochschild homology of Green functors, first introduced by Blumberg, Gerhardt, Hill, and Lawson. (C) 2022 Elsevier B.V. All rights reserved.UPHES
Categorified Jones-Wenzl projectors for odd Khovanov homology
No full textThesis (Ph.D.)--Michigan State University. Mathematics - Doctor of Philosophy, 2025The Jones-Wenzl projectors are particular elements of the Temperley-Lieb algebra essential to the construction of quantum 3-manifold invariants. As a first step toward categorifying quantum 3-manifold invariants, Cooper and Krushkal categorified these projectors. In another direction, Naisse and Putyra gave a categorification of the Temperley-Lieb algebra compatible with odd Khovanov homology, introducing new machinery called grading categories.The first goal of this thesis is to provide a generalization of Naisse and Putyra's work in the spirit of Bar-Natan's canopolies or Jones's planar algebras, replacing grading categories with grading multicategories. From this updated viewpoint, we describe an invariant of diskular tangles from odd Khovanov homology, naturally extending Naisse and Putyra's tangle theory. In this thesis, the main application of our theory for diskular tangles is a proof of the existence and uniqueness of categorified Jones-Wenzl projectors in odd Khovanov homology. These results have a nearly immediate award: the existence of a new, "odd" categorification of the colored Jones polynomial. Finally, a major motivation to develop a tangle theory for odd Khovanov homology is to ultimately determine the state of its functoriality. In forthcoming work by the author, we study this question by approximating Khovanov's argument for the original theory. In doing so, we develop a theory of Hochschild homology for modules and algebras graded by categories, indicating that the new constructions offered by grading categories are also deserving of study.Description based on online resource. Title from PDF t.p. (Michigan State University Fedora Repository, viewed ).Includes bibliographical references
'You don't talk about love in government'
No full textThis roundtable discussion explores the politics of Sure Start from its earliest days, and the thinking behind it. Tessa Jowell was the Labour Minister responsible for setting it up and she talks to the psychotherapist and author of Love Matters and The Selfish Society, Sue Gerhardt, and Sarah Stewart Brown, Professor of Public Health at Warwick University. They discuss the central importance of early infancy in determining the life chances and psychological wellbeing of both children and adults
Topological Distances between Directional Transform Representations of Graphs
No full textThesis (Ph.D.)--Michigan State University. Computational Mathematics, Science and Engineering - Doctor of Philosophy, 2025Shape analysis is important in fields like computational geometry, biology, and machine learning, where understanding differences in structure and tracking changes over time is useful. Topological Data Analysis (TDA) provides tools to study shape in a way that is resistant to noise and captures both fine and large-scale features. This dissertation focuses on directional transforms, a method that encodes shape by looking at its structure from different directions.First, we introduce the Labeled Merge Tree Transform (LMTT), a new way to compare embedded graphs using merge trees and directional transforms. We test this method on real-world datasets and show that it works better than existing distance measures in some cases. Next, we develop a kinetic data structure (KDS) for bottleneck distance, which allows us to update shape comparisons efficiently when the data changes over time. We apply this method to the Persistent Homology Transform (PHT) and show that it reduces computation time while keeping accurate results. Finally, we explore a future direction that extends the kinetic data structure to the Wasserstein distance. These contributions improve the use of topology in studying dynamic shapes and open new research possibilities in both theory and practical applications.Description based on online resource. Title from PDF t.p. (Michigan State University Fedora Repository, viewed ).Includes bibliographical references
Families of Knot Floer Homology Theories and Deeply Slice Knots
No full textThesis (Ph.D.)--Michigan State University. Mathematics - Doctor of Philosophy, 2024In this dissertation, we present the culmination of two projects, after an overview of theprimary tool involved in the research, Heegaard Floer theory. In this overview, we discuss the origins of Heegaard Floer homology, an invariant associated to a Spinc 3-manifold, as well as its flavors. We then present multiple flavors of knot Floer homology, a refinement of that theory. The first project is a structural theorem for a family of knot invariants due to Dowlin. L-space knots are knots which admit surgeries that have simple Heegaard Floer homology and thin knots are ones whose knot Floer homology is concentrated in a single \u3b4-grading. Each class of knots has well known knot Floer complexes. As such, we show that for L-space knots and thin knots, the theories that Dowlin constructed are a change of coefficients from an older theory, the minus flavor of knot Floer homology. Many supporting examples are shown in its final section. The proof uses a popular cancellation lemma for chain complexes with the special shapes involved. The second project is a collaboration with McConkey, St. Clair, and Zhang. In this dissertation, we show that the Whitehead double of the dual knot to 1/n surgery on the knot 61 in the 3-sphere is deeply slice in a contractible 4-manifold. That is, it bounds a smoothly embedded disc in the manifold, but not in a collar neighborhood of its boundary, the surgered manifold. This is partial progress in answering one of the Kirby questions regarding nullhomotopic deeply slice knots, as referenced in earlier work of Klug and Ruppik. To prove our theorem, we make use of the immersed curves perspective of bordered Floer homology and knot Floer homology, which we introduce in previous sections.Description based on online resource. Title from PDF t.p. (Michigan State University Fedora Repository, viewed ).Includes bibliographical references
- …
