Students will present an interesting application of matrix algebra that could supplement a Math 322 class.

Comparing ethnographic and agricultural data collected from two neighboring Biangai villages (Morobe Province, Papua New Guinea), one engaged in a small-scale conservation effort and the other stakeholders in a large industrial gold mine, this paper analyzes the linkages between alternative development regimes, agricultural transformation and human-environmental relations. Working the land is not simply about production, but also about knowing the landscape and its products as nodes in human social relations. Mining regimes disentangle the multi-species networks experienced in the garden, and reassemble them into other spaces. Thus, in the mining inspired transformations of agricultural practices, Biangai are also transforming how they experience their own multi-species community – its past, present and future.

Sponsored by the Department of Anthropology Colloquium Series.

Speaker: Devin Willmott

Title: Generative Neural Networks in Semi-Supervised Learning



Abstract: Semi-supervised learning is a relatively new machine learning concept that seeks to use both labeled and unlabeled data to perform supervised learning tasks. We will look at two network types with some promising applications to semi-supervised learning: ladder networks and adversarial networks. For each, we will discuss the motivations behind their architectures & training methods, and derive some favorable theoretical properties about their capabilities.

 The transition metal oxides have a wide spectrum of physical and chemical functionalities, useful for many potential applications in energy technologies. However, the underlying physical mechanisms have been still unclear whether performance is intrinsic to materials themselves or attributed to extrinsic factors. The synthesis of phase pure materials has been a challenging task because their polymorphs are closely related to each other in a thermodynamic framework. Here, we report epitaxial stabilization of single crystalline oxides for energy applications and investigate their intrinsic functionalities. First, our epitaxial VO2(B) and TiO2(B) films offer excellent long-term stability with extremely high capacity for Li ion battery electrode. Second, we design and create unique cell geometry of micrometer-thick epitaxial nanocomposite films which contain yttria-stabilized ZrO2 (YSZ) nanocolumns. The ion conductivity of these nanocolumns is enhanced by over two orders of magnitude compared to plain YSZ films, showing the strong practical potential of these nanostructured films for use in much lower operation temperature ionic devices. Our successful epitaxy of oxides will open the door to study their fundamental properties for potential energy applications and understand their intrinsic physics. 

Title: Kronecker's Theory of Binary Bilinear Forms with Applications to Representations of Integers as Sums of Three Squares

Abstract: In 1883 Leopold Kronecker published a paper containing “a few explanatory remarks” to an earlier paper of his from 1866. His work loosely connected the theory of integral binary bilinear forms to the theory of integral binary quadratic forms. In this defense we shall discover the key statements within Kronecker's paper and offer insight into new, detailed arithmetic proofs. Further, I will present some additional results on the proper and complete class numbers for bilinear forms, before demonstrating their use in rigorously developing the connection between binary bilinear forms and binary quadratic forms. We conclude by giving an application of this material to the number of representations of an integer as a sum of three squares and show the resulting formula is equivalent to the well-known result due to Gauss.

Title: Constructing the p-adic Integers

Abstract: For a prime p, the p-adic integers Z_p is the valuation ring of  the field of  p-adic numbers Q_p. In this talk, we will explicitly construct Zp as a ring of coherent sequences and explore its algebraic and topological properties. We will then explore the multiplicative structure of Q_p using Hensel's Lemma. 

Title: On Skew-Constacyclic Codes

Abstract: Cyclic codes are a well-known class of linear block codes with efficient decoding algorithms. In recent years they have been generalized to skew-constacyclic codes; such a generalization has previously been shown to be useful. After a brief introduction of skew-polynomial rings and their quotient modules, which we use to study skew-constacyclic codes algebraically, we motivate and define a notion of idempotent elements in these quotient modules. We are particularly concerned with the existence and uniqueness of idempotents that generate a given submodule; as such, we generalize relevant results from previous work on skew-constacyclic codes by Gao/Shen/Fu in 2013 and well-known results from the classical case.

See https://math.as.uky.edu/public-lecture-some-intersections-art-and-science-0 for more information.