Class Notes for Math 918: Homological Conjectures, Instructor Tom Marley

This course was an overview of what are known as the “Homological Conjectures,” in particular, the Zero Divisor Conjecture, the Rigidity Conjecture, the Intersection Conjectures, Bass’ Conjecture, the Superheight Conjecture, the Direct Summand Conjecture, the Monomial Conjecture, the Syzygy Conjecture, and the big and small Cohen Macaulay Conjectures. Many of these are shown to imply others. This document contains notes for a course taught by Tom Marley during the 2009 spring semester at the University of Nebraska-Lincoln. The notes loosely follow the treatment given in Chapters 8 and 9 of Cohen-Macaulay Rings, by W. Bruns and J. Herzog, although many other sources, including articles and monographs by Peskine, Szpiro, Hochster, Huneke, Grith, Evans, Lyubeznik, and Roberts (to name a few), were used. Special thanks to Laura Lynch for putting these notes into LaTeX.

Class Notes for Math 918: Cohen Macaulay Modules, Instructor Roger Wiegand

Topics covered are: Cohen Macaulay modules, zero-dimensional rings, one-dimensional rings, hypersurfaces of finite Cohen-Macaulay type, complete and henselian rings, Krull-Remak-Schmidt, Canonical modules and duality, AR sequences and quivers, two-dimensional rings, ascent and descent of finite Cohen Macaulay type, bounded Cohen Macaulay type.

Class Notes for Math 918: Local Cohomology, Instructor Tom Marley

Topics include: Injective Module, Basic Properties of Local Cohomology Modules, Local Cohomology as a Cech Complex, Long exact sequences on Local Cohomology, Arithmetic Rank, Change of Rings Principle, Local Cohomology as a direct limit of Ext modules, Local Duality, Chevelley’s Theorem, Hartshorne- Lichtenbaum Vanishing Theorem, Falting’s Theorem.

Class Notes for Math 871: General Topology, Instructor Jamie Radcliffe

Topics include: Topological space and continuous functions (bases, the product topology, the box topology, the subspace topology, the quotient topology, the metric topology), connectedness (path connected, locally connected), compactness, completeness, countability, filters, and the fundamental group.

Germline-Specific MATH-BTB Substrate Adaptor MAB1 Regulates Spindle Length and Nuclei Identity in Maize

Germline and early embryo development constitute ideal model systems to study the establishment of polarity, cell identity, and asymmetric cell divisions (ACDs) in plants. We describe here the function of the MATH-BTB domain protein MAB1 that is exclusively expressed in the germ lineages and the zygote of maize (Zea mays). mab1 (RNA interference [RNAi]) mutant plants display chromosome segregation defects and short spindles during meiosis that cause insufficient separation and migration of nuclei. After the meiosis-to-mitosis transition, two attached nuclei of similar identity are formed in mab1 (RNAi) mutants leading to an arrest of further germline development. Transient expression studies of MAB1 in tobacco (Nicotiana tabacum) Bright Yellow-2 cells revealed a cell cycle-dependent nuclear localization pattern but no direct colocalization with the spindle apparatus. MAB1 is able to form homodimers and interacts with the E3 ubiquitin ligase component Cullin 3a (CUL3a) in the cytoplasm, likely as a substrate-specific adapter protein. The microtubule-severing subunit p60 of katanin was identified as a candidate substrate for MAB1, suggesting that MAB1 resembles the animal key ACD regulator Maternal Effect Lethal 26 (MEL-26). In summary, our findings provide further evidence for the importance of posttranslational regulation for asymmetric divisions and germline progression in plants and identified an unstable key protein that seems to be involved in regulating the stability of a spindle apparatus regulator(s).

Dynamic networks, text analysis and Gephi: the art math

In numerosi campi scientici l'analisi di network complessi ha portato molte recenti scoperte: in questa tesi abbiamo sperimentato questo approccio sul linguaggio umano, in particolare quello scritto, dove le parole non interagiscono in modo casuale. Abbiamo quindi inizialmente presentato misure capaci di estrapolare importanti strutture topologiche dai newtork linguistici(Degree, Strength, Entropia, . . .) ed esaminato il software usato per rappresentare e visualizzare i grafi (Gephi). In seguito abbiamo analizzato le differenti proprietà statistiche di uno stesso testo in varie sue forme (shuffolato, senza stopwords e senza parole con bassa frequenza): il nostro database contiene cinque libri di cinque autori vissuti nel XIX secolo. Abbiamo infine mostrato come certe misure siano importanti per distinguere un testo reale dalle sue versioni modificate e perché la distribuzione del Degree di un testo normale e di uno shuffolato abbiano lo stesso andamento. Questi risultati potranno essere utili nella sempre più attiva analisi di fenomeni linguistici come l'autorship attribution e il riconoscimento di testi shuffolati.

Create Math Recital

Guest musicians: Heather Lingle and Mark Hayden

Gute Arbeit gibt herrlichen Lohn, in einer Predigt über das Evangelium am Sonntage Septuagesimae, Math. XX. 1. - 16. in der Kirche St. Leonhard in Stutgard, 1738 : mit einer eingeflossenen Anweisung, wie die vorsehende Execution des verurtheilten Juden, Joseph Süß Oppenheimers, christlich anzusehen und zu gebrauchen seye, ...

von Georg Cunrad Rieger

2007 Sonia Kovalevsky Math for Girls Day Program

2nd Annual Lincoln University Sonia Kovalevsky Math for Girls Day program on April 20, 2007

2007 Sonia Kovalevsky Math for Girls Day Featured Workshop: Knot Theory

2nd Annual Lincoln University Sonia Kovalevsky Math for Girls Day featured workshop by Mrs. Bernadette Turner on the topic of knot theory.

2009 Sonia Kovalevsky Math for Girls Day Program

4th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program on April 24, 2009.

2009 Sonia Kovalevsky Math for Girls Day Flyer

4th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 24, 2009.

2008 Sonia Kovalevsky Math for Girls Day Report

The report for the third annual Lincoln University Sonia Kovalevsky (LUSK) Math for Girls Day held on April 18th, 2008 from 8:30am to 2:00pm on the campus of Lincoln University in Jefferson City, MO.