Algebra/Number Theory/Combinatorics seminar

More algebraic structures from knot theory

Category

Speaker

Sam Nelson (Claremont McKenna College)

Abstract

Quandles are a type of non-associative algebraic structure defined from the combinatorics of knot diagrams. In this talk will recall the basics of quandle theory and look at some generalizations of quandles including biquandles, racks and biracks. If time permits, we will also look at tangle functors and a connection to Hopf algebras.

Where

ML 211

Misc. Information

Inconsistencies with Nonparametric Procedures and Statistics: Combinatoric and Asymptotic Results

Category

Speaker

Anna E. Bargagliotti (University of Memphis)

Abstract

Nonparametric statistical tests can be used to differentiate among alternatives. Each test is uniquely identified with a procedure that analyzes ranked data. Procedure results are then incorporated into a test statistic. Inconsistencies among tests occur at both the procedure level and the statistic level. In this talk, I will characterize symmetry structures of data that explain why different procedures can output different rankings when analyzing the same data. In addition, I will quantify the number of ways that two ranked data sets can be aggregated and define a strict condition data must satisfy in order to ensure consistent procedure results. Finally, I will discuss how procedure inconsistencies affect the test statistics. Using the Kruskal-Wallis test as an example, I will outline how to asymptotically find the probability with which the null is rejected.

Where

ML 211

Misc. Information

A very brief introduction to fields of norms

Category

Speaker

Ghassan Sarkis (Pomona College)

Abstract

We will present the field-of-norms construction of Fontaine and Wintenberger, which associates certain totally ramified extensions of local fields with positive-characteristic fields in a way that relates the Galois group of the extension to a subgroup of automorphisms of the positive-characteristic field. Time permitting, we will discuss applications the field-of-norms theory to p-adic dynamical systems.

Where

ML 211

Misc. Information

On Siegel's lemma

Category

Speaker

Lenny Fukshansky (Claremont McKenna College)

Abstract

Siegel's lemma in its simplest form is a statement about the existence of small-size solutions to a system of linear equations with integer coefficients: such results were originally motivated by their applications in transcendence. A modern version of this classical theorem guarantees the existence of a whole basis of small "size" for a vector space over a global field (that is number field, function field, or their algebraic closures). The role of size is played by a height function, an important tool from Diophantine geometry, which measures "arithmetic complexity" of points. For many applications it is also important to have a version of Siegel's lemma with some additional algebraic conditions placed on points in question. I will discuss the classical versions of Siegel's lemma, along with my recent results on existence of points of bounded height in a vector space outside of a finite union of varieties over a global field.

Where

Millikan 211

Misc. Information

Interlocking Linkages

Category

Speaker

Julie Glass (California State University East Bay)

Abstract

This talk will introduce the audience to some of the history and basic ideas used in the study of chains in the area of computational geometry. A chain is a collection of rigid bars connected at their vertices (also known as a linkage), which form a simple path (an open chain) or a simple cycle (a closed chain). A folding of a chain (or any linkage) is a certain reconfiguration obtained by moving the vertices. A collection of chains are said to be interlocked if they cannot be separated by foldings. This talk will explain some standard techniques using geometry and knot theory to address the problem of when linkages are interlocked. Finally, we will answer the question, “Can a 2-chain and a k-chain be interlocked?” This talk will be accessible to a broad audience.

Where

Millikan 211

Misc. Information

Organizational meeting

Category

Speaker

All interested Claremont faculty invited!

Abstract

We will set up the fall schedule for the seminar. Local volunteers and other speaker suggestions needed!

Where

Millikan 211, Pomona College

Misc. Information

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