Talks (unless otherwise indicated) are in Davis 301 from 4:00–5:00 PM on Fridays. Refreshments begin at 3:30 PM on the second floor of Davis.

To make sure you get email updates, add yourself to the mathstu (if a student) or mathothers (if not) email groups. Or check the Colby Math Facebook page.

You can see next semester’s schedule.

 

February 25
Sarah Brauner
University of Minnesota
Card shuffling and a strange type of multiplication

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Abstract

How many times do you need to shuffle a deck of cards to ensure it is adequately mixed?
In this talk, I will describe a framework to answer this question by introducing a strange type of multiplication on words. Beyond probabilistic motivations, this product structure has many interesting connections to combinatorics and representation theory. This is joint work with Patty Commins and Vic Reiner.

 

March 4
Jonathan Schneider
Colby College
Generic codimension-1 smooth maps

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Abstract

Much of topology, including knot theory, entails representing objects in nice, simple spatial configurations. Spatial arrangements in general can be quite complicated, but the generic positions of an object consist of only finitely many uniform pieces, meeting along singularities of finitely many types. In this talk, we’ll take a stroll through the zoo of generic singularity types for objects of dimension ≤3.

 

March 11
Lara Pudwell
Valparaiso
Patterns in Permutations

Title

Abstract

A permutation is a list of numbers where order matters.  While it is well-known that there are n! ways to put n different numbers in order, there are a variety of follow-up research topics, especially when we study permutations that have specific properties.  In this talk, we will focus on permutation patterns — that is, smaller permutations contained inside of larger permutations.  From a pure mathematics perspective, permutation patterns lead to a variety of interesting counting problems.  Looking further afield, we will see how permutations with zero copies of a given pattern arise naturally in computer science, and we will consider a situation where packing as many copies as possible of a pattern into permutations has a surprising connection to physical chemistry.

April 1
Román Aranda Cuevas
Binghamton University
Knotted surfaces in bridge position

Title

Abstract

It is a known fact that there are no knots in 4-space. On the contrary, there exist embeddings of 2-dimensional spheres into $\mathbb{R}^4$ that are “knotted.” Personally, it is non-trivial to imagine (or even draw) a knotted sphere in dimension four. In this talk, we will introduce ways to represent such surfaces using ideas of knot theory in dimension three. We will discuss a numerical invariant called “the Kirby-Thompson of a knotted surface,” and we will compute it for an infinite family of spheres in 4-space. This talk is based on joint work with S. Taylor, P. Pongtanapaisan, and C. Zhang. This talk is aimed to undergraduate students: No background will be assumed.

 

April 29 – Davis 201

Cindy Zhang
Colby College
Honors Talk – Decomposing Low-dimensional Spaces

Title

Abstract

Decomposition of spaces into smaller and simpler pieces turns out to be a powerful tool for studying them. In this talk, we will explore spaces in low dimensions and particular ways of decomposing them. We will start with dimensions two and three, where we are able to actually visualize the spaces. Then, we will port the ideas to dimension four, introduce trisection of a 4-dimensional space—a natural kind of decomposition into three elementary pieces, and discuss what insights into the fourth dimension such decompositions can yield.

May 2 (Monday)
Jack Nguyen
Colby College
Rational Approximation by Lattice Reduction

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Abstract

In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. In this talk, we will learn about Dirichlet’s theorem, which guarantees infinitely many rational approximations with a certain level of accuracy to a given irrational number. Such an approximation is sometimes called a solution to Dirichlet’s theorem. Regarding the problem of generating solutions to Dirichlet’s theorem, lattice basis reduction algorithms are an excellent tool for finding slightly weaker solutions than what Dirichlet’s theorem guarantees. I will discuss a recent paper that uses the well-known LLL algorithm for lattice basis reduction to generate sequences of “weak” solutions with prescribed quality.

May 4 (Wednesday)
Eduardo Sosa and Jakub Bystricky
Colby College
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