The Official Blog of the UMass Math Club

We will meet in LGRT 1634 at 5 pm just as usual.

The abstract of the talk is as follows:

The Radon transform is a way of transforming one function into another which has applications in mathematics and image processing. I will define the Radon transform as well as the closely related X-ray transform. I will recall the more famous Fourier transform, and then discuss the connection between these operators (which seems to have given rise to the popularity of the Radon transform in medical imaging)

 

It was really unfortunate that we had to cancel the math club last week due to the snow. We will reschedule GaYee’s talk at some time this semester, so don’t miss it!

This week, we are happy to have Eric Sommers as a speaker. He will talk about “An Introduction to Representation Theory”.

Here is his abstract:

I’ll give a survey of the main ideas behind the representation theory of finite groups. Representation theory is the study of the ways in which a group can be represented by a set of matrices. Knowing some linear algebra (Math 235) is helpful, but not required. It is not necessary to know what a group is– I will give the definition. This is a beautiful subject, accessible to all math majors, but not something that shows up in our undergraduate curriculum (although our friends in chemistry do see it).

We appreciated the nice opening math club talk given by Pat Dragon. Here is his abstract.

A de Bruijn sequence is a binary string of length $2^n$ which, when viewed cyclically, contains every binary string of length $n$ exactly once as a substring. For example, 00010111 suffices for $n = 3$. Knuth refers to the lexicographically least de Bruijn sequence for each $n$ as the “Granddaddy” sequence due to its venerable origin. In 1934 Martin originally constructed these sequences and later it was shown by Fredericksen et al that they can also be constructed by concatenating the aperiodic prefixes of the binary necklaces of length $n$ in lexicographic order. In a recent publication, we proved that the Granddaddy has a lexicographic partner. The “Grandmama” sequence is constructed by concatenating the aperiodic prefixes of necklaces in co-lexicographic order. This talk will introduce de Bruijn sequences, the FKM algorithm, and some applications.

Sorry for the late announcement, but if you can, please join us tomorrow as Math club hosts its final talk of the semester. We meet Wednesday 4/26, from 5-6 pm in LGRT 1528. Dan Nichols will give what may well be his final UMass math club talk, on Finite Fields and the Mathematics of Forward Error Correction. His abstract is below.

Finite Fields and the Mathematics of Forward Error Correction

Error-correcting codes for reliably storing and transmitting data are an essential tool of the information age, and many of the most widely used algorithms are based on number theoretic concepts such as finite field arithmetic. I will give a brief overview of the mathematics of coding theory and describe several popular types of codes including Reed-Solomon codes.

There will be a final math club next week, with no talk scheduled. We’ll just enjoy pizza and some down time together to do some mathy things, perhaps play some set, or watch some math videos.

Please join us on Wednesday, April 12 when Math club will feature a talk from graduate student Tori Day titled “Hidden Figures: The African American Women Mathematicians of NASA Who
Helped Fuel America’s Space Achievements”. We meet from 5-6 pm in LGRT 1528. Pizza and soda will be provided. Tori’s abstract is below.

In this talk, we will explore the lives and times of three of the central
figures of NASA (then NACA)’s West Computing Group: Dorothy Vaughan, Mary
Jackson, and Katherine Johnson. Along the way we will discuss their
contributions to mathematics and engineering and the Space Race, as well
as the challenges they overcame and the roads they paved. We will end
with a basic and broad overview of a paper co-authored by Katherine
Johnson in 1960 entitled Determination of Azimuth Angle at Burnout for
Placing a Satellite Over a Selected Earth Position.

Please join us this Wednesday, March 29, from 5-6 pm in LGRT 1528. We will hear from graduate student Filip Dul, who will speak about the Poincaré Recurrence Theorem. His abstract is below. Pizza and soda will be provided, as usual.

The Poincaré Recurrence Theorem

When air molecules are zooming around a room, can they all return to the locations they were in earlier? Can they all wind up in one corner of the room? In this talk we’ll learn about the Poincare Recurrence Theorem and its interesting implications for those two questions, which generated a big controversy in the late 19th century between physicists and mathematicians about the meaning of the Second Law of Thermodynamics.

Wednesday, March 8th, 5-6pm in LGRT 1528 we hear from Professor Tom Braden about the “Geometry of machines”:

Configuration spaces are one way to construct very interesting geometric
spaces. A configuration space is a space whose points represent
possible states in a mechanism or other physical system. Navigating
along a path inside the space is then represented by a motion of the
mechanism. Some quite complicated and high dimensional spaces which
cannot be visualized directly can be explored very concretely in this way.

I will focus mainly on configuration spaces of planar bar-and-joint
machines, which are machines in the plane made from rigid bars, hinges,
and anchors. Amazingly, a theorem of Kapovich and Milson says roughly
that any manifold can appear as (part of) the configuration space of
such a machine.

As always, there will be pizza and soda!

This Wednesday, 3/1, please join us in LGRT 1528 from 5 to 6 pm for Math club. We will hear a talk from Angelica Simonetti on braid groups, with pizza and soda provided. Here’s Angelica’s abstract:

Braid groups: from algebra to geometry

“Who has never seen a girl with her hair gathered in a braid? Braid groups are a perfect example of how mathematics can be deep, rich, even complicated and yet intuitive at the same time. In the talk we are going to present braid groups algebraically and show some of their geometric interpretations, including how they appear in the theory of mapping class groups.”

This Wednesday, 2/22, GaYee Park will give a Math Club talk about billiards on square-tiled surfaces. We meet as usual in LGRT 1528 from 5-6 pm, with pizza and soda provided. Here’s GaYee’s abstract:

Billiards on square-tiled surfaces:

If we shoot a ball from a point at a 45-degree angle on any flat bounded
surface, how does its path look like? Will the path return to its original
point? How long is each path? We already know for an n x m rectangular
surface, many properties of the path depend on the gcd (n,m) and lcm (n,m). We extend this question to other surfaces such as the Möbius strip, cylinder, Klein bottle, and others.

Math Club meets this Wednesday this week from 5:00-6:00 pm in LGRT 1528, where we’ll hear a talk from graduate student John Lee called “Understanding Chaos”. Pizza and soda will be provided. Here’s John’s abstract:

Understanding Chaos.

Some questions that you might ask yourself on a daily
basis are “What is the weather going to be like tomorrow?” or “If I leave
for class at 9:00, what time do I expect to get to there?”

Humans often have this desire to predict the future, realistically or not.
In this talk, we’ll discuss briefly, easy to predict events and some not
so easy to predict events. In particular we’ll introduce ideas needed to
understand chaos and what it means to be Dynamically Chaotic with some
real world examples.