4/26 – Dan Nichols: Finite Fields and the Mathematics of Forward Error Correction

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.

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4/12 – Tori Day – Hidden Figures: The African American Women Mathematicians of NASA Who Helped Fuel America’s Space Achievements

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.

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3/29 – Filip Dul: The Poincaré Recurrence Theorem

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.

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3/8 – Professor Tom Braden: Geometry of Machines

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!

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3/1 – Angelica Simonetti – Braid groups: from algebra to geometry

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.”

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2/22: GaYee Park – Billiards on square-tiled surfaces

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.

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2/15: John Lee – Understanding Chaos

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.

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2/8: Sean Hart – Voronoi Tessellation

Math club this week will meet Wednesday, 2/8 at 5 pm in LGRT 1528 to hear Sean Hart talk about the Voronoi tessellation. There will be pizza and soda, of course. Here’s Sean’s abstract:

The Voronoi tessellation is an oft rediscovered way of naturally
partitioning a space with certain distinguished points, called generators,
into smaller cells, with each cell corresponding to the region of space
closest to a particular generator. In this talk, we will define and
discuss some of the basic properties of the Voronoi tessellation, as well
as some generalizations and historical applications. We will also talk
briefly about a particular dynamical system one can define using the
Voronoi tessellation, and some of its properties.

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February 1: Tetsuya Nakamura – Spin Structures on a Band

Please join us in LGRT 1528 on Wednesday, 2/1/17 from 5 pm to 6 pm for the first talk of the Spring semester. We’ll hear from our own co-organizer Tetsuya Nakamura about a concept important to geometry, topology, and physics: spin structure. The talk will focus on examples and make use of clever visual aids. There will also be pizza and soda!

Here’s an abstract:

Spin Structure on a band:

Gluing two edges of a strip, we can make a closed band in a ring form. If we twist by a half turn before gluing, we get the famous Mobius band. If we perform a full twist and then glue the edges, we get a “more” twisted band, which as a surface, is still considered to be the same as the “non-twisted” band. In fact, any band with integer twists is considered the same as the non-twisted one, even though they look different in reality. In the talk we introduce the so called spin structure on the band, which recognizes this parity of twisting. In other words, we can distinguish amounts of half-twisting mod 4 by considering the band (surface) with the spin structure on it. We will give different definitions of the spin structure on a band and see how they are related to each other. These are demonstrated using papers, ropes and other materials, so we will use less mathematical formulas.

GSspinstrS1disk

(Image from Gompf and Stipsicz – Four Manifolds and Kirby Calculus)

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LAST MATH CLUB OF SPRING 2016

Please join us for the last math club meeting of the semester in LGRT 1528 from 5-6pm tonight. We’ll rally around pizza, soda and our love of math, and reminisce. It’s also a great chance for you to propose future math club activities or talks if you’d like to give one next semester. I’ll also bring Set.

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