Seminars and Colloquia by Series

Domino Tilings of the Chessboard: An Introduction to Sampling and Counting

Series
Undergraduate Seminar
Time
Monday, December 2, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Dana RandallGeorgia Tech

Domino tilings of finite grid regions have been studied in many contexts, revealing rich combinatorial structure.  They arise in applications spanning physics, computer science and probability theory and recreational mathematics.  We will look at questions such as counting and sampling from large combinatorial sets, such as the set of domino tilings, providing a small sample of some of the techniques that are used.  

 

Thinking Outside the Circle

Series
Undergraduate Seminar
Time
Monday, November 25, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Dr. Evans HarrellGeorgia Tech

Did you know that a wheel or a ball bearing does not need to be round? Convex regions that can roll smoothly come in many remarkable shapes and have practical applications in engineering and science. Moreover, the mathematics used to describe them, known as convex geometry, is a subject that beautifully ties together analysis and geometry. I'll bring some of these objects along and tell the class how to describe them effectively and recount their interesting history.

Surfaces and their Symmetries

Series
Undergraduate Seminar
Time
Monday, November 18, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Justin LanierGeorgia Tech

Surfaces are some of the most basic examples of spaces. Although topologists have studied surfaces for a long time, they continue to fascinate. I'll give an overview of the study of surfaces over the past 150 years by highlighting work of seven mathematicians. We'll discuss the classification of surfaces, and we'll also discuss mapping class groups, which are collections of symmetries of surfaces. I'll also give the flavor of four of my own research projects about surfaces, one for each of four broad mathematical areas: group theory, geometry, topology, and dynamics.

Introduction to the Probabilistic Method

Series
Undergraduate Seminar
Time
Monday, November 4, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Lutz WarnkeGeorgia Tech

The Probabilistic Method is a powerful tool for tackling many problems in discrete mathematics and related areas.
Roughly speaking, its basic idea can be described as follows. In order to prove existence of a combinatorial structure with certain properties, we construct an appropriate probability space, and show that a randomly chosen element of this space has the desired property with positive probability.
In this talk we shall give a gentle introduction to the Probabilistic Method, with an emphasis on examples.

Knots, Legendrian Knots, and Their Invariants

Series
Undergraduate Seminar
Time
Monday, October 28, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Dr. Caitlin LeversonGeorgia Tech
A knot can be thought of as a piece of string tied up, that then has its ends glued together. As long as we don’t cut the string, any way we move the string in space doesn’t change the knot we are considering. A surprisingly hard and interesting problem is, when handed two knots, how to determine if they are the same knot or not. We can further give structure to our knots and thus the problem, by adding geometric constraints to our knots, yielding what are called Legendrian knots. We can once again try to determine if two Legendrian knots are the same or not. In this talk I will introduce knots, Legendrian knots, and some ways we have to try to distinguish two knots or Legendrian knots, called knot invariants.

Surfaces: BIG and small

Series
Undergraduate Seminar
Time
Monday, October 21, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Dr. Marissa LovingGeorgia Tech

As a geometric group theorist, my favorite type of manifold is a surface and my favorite way to study surfaces is by considering the mapping class group, which is the collection of symmetries of a surface. In this talk, we will think bigger than your average low-dimensional topologist and consider surfaces of infinite type and their associated “big” mapping class groups.

Solutions of initial value problems of ordinary differential equations.

Series
Undergraduate Seminar
Time
Monday, October 7, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Luca DieciGeorgia Tech

This presentation reviews different concepts of solution of a differential equation, in particular stressing the need to modify the classical theory when we want to deal with discontinuous systems.  We will review the concept of classical solution, and then of Caratheodory solution and Filippov solution, motivating with simple examples the need for these extensions.

Variational Problems in Capillarity

Series
Undergraduate Seminar
Time
Monday, September 30, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
John McCuanGeorgia Tech

I will describe a few classical problems in capillarity and the associated classical variational framework.  These problems include the well-known shape and rise height problems for the meniscus in a tube as well as the problems associated with sessile and pendent drops. I will briefly discuss elements of recent modifications of the variational theory allowing floating objects.  Finally, I will describe a few open problems. 

Rational Tangles

Series
Undergraduate Seminar
Time
Monday, September 23, 2019 - 15:00 for
Location
Skiles 171
Speaker
Jennifer HomGeorgia Tech

A knot is a smooth embedding of a circle into R^3. Closely related are tangles, which are properly embedded arcs in a 3-ball. We will model certain tangles using jump ropes and relate this to Conway's classification of rational tangles.

Continuing the Fraction

Series
Undergraduate Seminar
Time
Monday, September 16, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Doron LubinskyGeorgia Tech

Continued fractions play a key role in number theory, especially in understanding how well we can approximate irrational numbers by rational numbers. They also play an important role in function theory, in understanding how well we can approximate analytic functions by rational functions. We discuss a few of the main achievements of the theory.

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