Seminars and Colloquia by Series

The exotic world of 4-manifolds.

Series
Research Horizons Seminar
Time
Wednesday, December 6, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John Etnyre – GT Math
Four dimensions is unique in many ways. For example $n$-dimensional Euclidean space has a unique smooth structure if and only if $n$ is not equal to four. In other words, there is only one way to understand smooth functions on $R^n$ if and only if $n$ is not 4. There are many other way that smooth structures on 4-dimensional manifolds behave in surprising ways. In this talk I will discuss this and I will sketch the beautiful interplay of ideas (you got algebra, analysis and topology, a little something for everyone!) that go into proving $R^4$ has more that one smooth structure (actually it has uncountably many different smooth structures but that that would take longer to explain).

Linear algebra of Hamiltonian matrices

Series
Research Horizons Seminar
Time
Wednesday, November 29, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chongchun Zeng – Georgia Tech
In this talk, we consider the structure of a real $n \times n$ matrix in the form of $A=JL$, where $J$ is anti-symmetric and $L$ is symmetric. Such a matrix comes from a linear Hamiltonian ODE system with $J$ from the symplectic structure and the Hamiltonian energy given by the quadratic form $\frac 12\langle Lx, x\rangle$. We will discuss the distribution of the eigenvalues of $A$, the relationship between the canonical form of $A$ and the structure of the quadratic form $L$, Pontryagin invariant subspace theorem, etc. Finally, some extension to infinite dimensions will be mentioned.

Diophantine Equations and p-adic Integration

Series
Research Horizons Seminar
Time
Wednesday, November 15, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
skiles 006
Speaker
Joseph Rabinoff – GT Math
A motivating problem in number theory and algebraic geometry is to find all integer-valued solutions of a polynomial equation. For example, Fermat's Last Theorem asks for all integer solutions to x^n + y^n = z^n, for n >= 3. This kind of problem is easy to state, but notoriously difficult to solve. I'll explain a p-adic method for attacking Diophantine equations, namely, p-adic integration and the Chabauty--Coleman method. Then I'll talk about some recent joint work on the topic.

Non-smooth dynamics in the environment and data science

Series
Research Horizons Seminar
Time
Wednesday, October 18, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rachel Kuske – Georgia Tech
This talk will cover some recent and preliminary results in the area of non-smooth dynamics, with connections to applications that have been overlooked. Much of the talk will present open questions for research projects related to this area.

How to stretch taffy most efficiently?

Series
Research Horizons Seminar
Time
Wednesday, September 27, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Balasz Strenner – Georgia Tech
Taffy pullers are machines designed to stretch taffy. They can modeled by surface homeomorphisms, therefore they can be studied by geometry and topology. I will talk about how efficiency of taffy pullers can be defined mathematically and what some of the open questions are. I will also talk about Macaw, a computer program I am working on, which does related computations and which will hopefully help answer some of the open questions.

How to stretch taffy most efficiently?

Series
Research Horizons Seminar
Time
Wednesday, September 27, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Balazs Strenner – GA Tech
Taffy pullers are machines designed to stretch taffy. They can modeled by surface homeomorphisms, therefore they can be studied by geometry and topology. I will talk about how efficiency of taffy pullers can be defined mathematically and what some of the open questions are. I will also talk about Macaw, a computer program I am working on, which does related computations and which will hopefully help answer some of the open questions.

Academic Webpage Workshop

Series
Research Horizons Seminar
Time
Wednesday, September 20, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tim Duff – GA Tech
An academic webpage allows you to better communicate your work and help you become more recognizable in your research community. We'll talk about the very basics of how to set one up and what you should put on it----no prior experience necessary! Please bring a laptop if you can---as usual, refreshments will be provided.

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