Seminars and Colloquia by Series

Learning latent combinatorial structures in noisy data

Series
Research Horizons Seminar
Time
Friday, October 2, 2020 - 12:30 for 1 hour (actually 50 minutes)
Location
Microsoft Teams
Speaker
Cheng MaoGeorgia Tech

Learning latent structures in noisy data has been a central task in statistical and computational sciences. For applications such as ranking, matching and clustering, the structure of interest is non-convex and, furthermore, of combinatorial nature. This talk will be a gentle introduction to selected models and methods for statistical inference of such combinatorial structures. I will particularly discuss some of my recent research interests.

Taming the randomness of chaotic systems

Series
Research Horizons Seminar
Time
Friday, September 25, 2020 - 12:30 for 1 hour (actually 50 minutes)
Location
Microsoft Teams
Speaker
Alex BlumenthalGeorgia Tech
All around us in the physical world are systems which evolve in chaotic, seemingly random ways: fire, smoke, turbulent fluids, the flow of gas around us. Over the last ~60 years, mathematicians have made tremendous progress in understanding these processes and how chaotic behavior can emerge and, remarkably, the extent to which chaotic systems emulate probabilistic randomness. This talk is a brief introduction to these ideas, with an emphasis on examples and pretty pictures. 

Invariant objects and Arnold diffusion. From theory to computation.

Series
Research Horizons Seminar
Time
Wednesday, March 4, 2020 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rafael de la LlaveGeorgia Tech

We consider the problem whether small perturbations of integrable mechanical systems can have very large effects.

Since the work of Arnold in 1964, it is known that there are situations where the perturbations can accumulate (Arnold diffusion). 

This can be understood by noting that the small perturbations generate some invariant objects in phase space that act as routes which allow accumulation of effects. 

We will present some rigorous results about geometric objects lead to Arnold diffusion as well as some computational tools that allow to find them in concrete applications.

Thanks to the work of many people, an area which used to be very speculative, is becoming an applicable tool.

The Shape of Things: Organizing space using algebra

Series
Research Horizons Seminar
Time
Wednesday, November 20, 2019 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Miriam Kuzbary

Determining when two objects have “the same shape” is difficult; this difficulty depends on the dimension we are working in. While many of the same techniques work to study things in dimensions 5 and higher, we can better understand dimensions 1, 2, and 3 using other methods. We can think of 4-dimensional space as the “bridge” between low-dimensional behavior and high-dimensional behavior.

 

One way to understand the possibilities in each dimension is to examine objects called cobordisms: if an (n+1)-dimensional space has an ``edge,” which is called a boundary, then that boundary is itself an n-dimensional space. We say that two n-dimensional spaces are cobordant if together they form the boundary of an (n+1)-dimensional space. Using the idea of spaces related by cobordism, we can form an algebraic structure called a group. In this way, we can attempt to understand higher dimensions using clues from lower dimensions.

 

In this talk, I will discuss different types of cobordism groups and how to study them using tools from a broad range of mathematical areas.

Variational models, PDEs, numerical analysis and applications

Series
Research Horizons Seminar
Time
Wednesday, November 13, 2019 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sung Ha KangGeorgia Tech

Starting from mathematical approaches for image processing, we will discuss different models, analytic aspects of them, and numerical challenges.  If time permits we will consider numerical applications to data understanding. A few other applications may be presented.

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