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Series: Research Horizons Seminar

In this talk, we will have an overview of: the Gaming Industry, specifically on the Video Slot Machine segment; the top manufactures in the world; the game design studio Gimmie Games, who we are, what we do; what is the process of making a video slot game; what is the basic structure of the math model of a slot game; current strong math models in the market; what is the roll of a game designer in the game development process; the skill set needed to be a successful Game Designer. Only basic probability knowledge is required for this talk.

Series: Research Horizons Seminar

On the two-dimensional square grid, remove each
nearest-neighbor edge independently with probability 1/2 and consider
the graph induced by the remaining edges. What is the structure of its
connected components? It is a famous theorem of Kesten that 1/2 is the
``critical value.'' In other words, if we remove edges with probability
p \in [0,1], then for p < 1/2, there is an infinite component remaining,
and for p > 1/2, there is no infinite component remaining. We will
describe some of the differences in these phases in terms of crossings
of large boxes: for p < 1/2, there are relatively straight crossings of
large boxes, for p = 1/2, there are crossings, but they are very
circuitous, and for p > 1/2, there are no crossings.

Series: Research Horizons Seminar

I will start with a brief presentation of the Probability activities in SOM. I will continue by presenting results obtained in SOM, over the past ten years, answering long standing questions insequences comparison.

Series: Research Horizons Seminar

A matroid is a combinatorial abstraction of an independence structure, such as linear independence among vectors and cycle-free-ness among edges of a graph. An algebraic variety is a solution set of a system of polynomial equations, and it has a polyhedral shadow called a tropical variety. An irreducible algebraic variety gives rise to a matroid via algebraic independence in its coordinate ring. In this talk I will show that the tropical variety is compatible with the algebraic matroid structure. I will also discuss some open problems on algebraic matroids and how they behave under operations on tropical varieties.

Series: Research Horizons Seminar

Quantum topology is a collection of ideas and techniques for studying
knots and manifolds using ideas coming from quantum mechanics and
quantum field theory. We present a gentle introduction to this topic via
Kauffman bracket skein algebras of surfaces,
an algebraic object that relates "quantum information" about knots
embedded in the surface to the representation theory of the fundamental
group of the surface. In general, skein algebras are difficult to
compute. We associate to every triangulation of the
surface a simple algebra called a "quantum torus" into which the skein
algebra embeds. In joint work with Thang Le, we make use of this
embedding to give a simple proof of a difficult theorem.

Series: Research Horizons Seminar

If Google Scholar gives you everything you want, what could Georgia Tech Library possibly do for you? Come learn how to better leverage the tools you know and discover some resources you may not. Get to know your tireless Math Librarian and figure out how to navigate the changes coming with Library Next. This is also an opportunity to have a voice in the Library’s future, so bring ideas for discussion. Refreshments will be served.

Series: Research Horizons Seminar

A matrix completion problem starts with a partially specified matrix, where some entries are known and some are not. The goal is to find the unknown entries (“complete the matrix”) in such a way that the full matrix satisfies certain properties. We will mostly be interested in completing a partially specified symmetric matrix to a full positive semidefinite matrix. I will give some motivating examples and then explain connections to nonnegative polynomials and sums of squares.

Series: Research Horizons Seminar

Refreshments will be provided before the seminar.

Collective behavior can be seen in many animal species, such as flocking birds, herding mammals, and swarming bacteria. In the continuum limit, these phenomena can be modeled by nonlocal PDEs. In this talk, after discussing some PDE models for collective dynamics, I will focus on the analysis of the Keller-Segel equation, which models bacterial chemotaxis. Mathematically, this equation exhibits an intriguing "critical mass phenomenon": namely, solutions exist globally in time for all initial data whose mass is below some certain constant, whereas finite-time blow-up always happen if the initial mass is above this constant. I will introduce some useful analysis tools that lead to this result, and discuss some active areas of current research.

Series: Research Horizons Seminar

Refreshments will be provided before the seminar.

It's important to have a personal academic webpage—one that is up-to-date, informative, and easy to navigate. This workshop will be a hands-on guide to making an academic webpage and hosting it on the School of Math website. Webpage templates will be provided. Please bring a laptop if you have one, as well as a photograph of yourself for your new website. Come and get the help you need to create a great webpage!

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

For every surface (sphere, torus, etc.) there is an associated graph called the curve graph. The vertices are curves in the surface and two vertices are connected by an edge if the curves are disjoint. The curve graph turns out to be very important in the study of surfaces. Even though it is well-studied, it is quite mysterious. Here are two sample problems: If you draw two curves on a surface, how far apart are they as edges of the curve graph? If I hand you a surface, can you draw two curves that have distance bigger than three? We'll start from the beginning and discuss these problems and some related computational problems on surfaces.