Seminars and Colloquia by Series

What is Heegaard Floer homology?

Series
Research Horizons Seminar
Time
Wednesday, April 12, 2017 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jen HomGeorgia Tech
Defined in the early 2000's by Ozsvath and Szabo, Heegaard Floer homology is a package of invariants for three-manifolds, as well as knots inside of them. In this talk, we will describe how work from Poul Heegaard's 1898 PhD thesis, namely the idea of a Heegaard splitting, relates to the definition of this invariant. We will also provide examples of the kinds of questions that Heegaard Floer homology can answer. These ideas will be the subject of the topics course that I am teaching in Fall 2017.

Groups Actions on Spanning Trees II

Series
Research Horizons Seminar
Time
Wednesday, April 5, 2017 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chi Ho YuenGeorgia Tech
I will continue the discussion on the group actions of the graph Jacobian on the set of spanning trees. After reviewing the basic definitions, I will explain how polyhedral geometry leads to a new family of such actions. These actions can be described combinatorially, but proving that they are simply transitive uses geometry in an essential way. If time permits, I will also explain the following surprising connection: the canonical group action for a plane graph (via rotor-routing or Bernardi process) is related to the canonical tropical geometric structure of its dual graph. This is joint work with Spencer Backman and Matt Baker.

Groups Actions on Spanning Trees

Series
Research Horizons Seminar
Time
Wednesday, March 15, 2017 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Matt BakerGeorgia Tech
Every graph G has canonically associated to a finite abelian group called the Jacobian group. The cardinality of this group is the number of spanning trees in G. If G is planar, the Jacobian group admits a natural simply transitive action on the set of spanning trees. More generally, for any graph G one can define a whole family of (non-canonical) simply transitive group actions. The analysis of such group actions involves ideas from tropical geometry. Part of this talk is based on joint work with Yao Wang, and part is based on joint work with Spencer Backman and Chi Ho Yuen.

Video Slot Game Design

Series
Research Horizons Seminar
Time
Wednesday, February 22, 2017 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hua XuGimmie Games
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.

Critical Percolation

Series
Research Horizons Seminar
Time
Wednesday, January 18, 2017 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael DamronGeorgia Institute of Technology
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.

Probability Theory in SOM, a Personal Perspective

Series
Research Horizons Seminar
Time
Wednesday, November 30, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christian HoudréGeorgia Institute of Technology
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.

Algebraic matroids and tropical varieties

Series
Research Horizons Seminar
Time
Wednesday, November 16, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Josephine YuGeorgia Institute of Technology
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.

Skein algebras and quantum topology

Series
Research Horizons Seminar
Time
Wednesday, November 9, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan PaprockiGeorgia Institute of Technology
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.

Math research in the age of Google Scholar and the revolutionary library

Series
Research Horizons Seminar
Time
Wednesday, November 2, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Liz HoldsworthGeorgia Institute of Technology
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.

Matrix Completion Problems and Sums of Squares

Series
Research Horizons Seminar
Time
Wednesday, October 26, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Greg BlekhermanGeorgia Institute of Technology
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.

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