| Date |
Speaker |
Topic |
| September 19 |
Alexander Garver |
Goodstein's Theorem and the Hydra Problem
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I will discuss Goodstein's Theorem and the Hydra Problem. I will mention the necessary terminology and state the results including the definitions of the Goodstein sequence, hydras, and winning strategies.
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| September 26 |
Brittany Baker |
Origami, Trisecting an Angle, and The Origami Box Problem
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This presentation is based on work done in the REU on the Mathematics of Paper Folding held at the University of Georgia in Summer 2009, supported in part by NSF grants DMS-0649242 and DMS-060137.
I will begin by talking about different types of origami. Then we will trisect an angle using origami. Finally, I will discuss the Origami Box Problem.
The Origami Box Problem: What is the largest volume that can be enclosed by folding a square sheet of paper, one unit on a side, into a closed box?
We consider different origami boxes with increasing volumes in our attempt to find the maximal volume of an origami box. We have not solved this problem: as will be seen, a solution would require a deep understanding of curved paper surfaces. However, we analyze a series of designs with larger and larger volume, and we identify a class of designs, which we call Inflated Sealed Sacks, to which the optimal design likely belongs. We believe that our best design is within a few percent of the optimum.
After doing this research we found significant related work done under similar names, “paper bag problem” or “tea bag problem”.
We finish with a few related open questions in origami, including our own origami cup problem. The Origami Cup Problem: What is the largest possible volume of a cup folded from a square sheet of paper, one unit on a side?
|
| October 3 |
Becky Patrias |
Flatland to Spaceland: Visualizing Spaces
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| |
Ever wonder how to visualize topological spaces that cannot be embedded in 3-space? Based on the book "The Shape of
Space" by Jeffrey R. Weeks, we will explore how to describe spaces embedded in three-space to a two-dimensional creature in order to shed
new light on describing spaces like S^3.
|
| October 10 |
Jonas Karlsson |
Learning to Love the Icosahedron
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| |
To know it is to love it! I will list a number of interesting properties of the icosahedron, most of them elementary, some of them less so. Topics include: the graph of the icosahedron and its combinatorial properties, construction of the geometric icosahedron, its symmetries and generalizations, "fibonaccihedra", the quintic equation, evolvents and singularities, quasicrystals and the satellite tobacco necrosis virus.
|
| October 17 |
Adil Ali |
Adil's Talk on Representation Theory
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| |
Representation Theory is ubiquitous throughout modern Algebra and Analysis. Representations serve as an indispensable tool for recovering structure of a group(finite,topological,etc...) through its action on various vector spaces. I will give a broad overview of basic representation theory, especially Schur's Lemma and the other crucial results for finite groups, before augmenting the discussion to include semisimple groups.
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| October 24 |
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No Junior Colloquium this week
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| October 31 |
Hui Li |
The passage from 3d to 2d in mathematical elasticity
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| |
The derivation of 2d theories from 3d theory is a fundamental question with a long history in mathematical elasticity. The first rigorous approach is obtained in 1993 based on the application of Gamma-convergence. Then, in 2002, a rigidity theorem proved by Friesecke, James and Muller and this theorem made it possible for researchers to justify a hierarchy of 2d theories. In this talk, I will start with the brief history, then introduce the basic tool Gamma-convergence and its fundamental property, finally I will present the rigidity theorem and if time permitted, I will also show the key points of the proof.
|
| November 7 |
Yi Wang |
TBA
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| |
I will talk about the problems of denoising images corrupted by impulsive noise and blind inpainting (i.e., inpainting when the deteriorated region is unknown). Our basic approach is to model the set of patches of pixels in an image as a union of low dimensional subspaces, corrupted by sparse but perhaps large magnitude noise. For this purpose, we develop a robust and iterative RANSAC like method for single subspace modeling and extend it to an iterative algorithm for modeling multiple subspaces. I will also cover the convergence for both algorithms and demonstrate state of the art performance of our method for both imaging problems.
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| November 14 |
Xingjie Li |
Sharp Stability Estimation of Fully Atomistic and the Quasicontinuum Embedded Atom Model
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| November 21 |
Dario Valdebenito |
Fractional Laplacian and a non-Lipschitz nonlinearity
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| |
In this talk we study the equation
(-\Delta)^\alpha u=u^p-u^q in R^N, u>0,
where 0 |
| November 28 |
Patrick Campbell |
s
Extracurricular Excursions in Computer Vision
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| |
I will talk about a couple of peripheral projects that I'm working on.
1) Modeling the retina with a webcam and the programming language Erlang. Trevor Bain, Jonas Karlsson and I started this project last summer.
2) An iPhone app that a couple of high school students are making with me to use phones camera to measure distances.
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| December 5 |
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No Junior Colloquium this week
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