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Discrete CATS Seminar--Dissertation Defense--Clifford Taylor

Title:  Deletion-Induced Triangulations

Abstract:   Let $d > 0$ be  a fixed integer and let $\A \subseteq \mathbb{R}^d$ be a collection of $n \geq d+2$ points which we lift into $\mathbb{R}^{d+1}$. Further let $k$ be an integer satisfying $0 \leq k \leq n-(d+2)$ and assign to each $k$-subset of the points of $\A$ a (regular) triangulation obtained by deleting the specified $k$-subset and projecting down the lower hull of the convex hull of the resulting lifting. Next, for each triangulation we form the characteristic vector outlined by Gelfand, Kapranov, and Zelevinsky by assigning to each vertex the sum of the volumes of all adjacent simplices. We then form a vector for the lifting, which we call the compound GKZ-vector, by summing all the characteristic vectors. Lastly, we construct a polytope $\Sigma_k(\A) \subseteq \mathbb{R}^{| \A |}$ by taking the convex hull of all obtainable compound GKZ-vectors by various liftings of $\A$, and note that $\Sigma_0(\A)$ is the well-studied secondary polytope corresponding to $\A$. We will see that by varying $k$, we obtain a family of polytopes with interesting properties relating to Minkowski sums, Gale transforms, and Lawrence constructions, with the member of the family with maximal $k$ corresponding to a zonotope studied by Billera, Fillamen, and Sturmfels. We will also discuss the case $k=d=1$, in which we can outline a combinatorial description of the vertices allowing us to better understand the graph of the polytope and to obtain formulas for the numbers of vertices and edges present.

Date:
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Location:
POT 745
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Mathskeller Open House

 

With new renovations completed over the 2014-15 winter break, the UK Mathskeller unveiled its new look at an open house on Wednesday, March 4, 2015 - hosted by the Department of Mathematics and College of Arts and Sciences, in room 63 in the basement of the White Hall Classroom Building. 

Opened in 2001 with 20 computers and a large printing budget, the Mathskeller, a computing and mathematics learning center managed by the Department of Mathematics and the Mathematical Sciences Computing Facility, was established to implement a technology-assisted instructional model. Fourteen years later, the center is home to only four computers, printers aren't used nearly as much, and the facility looks nothing like a basement classroom.

Instead, the center resembles a modern, collective learning space. And while there may be fewer wires and less printing, technology still has a leading role at the center.

Today's students, at least UK students utilizing the revitalized Mathskeller, are also taking advantage of the multiple mobile workspaces, bright LED-lit atmosphere, comfortable seating, tutors and chalkboard-lined walls. The renovated Mathskeller still features a kitchenette and group study or meeting room, and has added more storage, new carpet, additional study tables by removing a closet, and even a new computerized sign-in method. 

>>View a photo album of the renovations

Date:
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Location:
CB 63, White Hall Classroom Building basement
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Celebration of Mind

 

Have you heard of M.C. Escher? Origami?

The widespread popularity of these and many other intellectual staples of popular culture is largely due to one man: Martin Gardner.
 
He is said to have created more mathematicians than any other person in history, through his numerous books and long-running recreational math column in Scientific AmericanWidely revered among mathematicians, Gardner passed away in 2010. However his influence and legacy continue to inspire us to approach seemingly intractable problems from unconventional angles.
 
"Gardner's greatest skill was his ability to communicate complex mathematical ideas to the layperson," said math graduate student Cyrus Hettle. "His books and especially his long-running column in Scientific American are full of ideas that are central to modern mathematics, but Gardner – whose mathematical education never went beyond calculus – made them accessible to anyone with a high school mathematics education." 
 
"Gardner also presented mathematics in a truly multidisciplinary way. Not only did he explain mathematics using puzzles, games, and magic tricks, he found mathematics and mathematical ideas in poetry and art," Hettle explained.
 
The Celebration of Mind is an international celebration of Gardner, who would have turned 100 this year. "This is the fourth Celebration of Mind at UK, and I'm excited to be a part of this global event," said Hettle, who is heading up this year's festivities.
 
There are over 80 events worldwide, on every continent except Antarctica. UK's event will be on Monday, November 3, from 4:45 to 5:45 p.m. at the Math House. Refreshments will be served, as well as confections for the mind - all the mathematical games, puzzles, and magic tricks one can imagine to honor the contributions of Gardner.
 
Faculty, students, and all others with an interest in mathematics are invited to attend!
 
For more information, contact Cyrus Hettle at cyrus.h@uky.edu
 
Also check out the International Celebration of Mind website at celebrationofmind.org.
Date:
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Location:
Math House, 654 Maxwelton Ct
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2015 van Winter Memorial Lecture

TItle: "The Master's Hand" Can image analysis detect the hand of the Master? 

Abstract:  The talk will describe wavelets, a mathematical tool used for the analysis and compression of images (including for digital cinema).Then it will go on to discuss how they have been used recently for the study of paintings by e.g. Van Gogh, Goossen van der Weyden, Gauguin, and Giotto.

About the speaker: Professor Daubechies obtained her Ph.D. in theoretical physics in 1980, and worked at the Vrije Universiteit Brussel until 1987. At the Courant Institute of Mathematical Sciences in New York, she made her best-known discovery: based on quadrature mirror filter-technology, she constructed compactly supported continuous wavelets that would require only a finite amount of processing. This breakthrough enabled wavelet theory to enter the realm of digital signal processing.

In July 1987, Dr. Daubechies joined the AT&T Bell Laboratories' New Jersey facility at Murray Hill. From 1994 to 2010, Dr. Daubechies was a Professor of Mathematics at Princeton University where she directed the Program in Applied and Computational Mathematics. She was the first female full Professor of Mathematics at Princeton. Dr. Daubechies currently works as a James B. Duke Professor of Mathematics at Duke University.

Professor Daubechies received the Louis Empain Prize for Physics in 1984. In 1994, she received the American Mathematical Society (AMS) Steele Prize for Exposition for her book “Ten Lectures on Wavelets”, and gave a plenary lecture at the International Congress of Mathematicians in Zurich. In 1997, she was awarded the AMS Ruth Lyttle Satter prize. Professor Daubechies was elected to the United States National Academy of Sciences in 1998. In 2000, Professor Daubechies became the first woman to receive the National Academy of Sciences Award in Mathematics for excellence in published mathematical research. In 2006 she was the Emmy Noether Lecturer at the San Antonio Joint Mathematics Meetings. She won 2012 BBVA Foundation Frontiers of Knowledge Award in the Basic Sciences category (jointly with David Mumford) and the 2012 Nemmers Prize in Mathematics from Northwestern University. She was the first woman president of the International Mathematical Union (2011- 2014).

Additional information is available at www.math.uky.edu/van-winter

Photo credit of Ingrid Daubechies - David von Becker

Date:
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Location:
Chemistry-Physics 155
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