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.

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

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

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 American. Widely 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.

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