mathematics

Discrete CATS Seminar--Dissertation Defense--Clifford Taylor

Date: 
Monday, April 13, 2015 - 2:00pm to 3:00pm
Location: 
POT 745
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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.

UK's Bagh Quoted in Wall Street Journal Story on NCAA Tournament Brackets

Adib Bagh, assistant professor in the departments of mathematics and economics at the University of Kentucky, was recently quoted in a March 16 Wall Street Journal article examining office bracket pools for the NCAA men's basketball tournament.

Shining a Light on Connections Between Worlds of Art and Science

The Art Museum at the University of Kentucky is hosting "Looking for Light: Chemistry, Art, Story, and Song," the third annual event of the Math, Arts, and Sciences Coalition (M.A.S.C.).

Planning Under Uncertainty: The NSF Grant with Josiah Hanna

In the summer of 2014, several undergraduate and graduate students from the College of Arts and Sciences received a grant from the National Science Foundation. This NSF grant gave them the means to pursue research in various fields as they explored their interests and prepared for their potential futures.In this podcast, Josiah Hanna, a recent graduate in Mathematics and Computer Science, tells us about his research interests and the impact that the NSF grant will have upon his future.

This podcast was produced by Casey Hibbard

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Planning Under Uncertainty: The NSF Grant with Josiah Hanna by UK College of Arts & Sciences is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Mathematics Names New Royster, Edwards Chairs

The University of Kentucky Department of Mathematics, within the College of Arts and Sciences, is proud to announce the appointment of Benjamin Braun to the Wimberly and Betty Royster Research Professorship, and Uwe Nagel to the Ralph E. and Norma L. Edwards Research Professorship.

Mathskeller Open House

Date: 
Wednesday, March 4, 2015 - 3:00pm to 4:30pm
Location: 
CB 63, White Hall Classroom Building basement
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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

Department of Mathematics awarded National Science Foundation Grant - "UK at the Half" with Carl Nathe

The Department of Mathematics within the College of Arts and Sciences was recently awarded a grant from the National Science Foundation. In this recent episode of "UK at the Half," which aired on Saturday during the UK vs. Texas A&M game, Nathe speaks with President Eli Capilouto, Elizabeth Lorch, and Peter Perry about how the NSF grant reflects the success of UK's past and ensures that future students will also have opportunities to grow and achieve. "UK at the Half" airs during halftime of each UK football and basketball game broadcast on the radio and is hosted by Carl Nathe of UK Public Relations and Marketing. 

Mathematics Receives More than $550,000 to Support Inclusive, Diverse Graduate Program

Reflecting the University of Kentucky's growing leadership in ensuring more diversity in graduate studies, President Eli Capilouto Friday announced that the university's Department of Mathematics, within the College of Arts and Sciences, has been awarded a $559,626 National Science Foundation grant to fund the new Graduate Scholars in Mathematics program.

UK Students Win Kentucky Academy of Science Research Competitions

Thirteen University of Kentucky students took home top honors at the Kentucky Academy of Science 100th Annual Meeting in November, including eight students in the College of Arts & Sciences.

Undergraduate Researchers Receive Oswald Awards

The University of Kentucky Office for Undergraduate Research has presented 17 students with the Oswald Research and Creativity Program awards.

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