Title:  On Certain Convex Sets of Measures and on Phases of Reacting Mixtures.

Abstract:  In the 1970's, Walter Noll developed a modern version of the elements of Gibbsian thermostatics for describing the equilibrium of mixtures. In this talk, we will see how we can use mathematical tools to explain why Gibbs said "it does not seem probable that r can ever exceed n+2" where n stands for number of components in a mixture and r stands for the number of coexistent phases. We will also exploit some other properties of a mixture when a it is in equilibrium.

Title:  On the flag enumeration of the subspace lattice

Abstract:   We consider the q-analogue of the Boolean algebra: the lattice of subspaces of an n-dimensional vector space over the finite field of q elements. The quasi-symmetric function (Ehrenborg, 1996) of this lattice encodes the flag f-vector which is the multinomial Gaussian coefficients. We express the quasi-symmetric function using quasi-symmetric functions in variables that q-commute, which can be seen as an extension of the q-binomial theorem. All the expressions of q are in fact polynomials in this variable. Hence it is natural to evaluate these expressions for other values than prime powers. When setting q to be a root of unity we obtain a version of the cyclic sieving phenomenon (due to Reiner, Stanton and White, 2004) of the Boolean algebra on the subspace lattice. Finally, we present applications of the ab-index on the subspace lattice to a descent set statistic on permutations, which is a q-analogue of the classical descent set statistic evaluated using the inversion statistics of the permutations with given descent set. When we evaluate the flag h-vector of the subspace at a primitive kth root of unity, all of the values are real when k divides n or n-1. Furthermore, when k divides n we are able to determine the extreme values, extending results of De Bruijn (1970) and Niven (1968). When k divides n-1 we are able to express certain entries of the vector in terms of the descent set statistic.

Title:  Not all Simplicial Polytopes are Weakly Vertex-Decomposable

Abstract:  The Simplex Method solves linear programs by testing adjacent vertices in the feasible set (a polytope) in sequence such that each new vertex in the sequence improves or stays the same with respect to the objective function. It is natural to ask how long the Simplex Method could take to solve a given linear program. Stating this in the language of polytopes, we would like to find a bound on the diameter of d-dimensional polytopes with a fixed number of vertices, say n. In 1980, Billera and Provan defined the notions of k-decomposability and weak k-decomposability for simplicial complexes and computed bounds on the diameter of complexes admitting such decompositions. In particular, these bounds become linear in n and d when k=0. Hence, it is reasonable to ask if all simplicial complexes admit such a decomposition. In 2010, De Loera and Klee identified a simple transportation polytope in each dimension greater than three whose dual polytope is not weakly vertex-decomposable. We will introduce the notion of weak k-decomposability and transportation polytopes, and then we will see why the family of polytopes constructed by De Loera and Klee fail to be weakly vertex-decomposable.

To celebrate this day, we will be showing the film "A Class Apart."

Se mostrará la película "A Class Apart."

If the place where one lives is the site where sustainability should begin, the driving question of any serious sustainability project or program is: how do you get there from here? That is the ultimate question of my forthcoming co-authored book. Using detailed case studies of seven North American urban sustainability programs, my presentation will focus on the political agencies shaping them and the structural elements either impeding or facilitating these efforts. To accomplish this task, I will utilize three theories of urban power-growth coalition, urban regime, and neo-Gramscian models--to explore the dynamics of power and politics to better understand these cases and examine the requirements for building sustainable cities that can become practical utopias on terra firma.



Dr. Yanarella is a Professor and the Chair of the Political Science Department. His primary teaching and research interests include critical policy studies of the energy and environment, agricultural and ecological policy, and national security and arms control. He serves as the Associate Director of the Center for Sustainable Cities. Dr. Yanarella's teaching and research interests align well with the mission of the Environmental and Sustainability Studies Program, and his experience as an administrator provide valuable guidance to the program.



For more information, contact Bob Sandmeyer (bob.sandmeyer@uky.edu) at (859) 257-7749

Please see the conference website at http://math.as.uky.edu/scattering-and-inverse-scattering-multidimensions for conference details and registration information.

Title:  Constructing ideals with large projective dimension

Abstract:  Projective dimension is a homological measure of the complexity of algebraic objects. Motivated by computational considerations, M. Stillman asked for upper bounds on the projective dimension of homogeneous ideals in polynomial rings, based solely on invariants of the ideal, not of the ambient ring. In this talk, we discuss several constructions that shed some light on what ideal invariants can or cannot be used to bound projective dimension and we give  lower bounds on any possible answer to Stillman's question. The talks is based on joint work with Huneke-Mantero-McCullough and Beder-McCullough-Nunez-Snapp-Stone.

Jana Morgan, Ph.D, comes from the University of Tennessee as WIPS' featured speaker this spring semester. Her research involves issues of inequality, exclusion and representation. Mainly, she focuses on exploring how economic, social and political inequalities affect marginalized groups and undermine democratic institutions and outcomes. She will be presenting her latest work titled: "Patterns of Inequality and Latin American Support for Redistribution."

The axion is a well-motivated dark matter candidate, but is challenging to search for. We propose a new way to search for QCD axion and axion-like-particle (ALP) dark matter. Nuclei that are interacting with the background axion dark matter acquire time-varying CP-odd nuclear moments such as an electric dipole moment. In analogy with nuclear magnetic resonance, these moments cause precession of nuclear spins in a material sample in the presence of a background electric field. This precession can be detected through high-precision magnetometry. With current techniques, this experiment has sensitivity to axion masses below 10^-9 eV, corresponding to theoretically well-motivated axion decay constants around the grand unification and Planck scales. With improved magnetometry, this experiment could ultimately cover the entire range of masses below 10^-6 eV, just beyond the region accessible to current axion searches. A discovery in such an experiment would not only reveal the nature of dark matter and confirm the axion as the solution of the strong CP problem, but would also provide a glimpse of physics at the highest energy scales, far beyond what can be directly probed in the laboratory.

Abstract: One of the best-motivated classes of dark-matter candidate is the Weakly-Interacting Massive Particle (WIMP). In this talk, I will discuss WIMPs in the context of direct-detection experiments. First, I will discuss a new signal for WIMP dark matter: gravitational focusing in direct-detection experiments. This effect leads to an energy-dependent phase-shift in the peak direct-detection event rate throughout the year. I will discuss this in light of current putative annual-modulation claims. Second, I will discuss what we can learn about WIMPs in the "early-discovery" days once WIMPs are conclusively found in direct-detection experiments. I will show that what we can learn about WIMPs depends sensitively on the ensemble of experiments that are running at the time of discovery.