The Association for Women in Mathematics (AWM) will be hosting a welcome event to kick off the beginning of the semester! We will talk a little bit about what our club is about and the types of events we will be hosting throughout the semester, and also play some ice breaker games so everyone can…
For models with high-dimensional input spaces, constructing accurate response surfaces can be prohibitively expensive. Additionally, the high-dimensionality of the parameter spaces can impact the computational cost of a parameter investigation. Using an active subspace construction, we can efficiently approximate complex models by constructing low-order response surfaces based on a smaller subspace of the high-dimensional parameter…
In June 23, 2006's "Science" magazine, Pendry et al and Leonhardt independently published their papers on electromagnetic cloaking. In Nov.10, 2006's Science magazine, Pendry et al demonstrated the first practical realization of such a cloak with the use of artificially constructed metamaterials. Since then, there is a growing interest in using metamaterials to design invisibility cloaks.…
The Association for Women in Mathematics (AWM) will be hosting our weekly brown bag lunch. Attendees bring their own lunches, and have the opportunity to be in a casual discussion environment, while we provide a tasty treat! AWM is NOT exclusively for women, and we would like to emphasize that everyone is welcome join us…
In the 1980’s Furuta and Fintushel-Stern applied the theory of instantons and Chern-Simons invariants to develop a criterion for a collection of Seifert fibred homology spheres to be independent in the homology cobordism group of oriented homology 3-spheres. These results, together with some 4-dimensional constructions can be used to show that iterated Whitehead doubles of positive…
A generic rectangulation is a tiling of a rectangle by rectangles, with no four rectangles sharing a single corner (think: no Arizona, Colorado, New Mexico and Utah). For example: We want to ignore lengths of edges and just look at the different configurations of rectangles. In this way of thinking, the rectangulations and are the…
Clustering is a fundamental unsupervised learning technique that aims to discover groups of objects in a dataset. Biclustering extends clustering to two dimensions where both observations and variables are grouped simultaneously, such as clustering both cancerous tumors and genes or both documents and words. In this work, we develop and study a convex formulation of the…
Modeling of fluid flows through porous deformable media is relevant for many applications in biology, medicine and bioengineering, including blood flow through human tissues and fluid flow inside cartilages and bones. These fluid-structure mixtures are described mathematically by nonlinear poro-visco-elastic systems in bounded domains, with mixed boundary conditions. In this talk, I will present well-posedness…
In this lecture we will present basis theoretical and algorithmic properties of Monte Carlo methods. In particular, their convergence properties and implementational simplicity will be highlighted. There are a variety of Monte Carlo methods but we will focus on two, namely, Monte Carlo integration and Markov Chain Monte Carlo. Prior knowledge of Monte Carlo methods…
Dehn surgery is a fundamental operation in three-manifold topology which turns a knot into a new three-manifold. We characterize Dehn surgeries between certain lens spaces and relate this to an elementary question in knot theory. This is joint work with Allison Moore.
Lie Algebras, manifolds, varieties. We have all heard terms like these, but may not know quite what they mean. This week we will have introductory "What Is?" talks. These talks are intended to build your vocabulary/intuition for future talks. This week we will hear about: Lie Algebras, Leibniz Algebras, Representations, Algebraic Varieties.
In the theory of Donaldson-Thomas invariants for quivers one finds identities for quantum dilogarithm series. The combinatorial interpretation of the simplest of these identities is equivalent to a clever way of counting partitions. The combinatorial interpretation of more involved dilogarithm identities is not known. In the talk we will explore the geometry (DT invariants), topology…
Nik Bravo: Title: Data-Driven Model Development and Feedback Control Design for PZT Bimorph Actuators Abstract: In the talk, we discuss the development of a high-fidelity and surrogate model for a PZT bimorph used as an actuator for micro-air vehicles including Robobee. The models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in…
Coupled array of Chua's circuits has been studied for many years. Some experimental and numerical study of traveling waves were conducted by Perez and Chua in 1993. Existence of periodic traveling waves were proved by S.-N. Chow, M. Jiang and X.-B. Lin in 2013. This talk is based on a joint work with F. Geng…
Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented 4-manifold X with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded 3-manifold Y representing a generator of H_3(X), a suitable version of the Heegaard Floer d invariant of Y, defined using twisted coefficients, is a diffeomorphism…