The 21st century has seen a boom in the production of data as well as methods to analyze data. One such methodology is Topological data analysis (TDA), where concepts from topology are used to infer the patterns underlying data sets. I will provide a basic and accessible introduction to persistent homology, a common type of TDA that is…
We discuss the reasons for the introduction of Valuation Adjustments as a consequence of the financial crisis of 2007-9. We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a defaultable counterparty. The investor does not know the expected rate of return of the counterparty bond, but…
Kornelia Bastin, OR PhD Student People are faced with an overwhelming amount of news, only some of which comes from credible sources and is fact verified. The main idea behind this project is to address such issues. The scope of work includes creating an accessible and efficient method for members of the public to get…
Sandia National Laboratories is a federally funded research and development center that develops and applies science, technology, and engineering solutions for pressing national security challenges. Mathematics at all levels of rigor underpins every aspect of the work we do, and Sandians with academic degrees in applied mathematics impact a wide range of areas such as…
Topological Data Analysis (TDA) is a relatively young field in both algebraic topology and machine learning. Tools from TDA, in particular persistent homology, have proven successful in many scientific disciplines. Persistence diagrams, a typical way to study persistent homology, contain fruitful information about the underlying objects. However, performing statistical methods directly on the space of persistence diagrams is…
Email Jordan at jemassa@sandia.gov your resume and availibility.
Elliptic integrands are used to model anisotropic energies in variational problems. These energies are employed in a variety of applications, such as crystal structures, capillarity problems and gravitational fields, to account for preferred inhomogeneous and directionally dependent configurations. After a brief introduction to variational problems involving elliptic integrands, I will present an overview of the…
Kitware researchers Dr. Rachel Clipp and Dr. Matt Brown will talk about their transition from academic research to R&D at a private company as well as some of their active projects. Kitware is a software research and development company with expertise in computer vision, data and analytics, high-performance computing and visualization, medical computing, and software…
Experts have long realized the parallels between elliptic and parabolic theory of partial differential equations. It is well known that elliptic theory may be considered a static, or steady-state, version of parabolic theory. And in particular, if a parabolic estimate holds, then by eliminating the time parameter, one immediately arrives at the underlying elliptic statement.…
Imagine tying up your shoelaces into a knot. How can we measure the difficulty of unknotting this mess? In this talk, we will study mathematical knots and various measurements of their complexity with a view towards efficient unknotting. This talk should be accessible to all undergraduates.
Hierarchical models are statistical log-linear models that record the dependency relations among random variables in statistics. Diaconis and Sturmfels in '98 propose using ideals to study these models. I will start by introducing hierarchical models and their ideals. In this talk we'll show that studying an entire family of ideals simultaneously can lead to greater insight than studying them individually. No…
The NCSU Counseling center will provide a training for graduate students and the department for suicide prevention, using the QPR methodology. As members of the campus educational community, it is important for all of us to support the mental health of our students. The training will introduce important campus resources.
Triangle Lectures in Combinatorics Saturday, November 16, 2019 Lecture Hall: SAS Hall, Room 1102 North Carolina State University Raleigh, North Carolina The Triangle Lectures in Combinatorics (TLC) is a series of combinatorial workshops held each semester on a Saturday in the Research Triangle region of North Carolina, funded by the National Science Foundation. The workshop just under two…
Differential games, as an offspring of game theory and optimal control, provide the modeling and analysis of conflict in the context of a dynamical system. Computing Nash equilibria is one of the core objectives in differential games, with a major bottleneck coming from the notorious intractability of N-player games, also known by the curse of…
A group G is called coherent if every finitely generated subgroup of G is finitely presented. This is a property enjoyed by the fundamental groups of 3-manifolds, and it is deeply related to the geometry of the group. We show that free-by-free groups satisfying a particular homological criterion are incoherent. This class is large in…