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Tao Pang, NCSU, Some Topics on Financial Mathematics
SAS 1102Several topics will be presented in this talk. In the first part, we consider some portfolio optimization problems with stochastic dividends, stochastic volatility or delays. The Hamilton-Jacobi-Bellman (HJB) equations are derived, which are second order nonlinear PDEs. We then establish the existence results of the HJB equations and prove the verification theorems. In the second…
Grey Ballard, Wake Forest University, Tensor Decompositions for Multidimensional Data Analysis
SAS 4201An increasing number of scientific and enterprise data sets are multidimensional, where data is gathered for every configuration of three or more parameters. For example, physical simulations often track a set of variables in two or three spatial dimensions over time, yielding 4D or 5D data sets. Tensor decompositions are structured representations of multidimensional data…
Allison Miller, UT Austin, Winding number of satellite operators and concordance
SAS 4201Historically, the study of the collection of concordance classes of knots has focused on understanding its group structure while devoting relatively little attention to the natural metric induced by the 4-genus. Cochran and Harvey investigated the metric properties of the maps on concordance induced by satellite operators, asking when two patterns P and Q are of bounded distance in their…
Antonio Marigonda, University of Verona, Italy, Sovereign debt management problem with currency devaluation
SAS 4201We propose a model of sovereign debt management, where a state trade some bonds to service the debt with a pool of risk-neutral competitive foreign investors. At each instant of time, the government decides which fraction of the GDP (subject to random fluctuations) must be used to repay the debt, by paying a social cost.…
Michael Ruddy, NC State, What is Inquiry-Based Learning?
SAS 1102There is an increased interest in alternatives to the traditional lecture-based instruction in math courses. Inquiry-Based Learning (IBL) is a teaching philosophy that challenges students to think more like mathematicians by posing questions rather than presenting established facts. In this talk, I will start by introducing some of the core tenets of IBL. I will…
Cynthia Vincent, NC State, Convex sets and the geometry of numbers
Quite a large polygon can squeeze between the integer points in the plane, but what if it has to be symmetric bout the origin (and avoid all other integer points)? In this talk, I’ll discuss Minkowski’s theorem, which bounds the area of such shapes, and a surprising consequence for the problem of writing integers as sums of squares of other…
Seth Sullivant, NC State, Algebraic Statistical Models in Phylogenetics
SAS 4201Phylogenetics is the branch of mathematical biology concerned with constructing evolutionary relationships between collections of species. These lectures will introduce these models, in particular emphasizing the ways that algebraic statistics can be used to analyze properties of the models. Viewed from the perspective of algebraic statistics, the corresponding algebraic varieties that arise are often familiar…
Nathan Reading, NC State, To scatter or to cluster?
SAS 4201Scattering diagrams arose in the algebraic-geometric theory of mirror symmetry. Recently, Gross, Hacking, Keel, and Kontsevich applied scattering diagrams to prove many longstanding conjectures about cluster algebras. Scattering diagrams are certain collections of codimension-1 cones, each weighted with a formal power series. In this talk, I will introduce cluster scattering diagrams and their connection to cluster algebras, focusing on rank-2 (i.e.…
Tea and Cookies
SAS 4104John Lowengrub, University of California, Irvine, BioDDFT: A hybrid continuum-discrete mechanical collective cell model
SAS 4201The regulation of cell division, cell sizes and cell arrangements is central to tissue morphogenesis. To study these processes, we develop a mechanistic hybrid continuum-discrete mathematical model of cell dynamics that has advantages over previous approaches. This model borrows ideas from statistical physics, materials science and applied mathematics and follows the framework of dynamic density…
Wilkins Aquino, Duke University, A Locally Adapted Reduced Basis Method for Solving Risk-Averse PDE-Constrained Optimization Problems
SAS 4201The numerical solution of large-scale risk-averse PDE-constrained optimization problems requires substantial computational effort due to the discretization in physical and stochastic dimensions. Managing the cost is essential to tackle such problems with high dimensional uncertainties. In this work, we combine an inexact trust-region (TR) algorithm from with a local, reduced basis (RB) approximation to efficiently solve risk-averse optimization problems…
Jennifer Hom, Georgia Tech, Heegaard Floer and homology cobordism
SAS 4201We study applications of Heegaard Floer homology to homology cobordism. In particular, to a homology sphere Y, we associate a module HF_conn(Y), called the connected Heegaard Floer homology of Y, and show that this module is invariant under homology cobordism and isomorphic to a summand of HF_red(Y). The definition of this invariant relies on involutive…
Elmas Irmak, University of Michigan, Simplicial Maps of Complexes of Curves and Mapping Class Groups of Surfaces
SAS 4201I will talk about recent developments on simplicial maps of complexes of curves on both orientable and nonorientable surfaces. I will also talk about joint work with Prof. Luis Paris. We prove that on a compact, connected, nonorientable surface of genus at least 5, any superinjective simplicial map from the two-sided curve complex to itself is induced…
Daniel Bernstein, NC State, Unimodular hierarchical models
The Zariski closure of a discrete log-linear statistical model is a toric variety. In the last twenty years, this fact has lead not only to the development of useful algorithms for working with data, but developments in algebraic geometry and combinatorics as well. I will discuss a particular subset of the discrete log-linear models known…
What is IBL? (part 2)
SAS 1102We'll start with a panel of graduate instructors currently experimenting with IBL methods in their courses. We will then discuss and brainstorm ways to effectively get students to share their answers and ideas during lecture. For those that missed the first session, the following article gives an introduction to IBL: http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html
Let’s Talk IT: Moodle
SAS 4201Chris from DELTA will be leading an interactive seminar on what Moodle is, a jump start, and answering any questions you have for the platform and it's capabilities. You'll have the opportunity to go hands on with them as they walk you through the platform. Regardless of your experience with Moodle, I encourage you to…
Gabor Pataki, UNC-Chapel Hill, Bad semidefinite programs, linear algebra, and short proofs
SAS 4201Semidefinite programs (SDPs) -- optimization problems with linear constraints, linear objective, and semidefinite matrix variables -- are some of the most useful, versatile, and pervasive optimization problems to emerge in the last 30 years. They find applications in combinatorial optimization, machine learning, and statistics, to name just a few areas. Unfortunately, SDPs often behave pathologically: the optimal values of the primal…