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Today

Nathan Reading, NC State, To scatter or to cluster?

SAS 4201

Scattering 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.…

John Lowengrub, University of California, Irvine, BioDDFT: A hybrid continuum-discrete mechanical collective cell model

SAS 4201

The 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 4201

The 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 4201

We 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 4201

I 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 1102

We'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 4201

Chris 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 4201

Semidefinite 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…

Weiwei Hu, Oklahoma State University, An Approximating Control Design for Optimal Mixing by Stokes Flows

SAS 4201

We consider an approximating control design for optimal mixing of a non-dissipative scalar eld in unsteady Stokes ows. The objective of our approach is to achieve optimal mixing at a given nal time, via an active control of the ow velocity through boundary inputs. Due to the zero diusivity of the scalar eld, establishing the well-posedness of its…

Zack Morrow, NC State, SIAM Student Chapter Tutorial Series, Sparse methods for high-dimensional problems

SAS 2235

In full-tensor extensions of 1D interpolation or quadrature rules, the number of nodes will grow exponentially in the dimension—commonly called the “curse of dimensionality.” In this talk, we present an overview of sparse grids, in which the number of nodes grows only polynomially in the dimension. First, we will do an overview of 1D interpolation for…

Michael Overton, NYU, Nonsmooth, Nonconvex Optimization: Algorithms and Examples

SAS 1102

In many applications one wishes to minimize an objective function that is not convex and is not differentiable at its minimizers.  We discuss two algorithms for minimization of nonsmooth, nonconvex functions.  Gradient Sampling is a simple method that, although computationally intensive, has a nice convergence theory.  The method is robust and the convergence theory has…

Radmila Sazdanović to speak at Coffee and Viz Series

James B. Hunt Jr. Library at Centennial Campus

Radmila Sazdanović will speak at the Coffee and Viz series in the Teaching and Visualization Lab, James B. Hunt Jr. Library on Friday March 16, 9:30-10:30 am about Visual Mathematics: the role of visualizations in math research.

Michael L. Overton, NYU Courant, Numerical Investigation of Crouzeix’s Conjecture

SAS 4201

In many applications one wishes to minimize an objective function that is not convex and is not differentiable at its minimizers.  We discuss two algorithms for minimization of nonsmooth, nonconvex functions.  Gradient Sampling is a simple method that, although computationally intensive, has a nice convergence theory.  The method is robust and the convergence theory has…