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February 2017

Owen Coss, NC State, “Computing real equilibria of the Kuramoto model “

February 21, 2017 | 3:30 pm - 4:30 pm EST

The Kuramoto model is used to describe synchronization behavior of a large set of oscillators. The equilibria of this model can be computed by solving a system of polynomial equations using algebraic geometry. Typical methods for solving such polynomial systems…

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March 2017

Bernd Sturmfels, University of California, Berkeley, “Gaussian mixtures and their tensors”

March 28, 2017 | 3:30 pm - 4:30 pm EDT

Mixtures of Gaussians are ubiquitous in data science. We give an introduction to the geometry of these statistical models, with focus on the tensors that represent their higher moments. The familiar theory of rank and borderrank for symmetric tensors is…

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April 2017

Wen-Shin Lee, University of Antwerp, “Sparse interpolation, Padé approximation, signal processing, and tensor decomposition”

April 11, 2017 | 3:30 pm - 4:30 pm EDT

A mathematical model is called sparse if it is a combination of only a few non-zero terms. The aim of sparse interpolation is to determine both the support of the sparse linear combination and the coefficients in the representation, from…

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Rainer Sinn, Georgia Tech, “Pythagoras numbers of real projective varieties”

April 18, 2017 | 3:30 pm - 4:30 pm EDT

The Pythagoras number of field F, studied in the theory of quadratic forms, is the smallest k such that every sum of squares in F is a sum of k squares. We will reinterpret this definition for coordinate rings of…

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Michael Burr, Clemson

April 25, 2017 | 3:00 pm - 4:00 pm EDT

September 2017

Erdal Imamoglu, NC State, Algorithms for Solving Linear Differential Equations with Rational Function Coefficients

September 19, 2017 | 4:30 pm - 5:30 pm EDT

We present two algorithms for computing hypergeometric solutions of a second order linear differential equation with rational function coefficients. Our first algorithm uses quotients of formal solutions, modular reduction, Hensel lifting, and rational reconstruction. Our second algorithm first tries to…

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November 2017

Wen-shin Lee, University of Antwerp, Belgium, Identification problem in exponential analysis

November 7, 2017 | 4:30 pm - 5:30 pm EST

The Blahut/Ben-Or/Tiwari sparse interpolation algorithm from computer algebra is closely related to Prony’s method for exponential analysis. In this talk, we focus on some challenges in exponential analysis. Estimating the spectral information of an exponential sum plays an important role in many signal…

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Gleb Pogudin, Courant Institute of Mathematical Sciences, Algorithms for Checking Global Identifiability

November 14, 2017 | 4:30 pm - 5:30 pm EST

The following situation arises in modeling: one has a system of differential equations with parameters and wants to determine the values of these parameters measuring unknown functions (assuming that perfect noise-free measurements are possible). Usually, some of the unknown functions…

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December 2017

Yang Qi, University of Chicago, On approximations and decompositions of a general tensor

December 5, 2017 | 4:30 pm - 5:30 pm EST

Tensors are closely related to secant varieties. In fact, the affine cone of the $r$th secant variety of the Segre variety is the set of tensors whose border rank is less than or equal to $r$. Similarly, we have a…

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January 2018

Deane Yang, New York University, Introduction to Convex Geometry and Brunn-Minkowski Theory

January 31, 2018 | 10:40 am - 11:30 am EST

Convex geometry is the study of convex bodies in Euclidean space. Despite the apparent simplicity of such objects, they are a source of many deep mathematical discoveries and mysteries. This talk will present a survey of Brunn-Minkowski theory, which is…

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February 2018

Harm Derksen, University of Michigan, Matrix Invariants and Complexity

February 19, 2018 | 3:00 pm - 4:00 pm EST

We consider the action of the group SL_n x SL_n on the space of m-tuples of n x n matrices by simultaneous left-right multiplication. Visu Makam and the speaker recently proved that invariants of degree at most mn^4 generate the invariant ring. This…

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April 2019

Jeaman Ahn, Kongju National University, Multivariate Hermite Interpolation via Explicit Groebner Basis

April 9, 2019 | 4:30 pm - 5:20 pm EDT

Multivariate Hermite interpolation problem asks to find a "small" polynomial that has given values of several partial derivatives at given points. It has numerous applications in science and engineering. Thus, naturally, it has been intensively studied, resulting in various beautiful ideas and techniques.  One…

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Aida Maraj, University of Kentucky, Quantitative Properties of Ideals arising from Hierarchical Models

April 16, 2019 | 4:30 pm - 5:30 pm EDT

We will discuss hierarchical models and certain toric ideals as a way of studying these objects in algebraic statistics. Some algebraic properties of these ideals will be described and a formula for the Krull dimension of the corresponding toric rings…

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John Perry, University of Southern Mississippi, The dynamic approach to Gröbner basis computation

April 23, 2019 | 4:30 pm - 5:30 pm EDT

Most algorithms to compute a Gröbner basis are “static”, inasmuch as they require as input both a set of polynomials and a term ordering, and preserve the term ordering throughout the computation.  This talk presents ongoing work on “dynamic” Buchberger…

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