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Applied algebraic geometry
Welcome!
Welcome!
This is the information page for the online seminar for the non-linear algebra group of Sandra di Rocco and Kathlén Kohn
Practical information
Practical information
The webinar series has finished for now!
Talks
Talks
July 2nd 2020
July 2nd 2020
A calculus for monomials in Chow group A^{n-3}(n)
A calculus for monomials in Chow group A^{n-3}(n)
Speaker: Jiayue Qi
Speaker: Jiayue Qi
Description:
We introduce an algorithm for computing the integral value of all monomialsin the Chow group A^{n-3}(n).
jiayuetalk2.pdfJune 25th 2020
June 25th 2020
Discriminants: Algebra, Geometry and Combinatorics
Discriminants: Algebra, Geometry and Combinatorics
Speaker: Sandra di Rocco
Speaker: Sandra di Rocco
Abstract:
Abstract:
This talk will serve as a survey on how to view the concept of discriminants (of polynomials) algebraically (via polynomials), geometrically (via hyperplane sections) and combinatorially(via convex polytopes).The interplay relies on classic projective geometry, characteristic classes and convex and toric geometry.
TalkKTH.pdfJune 11th 2020
June 11th 2020
Title: Three Perspectives of Schiemann's theorem
Title: Three Perspectives of Schiemann's theorem
Speaker: Felix Rydell
Speaker: Felix Rydell
Seminar_Presentation (2).pdfJune 4th 2020
June 4th 2020
Title: Wasserstein distance to an algebraic variety
Title: Wasserstein distance to an algebraic variety
Speaker: Lorenzo Venturello
Speaker: Lorenzo Venturello
Abstract:
Abstract:
I will give a gentle introduction to the concept of Wasserstein distance between two discrete probability distributions, which recently gained popularity in the context of machine learning. In particular, I will focus on the distance between a distribution and a model when the latter is defined by polynomial equations (i.e., a variety). This involves the study of distances whose unit norm is a polytope, and hence it can be fun for people in algebraic geometry as well as in combinatorics.
This is joint work with Türkü Özlüm Çelik, Asgar Jamneshan, Guido Montúfar and Bernd Sturmfels.
Wasserstein_distance_Fika_webinar.pdfMay 29th 2020
May 29th 2020
A nice compactification of moduli space for n distinct points on projective line
A nice compactification of moduli space for n distinct points on projective line
Speaker: Jiayue Qi
Speaker: Jiayue Qi
Description:
We introduce an elementary construction of a nice compactification ofmoduli space for n distinct points on projective line. And we introduce some interesting combinatorics properties of it. Later we say that with the help of those properties, it can be proved that the compactification is smooth, and of dimension (n-3).
20200529.pdfMay 20th 2020
May 20th 2020
Title: Stability of steady states and positivity of polynomials in Chemical Reaction Networks.
Title: Stability of steady states and positivity of polynomials in Chemical Reaction Networks.
Speaker: Angélica Torres
Speaker: Angélica Torres
Abstract:
Abstract:
The dynamics of a Chemical Reaction Network can be modelled with a system of ordinary differential equations that, under mass action-kinetics, are polynomial. In this talk I will introduce these dynamical systems, and with some examples, I will show how studying the positivity of certain polynomials allows to determine the stability of equilibrium points.
Fika - Angélica Torres.pdfMay 14th 2020
May 14th 2020
Title: Computational complexity of learning algebraic varieities
Title: Computational complexity of learning algebraic varieities
Speaker: Oliver Gäfvert
Speaker: Oliver Gäfvert
cimat_talk.pdfMay 7th 2020
May 7th 2020
Title: Introduction to Metric Algebraic Geometry
Title: Introduction to Metric Algebraic Geometry
Speaker: Lukas Gustafsson
Speaker: Lukas Gustafsson
Description:
Finding critical points of a function subject to equality constraints is a classical optimization problem which in the general case is solved through the application of Lagrange multipliers. If the function and constraints are algebraic we may apply algebraic methods to the problem instead. An example of this is the Euclidean distance to a fixed point p, restricted to an algebraic variety. For a fixed variety, over the complex numbers, the number of such "distance"-critical points is constant for any choice of p (in some dense open subset of the ambient space). This is what is called the Euclidean Distance Degree (EDD). I will elaborate on the EDD and how these ideas might be applied within algebraic statistics and other areas.
metricAG.pdfApril 30th 2020
April 30th 2020
Title: Polynomials in Nonparametric Regression
Title: Polynomials in Nonparametric Regression
Speaker: Orlando Marigliano
Speaker: Orlando Marigliano
Description:
In this talk, I introduce the boundary regression problem in nonparametric statistics and discuss a solution based on approximation with polynomials.
polynomials-nonparametric-regression.pdfApril 23rd 2020
April 23rd 2020
Title: Compactifications of the moduli space of cubic surfaces
Title: Compactifications of the moduli space of cubic surfaces
Speaker: Luca Schaffler
Speaker: Luca Schaffler
Abstract:
Abstract:
In algebraic geometry, an algebraic variety is a geometric object defined by polynomial equations. The space of parameters for a family of algebraic varieties may also be an algebraic variety called moduli space. In this talk I will motivate the study of compactifications of moduli spaces focusing on the case of moduli of cubic surfaces. The original results concern the interplay between different compactifications of the family of cubic surfaces coming from Geometric Invariant Theory and the Minimal Model Program.
This is joint work with Patricio Gallardo and Matt Kerr.
Talk_KTH_cubic_surfaces.pdfApril 16th 2020
April 16th 2020
Title: Invariant Theory for Maximum Likelihood Estimation
Title: Invariant Theory for Maximum Likelihood Estimation
Speaker: Kathlén Kohn
Speaker: Kathlén Kohn
Abstract:
Abstract:
We give a broad introduction to Hilbert's null cone in invariant theory and maximum likelihood estimation in statistics. The latter is a method to find a probability distribution that best fits some empirical data. We build a bridge between invariant theory and statistics: First, we observe that many statistical models are parametrized by a group action. Second, for such models we explain that maximum likelihood estimation is equivalent to null cone membership testing.
This is joint work with Carlos Améndola, Philipp Reichenbach, and Anna Seigal.
InvTheoryMLEfinal.pdfPage updated
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