Welcome to the webpage of our seminar. Your organizers are Carlos Amendola, Eliana Duarte and Thomas Kahle.
Here’s our line-up:
Next: May 25, 2023
- Location: 🔴 MPI-MiS Leipzig 🔴 (changed)
- Morning: Algebraic Statistics Reading Group special session
- 1:30 pm: Simon Telen
- Title: Toric varieties and Gibbs Manifolds in Convex Optimization
- Abstract: Entropic regularization for linear programming leads to intersecting a toric variety with the feasible polytope. In semidefinite programming, the toric variety is replaced by a new geometric object, called Gibbs manifold, and the feasible polytope becomes a spectrahedron. I will explain these concepts and present the example of (quantum) optimal transport. This is based on joint work with Dmitrii Pavlov, Bernd Sturmfels, François-Xavier Vialard and Max von Renesse.
Outlook
Past events
- April 24, 2023, 1:30pm at MPI-MiS Leipzig
- Speaker Lior Pachter (CalTech)
- Title: The chemical master equation and its application to genomics
- Abstract: Chemical master equations (CMEs) are of great interest in systems biology where they are used to model transcriptional dynamics. I will explain how CMEs arise naturally in attempts to interpret and analyze single-cell genomics data, and then survey some of interesting mathematics and statistics questions that emerge as a result.
- March 13, 2023 at MPI-MiS Leipzig
- Location: MPI-MiS Leipzig
- Time: 10:00 am
- Speaker: Jane Coons (U Oxford)
- Title: Rational partition models under iterative proportional scaling
- Abstract: The classical iterative proportional scaling algorithm,
or IPS, numerically computes the maximum likelihood estimate of a
given vector of counts for a log-linear partition model. We
investigate the conditions under which IPS produces the exact
maximum likelihood estimate, or MLE, in finitely many steps. Since
IPS produces a rational function at each step, a necessary
condition is that the model must have rational maximum likelihood
estimator. However, the convergence is highly
parametrization-dependent; indeed, one parametrization of a model
may exhibit exact convergence in finitely many steps while another
does not. We introduce the generalized running intersection
property, which guarantees exact convergence of IPS. As the name
suggests, this strictly generalizes the well-known running
intersection property for hierarchical models. This generalized
running intersection property can be understood in terms of the
toric geometry of the log-linear model, and models that satisfy
this property can be obtained by performing repeated toric fiber
products of linear ideals. We also draw connections between models
that satisfy the generalized running intersection property and
balanced, stratified staged trees.
- February 20, 2023 at TU Berlin
- Location: TU Berlin, Math Building, MA 608
- Time: 14:00 - 15:00
- Speaker: Paul Breiding (U Osnabrück)
- Title: Algebraic Compressed Sensing
- Abstract: We introduce the broad subclass of algebraic compressed
sensing problems, where structured signals are modeled either
explicitly or implicitly via polynomials. This includes, for
instance, low-rank matrix and tensor recovery. We employ powerful
techniques from algebraic geometry to study well-posedness of
sufficiently general compressed sensing problems, including
existence, local recoverability, global uniqueness, and local
smoothness.
- Notes: There will be a pretalk aimed at students taking place at 11:30-12:00 in MA 608, this
will be followed by lunch 12:15-13:45. At 17:30 we will walk to have dinner nearby. You are welcome to join!
- January 16, 2023, MPI-MiS Leipzig
- Speaker: Peter Stadler (U Leipzig)
- Title: Relational Data in Phylogentics
- Abstract: In the course of investigation evolutionary
relationships found in the genomes a set of species, several binary
relations appear. For example “best matches” refer pairs of genes x
and y so that y is one of the closest relatives of x in the species
that harbors y. Orthology designates pairs of genes whose last common
ancestor is a speciation event. Horizontal gene transfer is related to
the lower diverence time relation, satisfied by a pair of genes that
is younger than the divergence of the species in which they reside. I
will sketch the connections between the relations and the the
information that they convey about the gene trees, the phylogeny of
the underlying species, and the reconciliation of gene and species
trees.