Colloquium

Speaker: Maddie Weinstein (Stanford University)

"Metric Algebraic Geometry"

Time: 15:00 - 16:00

Room: MC 107

A real algebraic variety is a set of points in real Euclidean space that satisfy a system of polynomial equations. Metric algebraic geometry is the study of properties of real algebraic varieties that depend on a metric. In this talk, we introduce metric algebraic geometry through a discussion of Voronoi cells, bottlenecks, and the reach of an algebraic variety. We describe applications to the study of the geometry of data with nonlinear models and to low-rank matrix approximation.

Colloquium

Speaker: Anibal Medina-Mardones (Universite Sorbonne Paris Nord)

"New tools in applied topology for signal processing and data analysis"

Time: 15:00 - 16:00

Room: MC 107

We introduce two novel applied topology techniques to address real-world problems in different fields. The first, used in information theory for the study of complex systems, is a principled compression method of higher order signals obtained from a combinatorial version of the Laplace-Beltrami operator. The second, used for the study of conformation spaces of molecules, is an enhancement of the traditional persistent homology pipeline obtained from recent developments in the effective construction of cohomology operations.

Colloquium

Speaker: Aida Maraj (University of Michigan)

"Interactions of Algebra with Statistics and Formal Language Theory"

Time: 15:00 - 15:50

Room: MC 107 and zoom

Algebraic statistics identifies probability distributions with points and studies equations vanishing on these points. The first half of the talk will be on algebraic approaches to discrete and Gaussian models, with focus on when they have a toric structure. We will also briefly discuss the maximum likelihood degree of such models. The second part will concern analyzing quantitative and qualitative data of algebraic objects in the infinite setting, with a view toward applications. To do so, we will ask for an unusual involvement of formal languages and finite automata.

Transformation Groups Seminar

Speaker: Kumar Shukla (Western)

"Loop spaces of topological spaces"

Time: 10:30 - 12:00

Room: MC 107

Talk 1 of the learning seminar on Pontryagin rings in toric topology.