Geometry and Combinatorics

Speaker: Bill Trok (University of Kentucky)

"Very Unexpected Hypersurfaces"

Time: 14:30

Room: Zoom

Often in Algebraic Geometry linear systems will have an "expected dimension" which should hold most of the time, the problem then becomes to study when this expectation fails. In this talk we discuss a version of this problem. In particular we introduce the concept of a "very unexpected hypersurface" passing through a fixed set of points Z. These occur when Z imposes less than the "expected" number of conditions on the ideal sheaf of a generic linear subspace. We show in certain cases these can be characterized via combinatorial data and geometric data from the Hyperplane Arrangement dual to Z. We close by discussing relationships between this problem and certain motivating problems in Combinatorics, Matroid Theory and Hyperplane Arrangements.

Geometry and Topology

Speaker: Alexander Rolle (TU Graz)

"Multi-parameter persistence and density estimation"

Time: 11:30

Room: Zoom Meeting ID: 958 6908 4555

Multi-parameter persistent homology is an increasingly popular tool of topological data analysis. The multi-parameter setting creates theoretical and computational challenges compared to the one-parameter case, but it also has a larger class of potential applications. We show that ideas from the theory of multi-parameter persistent homology can be used to construct a novel method of density estimation with appealing theoretical properties. We will not assume familiarity with persistent homology or density estimation. This is joint work with Luis Scoccola.

Colloquium

Speaker: Caterina Consani (Johns Hopkins)

"On absolute geometry"

Time: 15:30

Room: MC 108

I will present some recent constructions aiming to define the notion of the absolute geometric point and the universal arithmetic over it (joint with A. Connes).

Algebra Seminar

Speaker: Sergio Ceballos (Western)

"Average behavior of the p-torsion of Jacobian groups in families of graphs"

Time: 13:30

Room: Zoom 998 5635 1219

The Jacobian group of a graph can be thought as a discrete analogue of the Jacobian of a Riemann Surface. We know very little about the structure of this group. In this talk, I will present some results concerning the distribution of Jacobian groups with nontrivial p-torsion in certain families of graphs.

Geometry and Combinatorics

Speaker: Christin Bibby (Louisiana State University)

"The Leray Model of the Orlik Solomon Algebra"

Time: 14:30

Room: Zoom

Geometry and Topology

Speaker: Katharine Adamyk (Western)

"Classifying Stable Modules over A(1)"

Time: 15:30

Room: Zoom Meeting ID: 958 6908 4555

The mod-2 Steenrod algebra A arises topologically as the algebra of stable operations on cohomology with coefficients in Z/2. There is a family of sub- Hopf algebras, A(n), that filter A. Given a module over A(n), one natural question to ask is whether it is the underlying A(n)-module for some A-module. (If it is, we say the A(n)-module lifts to an A-module.) In this talk, we approach the lifting question for the case n=1 via a classification theorem for a certain class of stable A(1)-modules.

In general, the stable category of modules over some ring, R, is obtained by factoring out the projective modules. When R is A(1), this is an especially nice category, and we will spend some time talking about its properties. We will also discuss Margolis homology, a useful invariant for A(1)-modules and its utility in the context of stable modules. The classification theorem describes A(1)-modules satisfying a condition on the Margolis homology groups.

Finally, we will discuss an application of the classification theorem to computing localized Adams spectral sequences and to the lifting problem.