A block design is a set of elements and a collection of -element subsets of (called blocks) with the property that each -element subset of occurs in exactly blocks. A -Steiner system is a system.
Using variants of the Hrushovski method we construct infinite block designs and Steiner systems that are a) -categorical and with more work b) have -transitive automorphism groups for prescribed .
The strongly minimal Steiner -Steiner system (M,R) from Baldwin and Pao (2021) can be `coordinatized' in the sense of Ganter and Werner (1975) by a quasigroup if is a prime-power. But for the basic construction this coordinatization is never definable in (M,R) by Baldwin (2023). Nevertheless, by refining the construction, if is a prime power there is a (2,k)-variety of quasigroups which is strongly minimal and definably coordinatizes a Steiner -system.
We compare these structures with Steiner systems given by Fra{\"\i}ss\'{e} constructions by Barbina and Casanovas (2019) and compare versions of the small intersection property for -categorical structures and countably saturated structures by Lascar (2002).
Infinite combinatorics from finite structures
Tue, Feb. 20 3:30pm (MATH 3…
Topology
Elizabeth Tatum (Universität Bonn)
X
In recent work, Guchuan Li, Sarah Petersen, and I have constructed models for -equivariant analogues of the integral Brown-Gitler spectra. In this talk, I will start by introducing the classical Brown-Gitler spectra and some of their applications. After that, I will discuss the -equivariant integral Brown-Gitler spectra, as well as the applications we are beginning to study.
Equivariant Brown-Gitler spectra
Tue, Feb. 20 4:50pm (MATH 3…
Grad Student Seminar
Alex LaJeunesse (University of Colorado)
X
Algebraic K-theory is a booming field that interacts with many diverse areas of mathematics. It’s universality makes it difficult to understand, but much progress has been made in recent years using a variety of “trace” methods; that is, approximating K-theory by simpler algebraic invariants. In this talk I will introduce algebraic K-theory and the related Hochschild homology, with the ultimate goal of constructing a useful map from the former to the latter.