Unless otherwise noted, all seminar meetings are on Thursdays at 4:00PM in Room 901 Van Vleck. Cookies and juice precede starting at about 3:45PM.
- Thursday, 1 February: TBA
- Thursday, 8 February: Ben Ellison, Lattice-ordered commutative f-rings
- Thursday, 15 February: Asher Kach, Reverse Mathematics and Vector
Spaces
- Thursday, 22 February: Dave Milovich, How to Make Resolutions
- Thursday, 1 March: no talk
- Thursday, 8 March: Dan Turetsky, TBA
- Thursday, 15 March: James Hunter, TBA
- Thursday, 22 March: TBA
- Thursday, 29 March: TBA
- Thursday, 5 April: No talk, due to Spring Break
- Thursday, 12 April: TBA
- Thursday, 19 April: Dave Milovich, Homogeneous compact products of
linear orders
- Thursday, 26 April: Dan McGinn, JRS Theories
- Thursday, 3 May: Dan McGinn, JRS Theories
- Ben Ellison, Lattice-ordered commutative f-rings:
In this talk, I will present the axioms for lattice-ordered commutative
f-rings. I will then show how we can use model theory to prove
certain properties that are difficult to prove directly.
- Asher Kach, Reverse Mathematics and Vector Spaces:
The statement, "A
vector space has dimension greater than one if and only if it has a
nontrivial proper subspace,"is a basic theorem of linear algebra.
In this talk we analyze the effective content of this theorem.
Before doing so, we introduce/review the
necessary definitions and facts from linear algebra, computable model
theory, and reverse mathematics. As time permits, we present the
proofs of the reverse mathematic reversals. All work presented is
joint with Rod Downey, Denis Hirschfeldt, Steffen Lempp, Joe Mileti,
and Antonio Montalban.
- Dave Milovich, How to Make Resolutions: In general
topology, there is a zoo of methods for constructing
counterexamples. Many of these methods are actually special cases
of a general construction called the resolution topology, which was
invented by Fedorchuk. Resolutions are the mathematical precise
version of a very intuitive visual process, and I will discuss several
simpler resolutions
that are easily illustrated on the blackboard, including the double
arrow space and the Alexandroff double line. I will also mention
some results proved by constructing more complex resolutions, including
the consistency, due to van Mill, of a homogeneous compactum having
character exceeding its pi-weight.
- Dave Milovich, Homogeneous compact products of linear orders: In 2005, Arhangelskii proved that, for a broad class of linear orders, if a product of them is homogeneous, then every factor must be first countable. I will present a simpler proof I developed independently for the special case of compact linear orders.