# Mathematical Sciences Research Institute

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1. # GTC Graduate Seminar: Partitionable Extenders: A Combinatorial Interpretation of the h-vector

Location: MSRI: Baker Board Room
Speakers: Joseph Doolittle (University of Kansas)

The h-vector of a pure simplicial complex is of critical importance to combinatorialists and algebraists. When the complex is partitionable, a combinatorial interpretation for the h-vector is well known. In joint work with Bennet Goeckner and Alexander Lazar, we introduce a new construction which allows for an interpretation of the h-vector as an error term between a partitionable complex and a partitionable relative complex. This construction is inductive and is not minimal. We will briefly discuss minimality and some other issues that arise.

Updated on Dec 06, 2017 01:17 PM PST
2. # GTC Main Seminar: On the treewidth of triangulated three-manifolds

Location: MSRI: Simons Auditorium
Speakers: Jonathan Spreer (Freie Universität Berlin)

In graph theory, as well as three-manifold topology, a wide range of parameters exist to decide how "simple", or "thin", a given graph or three-manifold is. These width-type parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for three-manifolds, play an important role when studying algorithmic problems in the field: There exist several topological problems -- some of them known to be computationally hard in general -- which become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded tree width.
In view of such algorithmic results, the question of whether there exists an explicit link between combinatorial concepts such as treewidth (applicable to a single input triangulation of a given three-manifold M) and results in three-manifold topology (applicable to all possible triangulations of M) has repeatedly been asked by researchers working in the computational branch of three-manifold topology.
In this talk I will present such a link, stating that there exist families of three-manifolds not admitting triangulations of bounded treewidth.

Updated on Dec 08, 2017 08:44 AM PST
3. # GFA Main Seminar: Ideals in L(L_p)

Location: MSRI: Simons Auditorium
Speakers: William Johnson (Texas A & M University)
I'll discuss the Banach algebra structure of the spaces of bounded linear operators on ell_p and L_p:=L_p(0,1).
The main new results are

1. The only non trivial closed ideal in L(L_p), for 1 <= p < infty, that
has a left approximate identity is the ideal of compact operators (joint
with N. C. Phillips and G. Schechtman).

2. There are infinitely many; in fact, a continuum; of closed ideals in
L(L_1) (joint with G. Pisier and G. Schechtman).

The second result answers a question from the 1978 book of A. Pietsch,
Operator ideals".
Updated on Dec 05, 2017 11:06 AM PST
4. # GFA Main Seminar: Ideals in L(L_p)

Location: MSRI: Simons Auditorium
Speakers: William Johnson (Texas A & M University)
I'll discuss the Banach algebra structure of the spaces of bounded linear operators on ell_p and L_p:=L_p(0,1).
The main new results are

1. The only non trivial closed ideal in L(L_p), for 1 <= p < infty, that
has a left approximate identity is the ideal of compact operators (joint
with N. C. Phillips and G. Schechtman).

2. There are infinitely many; in fact, a continuum; of closed ideals in
L(L_1) (joint with G. Pisier and G. Schechtman).

The second result answers a question from the 1978 book of A. Pietsch,
Operator ideals".
Updated on Dec 05, 2017 11:06 AM PST