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WEEKLY CALENDAR |
| Monday 31 |
3:10 pm, room 1431. Graph Theory and Combinatorics Seminar. Peter Hamburger, Western Kentucky University. On the Kneser index of graphs. The Kneser graph $K_{n:k}$ for positive integers $n\ge k$ has as its
vertex set the $k$-element subsets of some $n$-set, with disjoint sets
being adjacent. Every finite simple graph can be found as an induced
subgraph of some Kneser graph; this article explores some questions
arising from that fact. This is joint work with Attila Por, Western Kentucky University, and
Matt Walsh, Indiana University Purdue University Fort Wayne, IPFW.
4:10-5:30 pm, room 1432. Subfactor Seminar. Stuart White, University of Glasgow. Groupoid normalisers and tensor products. Given a unital inclusion $B\subset M$ of a subalgebra inside a finite von Neumann algebra, the normalisers of $B$ in $M$ are those unitaries $u\in M$ such that $uBu^*=B$ and the two-sided groupoid normalisers $GN_M(B)$ are those partial isometries $v\in M$ such that $vBv^*\subset B$ and $v^*Bv\subset B$. We shall consider two such inclusions $B_1\subset M_1$ and $B_2\subset M_2$ and examine the normalisers and groupoid normalisers of $B_1\ \overline{\otimes}\ B_2$ inside $M_1\ \overline{\otimes}\ M_2$ and the von Neumann algebars they generate. It is easy to construct examples inside the matrix algebras for which the normalisers of the tensor product generate a larger algebra than the tensor product of the algebra generated by the normalisers (and similarly for the two-sided groupoid normalisers). However, when each $B_i'\cap M_i\subseteq B_i$, we do have GN_{M_1}(B_1)''\ \overline{\otimes}\ GN_{M_2}(B_2)''=GN_{M_1\ \overline{\otimes}\ M_2}(B_1\ \overline{\otimes}\ B_2)''. This result is established by examining the behaviour of certain projections in the relative commutant of the basic construction and is joint work with Junsheng Fang, Roger Smith and Alan Wiggins. |
| Tuesday 1 | 4:10-5:15 pm, room 1431. Noncommutative Geometry Seminar. Jerry Kaminker, IUPUI. Higher spectral flow. It is well-known that the bounded self-adjoint Fredholm operators with both positive and negative essential spectrum provide a classifying space for odd K-theory. One can also consider analogous families of unbounded self-adjoint Fredholm operators. One is then led to study the eigenspaces of the operators and how they vary with the goal of obtaining invariants of the family. We will discuss some results obtained taking this point of view which relate the multiplicity of the spectrum to the triviality of the family as an element of K-theory. This is joint work with Ron Douglas. |
| Wednesday 2 |
4:10 pm, room 1310.
Topology
& Group Theory Seminar. Yuri Bahturin, Memorial University (Canada). Formal groups, group schemes and group gradings.
4:10-5:00 pm, room 1307. Partial Differential Equations Seminar. Antonio Fasano, University of Florence, Italy. A free boundary problem describing blood clotting by mechanical activation of platelets. Blood clotting is the result of a large number of chemical reactions leading in particular to the formation of fibrin in the blood stream. Fibrin modifies the rheological properties of blood and at the same time it is used by platelets to build up a gel-like structure, enclosing plasma, red blood cells and other blood constituents. This is what we call a blood clot. On a small scale this process occur normally in the body in order to repair micro-wounds and is also needed in exceptional circumstances to repair large wounds. Unfortunately it may take place in a rather massive way leading to vessels obstruction either due to blood stagnation, or to a mechanical activation of platelets (i.e. the exposure of platelets to a stress beyond some threshold for a sufficiently long time) in combination with fibrin accumulation. We present a mathematical model referring to the latter situation. The key point of the model is to select a range of parameters guaranteeing a clear separation of the various time scales involved in the process (chemical reactions, diffusion of the chemicals, fluid dynamics, advancement of the clotting front from the vessels walls). Under such conditions the chemistry is described by a set of o.d.e.'s, the fluid dynamics is quasi-steady and the progression of clotting is driven by the motion of two free boundaries: a boundary of platelets activation and the boundary of clot formation. The free boundary conditions are of an unusual type. Existence and uniqueness are proved and the consistency of the assumptions made on the time scales is investigated. |
| Thursday 3 | 4:10-5 pm, room 5211. Colloquium. Yair Minsky, Yale University. Geometry and rigidity of mapping class groups. The mapping class group of a compact surface S is the group of homeomorphisms of S modulo isotopy. Via its Cayley graph it can be viewed as an infinite-diameter metric space, whose large-scale geometry is strongly connected with the algebraic properties of the group. Â In joint work with Behrstock, Kleiner and Mosher, we study this large-scale geometry and prove in particular that its quasi-isometries are bounded perturbations of the action of the group. This implies (as was also independently shown by Hamenstadt) that the group is quasi-isometrically rigid. Tea at 3:30 pm in SC 1425. |
| Friday 4 |