Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, September 1, 2015.

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Tuesday, September 1, 2015

11:00 am in 243 Altgeld Hall,Tuesday, September 1, 2015

Chromatic splitting: the way things work at p=2

Agnes Beaudry (U Chicago)

Abstract: Recent computations show that the decomposition of $L_1L_{K(2)}S$ predicted by the chromatic splitting conjecture does not hold at $p=2$. I will explain how the situation differs and propose a different decomposition for $L_1L_{K(2)}S$ in this case.

12:00 pm in 345 Altgeld Hall,Tuesday, September 1, 2015

Recognizing three-manifolds

Saul Schleimer (University of Warwick)

Abstract: To the eyes of a topologist manifolds have no local properties: every point has a small neighborhood that looks like euclidean space. Accordingly, as initiated by Poincaré, the classification of manifolds is one of the central problems in topology. The "homeomorphism problem" is somewhat easier: given a pair of manifolds, we are asked to decide if they are homeomorphic. These problems are solved for zero-, one-, and two-manifolds. Even better, the solutions are "effective": there are complete topological invariants that we can compute in polynomial time. On the other hand, in dimensions four and higher the homeomorphism problem is logically undecidable. This leaves the provocative third dimension. Work of Haken, Rubenstein, Casson, Manning, Perelman, and others shows that these problems are decidable. Sometimes we can do better: for example, if one of the manifolds is the three-sphere then the homeomorphism problem lies in the complexity class NP. In joint work with Marc Lackenby, we show that recognizing spherical space forms also lies in NP. If time permits, we'll discuss the standing of the other seven Thurston geometries. View talk at https://youtu.be/4nu_dSCZ5V8

1:00 pm in 241 Altgeld Hall,Tuesday, September 1, 2015

Embeddability Problems for CR Hypersurfaces

Ming Xiao (UIUC Math)

Abstract: I will first review the history of embeddability problems for CR structures and then begin discussing new results.

1:00 pm in 345 Altgeld Hall,Tuesday, September 1, 2015

Not scheduled

3:00 pm in 241 Altgeld Hall,Tuesday, September 1, 2015

Triangle factors in graphs, directed graphs and weighted graphs

Theodore Molla   [email] (UIUC Math)

Abstract: In 1963 Corrádi and Hajnal proved that if G is a graph on n vertices, n is divisible by 3 and the minimum degree of G is at least 2n/3, then G contains a triangle factor, i.e. a collection of n/3 vertex disjoint triangles. Since every graph G on n vertices with independent number greater than n/3 does not have n/3 vertex disjoint triangles, this theorem is sharp. In this talk, we will describe several related theorems for graphs, directed graphs and weighted graphs. For example, we will discuss the following recent result: For every ε > 0 there exists γ > 0 such that if G is a graph on n vertices and the minimum degree of G is at least (1/2 + ε)n while the independence number of G is at most γn, then G has a triangle factor provided n is sufficiently large and divisible by 3.

3:00 pm in 243 Altgeld Hall,Tuesday, September 1, 2015

Bridgeland stability on surfaces with curves of negative self-intersection

Rebecca Tramel (UIUC Math)

Abstract: Let X be a smooth projective surface. In 2002, Bridgeland defined a notion of stability for objects in the derived category of X, which can be thought of as a generalization of slope stability for vector bundles on curves. The work of Bayer-Macri and of Toda shows that there are nice connections between deformations in Stab(X), the space of all Bridgeland stability conditions on X and the birational geometry of X.  I will consider the case of a surface which contains a rational curve C of negative self-intersection, and consider objects whose class is that of the skyscraper sheaf of a point. There is a distinguished chamber in Stab(X) called the geometric chamber, in which all such objects are stable. I will show that there is a wall to the geometric chamber along which the points of C are destabilized, and describe the moduli space of stable objects across this wall.