- September 5, 2006

**Organizational Meeting**

- September 12, 2006

**Anca Mustata**(UIUC Math)

**Title:**Algebraic Stacks

**Abstract:**Algebraic stacks are a useful extension of the notion of scheme in algebraic geometry. An example is the quotient of a scheme by the action of an affine algebraic group with finite stabilizers. In this talk I will present a basic stack construction via the notion of groupoid scheme. Even though the word is used in abundance, you do not need to know what a scheme is to follow this talk. You may replace it by mostly any other notion of space you may like: manifold, complex analytic space, or even topological space.

- October 10, 2006

**Rosona Eldred**(UIUC Math)

**Title:**H-spaces and Coherence

**Abstract:**A group is a monoid is an H-space. Monoids and groups have a set amount of associativity; different H-spaces can have differing levels of associativity that is communicated by coherence laws. These can be thought of as commutative polyhedral diagrams, or as maps involving different dimensional discs. As you vary the amount of coherence you want on your H-space, you get varying sorts of corresponding topological structures. For instance, an H-space with every possible coherence looks like an infinite loop space (maps from the infinite dimensional sphere into a space X). This talk is based somewhat off of week121 of John Baez's finds in mathematical physics.

- October 17, 2006

**Jennifer Vandenbussche**(UIUC Math)

**Title:**Friendship in Combinatorics

**Abstract:**The Friendship Theorem in combinatorics states that if every two people at a party have exactly one common friend, then there is one person who is friends with everyone. In 1978, Vera Sos suggested a generalization of this idea using hypergraphs. In this talk, I will briefly discuss the Friendship Theorem before introducing the concept of hypergraphs. I will discuss recent progress on Sos's generalization (joint work with Stephen Hartke). In particular, I will show how Integer Programming can be used to investigate combinatorial problems. This talk will be accessible to anyone but hopefully still interesting to combinatorialists - and I promise to use the words "eigenvalue" and "group" at least once for the algebraists in the crowd.

- October 31, 2006

**Erin Wolf Chambers**(UIUC CS)

**Title:**Computing interesting topological features

**Abstract:**Computational topology is a relatively new area in the intersection of theoretical computer science and topology that merges classical methods in topology with algorithmic questions motivated by applications in graphics, sensor networks, robotics, genetics, and many other areas. I will provide a survey of some algorithmic questions which have been addressed, such as computing shortest cycles which have interesting properties such as being non-contractible, separating, etc. (All CS and topology definitions will be provided, so very little background is necesesary.)

- November 14, 2006

**Sonja Stimac**(UIUC Math)

**Title:**On Ingram's Conjecture

**Abstract:**Ingram's conjecture states that inverse limit spaces of two tent maps with different slopes are not homeomorphic. In recent years there has been intensive research of topological properties of inverse limit spaces of tent maps with classification of these spaces as ultimate goal. I will give a survey of recent results, and discuss the current joint work with B. Raines, on how the use of symbolic dynamics can give some insight in the structure of the inverse limit spaces of tent maps with critical points approaching periodic points.