Topology Seminar

Seminars During Academic Year 2006-07

Fall 2006

Wednesday September 6, 2006 in Rawles Hall 104

Nansen Petroysan, Hirsch rank and actions of solvable groups

My goal will be to outline the proof of the following theorem: There must be a bound on the Hirsch rank of a solvable group if acts cellularly on a finitely dominated, finite dimensional complex such that there is a bound on the Hirsch ranks of the isotropy subgroups. I will then describe some applications and examples to free and proper group actions on spaces such as (S^n) x (R^k). If time permits, I will discuss the case when k=1 connecting it to a conjecture made by Mislin and Talelli in the early 90s. It states that any torsion-free group with periodic cohomology must have finite cohomological dimension, i.e. it must act freely and cellularly on a finite dimensional contractible complex.

Saturday September 16, 2006 in IUPUI - LD 229

Mike Mandell, Joint Purdue-IUPUI-IUB topology seminar: Toward Quillen-Steenrod Opns for BP

Saturday September 16, 2006 in IUPUI - LD 229

Chuck Livingston, Joint Purdue-IUPUI-IUB topology seminar: The Geography of 4-manifolds with specified groups

Thursday October 5, 2006 in Rawles Hall 104

Maria Basterra, Cohomology of highly structured ring spectra

Wednesday October 11, 2006 in Rawles Hall 104

David Cimasoni, Dimers on surface graphs and spin structures

In the 1960's, W. Kasteleyn showed that the partition function for the dimer model on a planar graph is equal to the Pfaffian of an N by N matrix, where N is the number of vertices of the graph. He also stated that for any graph G, the partition function can be written as a linear combination of 4^g Pfaffians, where g denotes the genus of a surface S where G can be embedded. A formal combinatorial proof of this fact was only given in 1999 by Gallucio-Loeb and Tesler. In this talk, we shall explain a geometric proof of this fact. In our formula for the partition function, each of the 4^g terms corresponds to a spin structure on S, and each coefficient in the linear combination is equal to the Arf invariant of the corresponding spin structure. This is joint work with Nicolai Reshetikhin.

Wednesday October 18, 2006 in Rawles Hall 104

Steve Mitchell, Schubert varieties in the affine Grassmannian

The loop space of a compact Lie group is homotopy equivalent to a certain infinite-dimensional projective algebraic variety, the "affine Grassmannian". This variety shares many of the beautiful features of ordinary Grassmannians; for example, it has a decomposition into Schubert cells whose closures are ordinary projective varieties. There are two striking differences, however: The affine Grassmannian is a topological group, and the principal bundle defining it as a homogeneous space is topologically trivial. In this largely expository talk I will present a topologist's perspective on the affine Grassmannian, and discuss some ongoing work involving its Schubert varieties: For example, which of these are nonsingular?

Saturday October 21, 2006 in SE 140

Vigleik Angeltveit, Two notions of a simplicial space up to homotopy

Saturday October 21, 2006 in SE 140

Tom Goodwillie, Differential operators in homotopy calculus

Saturday October 21, 2006 in SE 140

Ciprian Manolescu, A combinatorial description of knot Floer homology

Saturday October 21, 2006 in SE 140

Vladimir Turaev, Homotopy and cobordism of words

Sunday October 22, 2006 in SE 140

Stefan Schwede, On the homotopy groups of symmetric spectra

Sunday October 22, 2006 in SE 140

Craig Westerland, Free loop spaces and Koszul duality

Sunday October 22, 2006 in SE 140

Marc Culler, Mod p homology and hyperbolic volume

Wednesday October 25, 2006 in Rawles Hall 104

Jan Jaworowski, The degree of maps of free G-manifolds and the average

Tuesday October 31, 2006 in Rawles Hall 104

Cornelia Van Cott, Braid length and its relationship to the number of braid strands

Every knot can be represented by infinitely many different braids. In 2004, Gittings discovered some surprising examples of knots for which these braid representatives become simpler as the number of strands is increased. We will study this occurrence and discuss several general relationships between braid length and the number of braid strands.

Thursday November 2, 2006 in Rawles Hall 104

Matthew Ando, K(1)-localizations of topological modular forms and p-adic modular forms

We will explain how to construct a map of E-infinity ring spectra MString –> tmf. An important part of the story is the relationship between p-adic modular forms and K(1)-localizations of tmf. We shall see that the relationship between the Atiyah-Bott-Shapiro orientation of KO and the String orientation of tmf is another part of the story about Bernoulli numbers and Eisenstein series.

Wednesday November 8, 2006 in Rawles Hall 104

Christian Kassel, Braid groups and automorphisms of the free groups

Thursday November 16, 2006 in Rawles Hall 104

Jennifer Franko, Quantum Computing, Braids and Representations

Braid group representations can be used to describe the actions of the quantum bits in a topologicial quantum computer. The quantum bits themselves are encoded in states of quasi particles, called anyons. Trajectories of these quasi particles in 3-dimensional space-time form braids the closure of which are knots or links. Any invertible matrix which satisfies the Yang Baxter Equation can be used to obtain representations of the braid group. During this talk we will consider unitary solutions to the Yang Baxter equation and the construction of representations arising from these solutions as well link invariants these representations yield.

Tuesday November 28, 2006 in Rawles Hall 104

Jae Choon Cha, Witt class defect invariants of 3-manifolds and links

Wednesday November 29, 2006 in Rawles Hall 104

Marta Asaeda, TQFT and operator algebras

Wednesday December 6, 2006 in Rawles Hall 104

Koby Rubinstein, Sets of homotopy types in Sobolev spaces

Spring 2007

Wednesday January 10, 2007 in Rawles Hall 104

Paul Kirk, An interesting small symplectic 4-manifold

Thursday January 18, 2007 in Rawles Hall 104

Anar Akhmedov, Construction of new symplectic cohomology S^2 times S^2

In this talk we present new examples of symplectic manifolds with same integral cohomology as S^2 times S^2. We also discuss the generalization of these examples as well as its application in the construction of simply connected 4-manifolds with small Euler characteristic.

Saturday February 10, 2007 in IUPUI LD229

Richard Hind, Joint IU-IUPUI-Purdue seminar: Symplectic embeddings in Euclidean space

We will derive new estimates for the Gromov width of certain domains in R^4, that is, on the maximal radius of balls which can be symplectically embedded into the domain. Time permitting we will also discuss some analogous questions in R^6.

Saturday February 10, 2007 in IUPUI LD 229

Kevin Costello, Joint Purdue-IUPUI-IUB topology seminar: Renormalisation and the Batalin-Vilkovisky formalism

The Batalin-Vilkovisky formalism is a machine used by physicists to quantise gauge theories. I'll give an introduction to the BV formalism, and discuss a new approach to renormalisation in this context. If there's time, I'll discuss some applications to Chern-Simons theory.

Thursday March 8, 2007 in Rawles Hall 104

Christopher Dwyer, A completion theorem for twisted equivariant K-theory

Monday April 16, 2007 in Swain West 217

Matt Hedden, Knot Floer homology and algebraic curves

Monday April 16, 2007 in Swain East 245

Teena Gerhardt, Equivariant Homotopy and Algebraic K-theory

Tuesday April 17, 2007 in Rawles Hall 104

P. Heck, Z. Su, C. Van Cott, Three Talks

Wednesday April 18, 2007 in Rawles Hall 104

Paul Kirk, Small Symplectic 4-Manifolds

Wednesday April 25, 2007 in Rawles Hall 104

J. Yazinski, Immersed curves in the plane and Reidemeister move 2