January 24 
Greg Arone (UVa) 
Calculus of functors and embedding spaces: an overview 
January 31 
KaiUwe Bux (UVa) 
The dimension of the group of partially symmetric automorphisms of a free group
(Joint with Ruth Charney and Karen Vogtmann) We determine the virtual dimension of the group $P\Sigma(n,k)\subset Out(F_n)$ generated by automorphisms which send the first $k$ generators to conjugates of themselves (each x_i is going to a conjugate $wx_iw^{1}$). Thm: $vcd(P\Sigma(n,k))=2nk2$. 
February 7 
Eric Finster (UVa) 
The Model Structure on the Category of Small Categories 
February 14 
KaiUwe Bux (UVa) 
The dimension of the group of partially symmetric automorphisms of a free group II
(Joint with Ruth Charney and Karen Vogtmann) We determine the virtual dimension of the group $P\Sigma(n,k)\subset Out(F_n)$ generated by automorphisms which send the first $k$ generators to conjugates of themselves (each x_i is going to a conjugate $wx_iw^{1}$). Thm: $vcd(P\Sigma(n,k))=2nk2$. 
February 21 
Nicholas Hamblet (UVa) 
The Poset of Linear Subspaces of R^n Notes 
February 28 
No Seminar 

March 6 
No Seminar 
Spring Break 
March 13 
No Seminar 

March 20 
Pascal Lambrechts (U of Louvaine la Neuve) 
On SemiAlgebraic Forms 
March 27 
Nick Kuhn (UVa) 
The Homology of Symmetric Groups in Characteristic p 
April 3 
No Seminar 
No Seminar 
April 10 
Tom Mark (UVa) 
Exotic Stein fillings of contact 3manifolds 
April 17 
Josh Greene (Princeton) 
Floer homology and knot concordance
I will talk about two recent approaches to the study of smooth knot concordance, one coming from Donaldson theory, the other from Heegaard Floer homology. Then I will discuss how to combine the two to give a novel test for a knot to be slice, and apply the test to determine the concordance order of threestranded pretzel knots. 
April 24 
Michael Usher (Princeton) 
Spectral numbers in Novikov and Floer homology
The chain complexes in Novikov and Floer homology theories carry natural realvalued filtrations, allowing one to define the spectral number of any homology class as the infimum of the filtration levels of all chains representing that class; in the case of Hamiltonian Floer homology these numbers have had interesting applications to symplectic topology due to Schwarz, Oh, and others. I'll sketch a proof that the infimum in the definition of the spectral number is always attained. This fact allows some of the applications of the spectral numbers that have been carried out for special classes (e.g., rational or semipositive) of closed symplectic manifolds to be generalized to all closed symplectic manifolds. 