Geometry and Topology

Speaker: Pablo Pelaez (Duisburg-Essen)

"Rigid Motivic Homotopy Groups"

Time: 15:30

Room: MC 108

We will recall Voevodsky's definition of the presheaves of rigid motivic homotopy groups and show that they admit a canonical structure of presheaves with transfers when we consider rational coefficients and quasi-excellent base schemes.

Noncommutative Geometry

Speaker: Farzad Fathizadeh (York University)

"A Noncommutative Residue for Pseudodifferential Operators on the Noncommutative Two Torus"

Time: 12:30

Room: MC 107

I will first explain a pseudodifferential calculus for the canonical dynamical system associated to the noncommutative two torus which is a special case of Connes' pseudodifferential calculus for C^* dynamical systems. Then I will report on a recent joint work with M. W. Wong where we define a noncommutative residue for classical pseudodifferential operators on the noncommutative two torus, and prove that up to a constant multiple it is the unique trace on the algebra of classical pseudodifferential operators modulo infinitely smoothing operators.

Pizza Seminar

Speaker: Mehdi Garrousian (Western)

"Sudoku Enumeration and Hyperplane Arrangements"

Time: 16:30

Room: MC 107

There are various mathematical models and solution strategies for the sudoku puzzle. In this expository talk, I will use the language of graph theory and hyperplane arrangements to approach the sudoku enumeration problem. In particular, I will show how sudokus suggest a finite field interpretation of the characteristic polynomial of hyperplane arrangements. If time permits I will also discuss a Groebner basis algorithm for determining whether a given sudoku puzzle has a solution.

Noncommutative Geometry

Speaker: Sheldon Joyner (Western)

"The Grothendieck-Teichmuller group"

Time: 14:30

Room: MC 107

This talk will handle Drinfel'd's construction of the object of the title by means of deformations of braided monoidal categories.

Symplectic Learning Seminar

Speaker: M. VanHoof (Western)

"Resolving singularities of weighted projective spaces (2)"

Time: 10:30

Room: MC 104

This is the second part of our discussion of singularities of weighted projective spaces and their resolutions.

Symplectic Learning Seminar

Speaker: M. Mousavi (Western)

"Schur-Horn-Kostant theorem for Symplectomorphisms of toric manifolds"

Time: 13:30

Room: MC 104

We continue our exposition of the Schur-Horn-Kostant theorem for Symplectomorphisms groups of toric manifolds

Colloquium

Speaker: Victor Snaith (Sheffield)

"A history of the Arf-Kervaire invariant problem"

Time: 15:30

Room: MC 107

More than 50 years ago Michel Kervaire constructed a manifold with no differentiable structure. Constructing manifolds is the easy part - the trick is to construct an invariant, in this case the Arf-Kervaire invariant, which guarantees the existence or otherwise of the property one is after. The connection between framed manifolds and stable homotopy groups led (circa 1960) to the problem: Do there exist framed manifolds of odd Arf-Kervaire invariant?''. Recently Hill-Hopkins-Ravenel proved that the outcome is: mostly framed manifolds of Arf-Kervaire invariant one do not exist''.

Here is what Lewis Carroll has to say about non-existent things!

I know what you're thinking about,'' said Tweedledum; but it isn't so, nohow.'' Contrariwise,'' continued Tweedledee,if it was so, it might be; and if it were so, it would be; but as it isn't; it ain't. That's logic.''

Algebra Seminar

Speaker: Yusuf Mustopa (Michigan)

"Quartic surfaces as linear Pfaffians"

Time: 14:30

Room: MC 107

A theorem of Beauville implies that the general smooth quartic surface in $P^3$ may be expressed as the zerolocus of a Pfaffian associated to an 8 by 8 skew-symmetric matrix of linear forms. In this talk, I will discuss how the recent work of Aprodu-Farkas on the Green conjecture for curves on K3 surfaces may be used to generalize this statement to all smooth quartic surfaces in $P^3$. This is joint work with Emre Coskun and Rajesh Kulkarni.

Geometry and Topology

Speaker: Victor Snaith (Sheffield)

"Ossa's theorem and a non-factorisation result for stable homotopy classes of Arf-Kervaire invariant one"

Time: 15:30

Room: MC 107

Let $p$ be a prime. A 1989 theorem of Ossa calculates the connective unitary K-theory of the smash product of two copies of the classifying space for the cyclic group of order $p$ and purports to calculate the corresponding orthogonal connective K-theory when $p=2$. Sadly the latter is wildly wrong!

Using a simple K\"{u}nneth formula short exact sequence I shall derive Ossa's unitary connective K-theory result in an elementary manner. As a corollary, I shall derive the correct version of Ossa's orthogonal theorem.

As an application of this result I shall show that there do not exist stable homotopy classes of ${\mathbb RP}^{\infty} \wedge {\mathbb RP}^{\infty}$ in dimension $2^{s+1}-2$ with $s \geq 2$ whose composition with the Hopf map to ${\mathbb RP}^{\infty}$ gives a stable homotopy element having Arf-Kervaire invariant one.