Geometry and Topology

Speaker: Rick Jardine (Western)

"Simplicial sheaves, cocycles, and torsors"

Time: 15:30

Room: MC 108

This talk will be a partial introduction to the general subject area. We will discuss the homotopy theory of simplicial sheaves and presheaves, along with its interpretation in non-abelian cohomology and the theory of stacks.

This lecture was first given at a conference at the Fields Institute during the summer of 2013.

Analysis Seminar

Speaker: Yan Xu (Dongbei University of Finance and Economics)

"The ubiquitous B-splines from approximation to Combinatorics: Eulerian numbers, polytopes and Askey scheme"

Time: 14:30

Room: MC 108

Spline functions are original derived from approximation theory then were applied to established the theory of wavelets which is the most important tool in CAGD founded by engineers at the first beginning. They are also closely related with some branches in pure mathematics, such as Combinatorics and Asymptotic analysis. Due to the somewhat high distance between these fields, people working in Enumerative Combinatorics, Partition functions and Asymptotic analysis of biorthogonal systems do not seem to be fully aware of the results on the B-splines. This presentation may shed some lights on the connection between the related problems arising in different fields such as B-splines and Eulerian polynomials, Box-spline and the volume of polytopes, the asymptotic properties of splines and Askey scheme. It may useful to bring together some areas of research which have developed independently without much knowledge of each other.

Homotopy Theory

Speaker: Hugo Bacard (Western)

"p-adic homotopy theory"

Time: 14:30

Room: MC 108

Noncommutative Geometry

Speaker: Alim Eshmatov (Western)

"An Introduction to Homological Mirror Symmetry II"

Time: 14:30

Room: MC 107

Index Theory Seminar

Speaker: Matthias Franz (Western)

"The Lefschetz fixed-point formula"

Time: 14:00

Room: MC 107

Colloquium

Speaker: Richard Hind (Notre Dame University)

"Quantitative results in symplectic geometry"

Time: 15:30

Room: MC 108

Symplectic geometry sometimes seems much like Riemannian geometry, that is, rigid, and other times resembles differential topology, that is, there is much more flexibility in constructions. We will discuss examples like embedding and isotopy problems which are rigid only within a certain range of parameters. Quantitative symplectic geometry aims to determine the critical transition parameters.

PhD Thesis Defence

Speaker: Martin VanHoof (Western)

""Symplectomorphism Groups of Weighted Projective Spaces and Related Embedding Spaces""

Time: 14:00

Room: MC 108

We consider weighted projective spaces and homotopy properties of their symplectomorphism groups. In the case of one singularity, the symplectomorphism group is weakly homotopy equivalent to the Kahler isometry group of a certain Hirzebruch surface that corresponds to the resolution of the singularity. In the case of multiple singularities, the symplectomorphism groups are weakly equivalent to tori. These computations allow us to investigate some properties of related embedding spaces.

Algebra Seminar

Speaker: Marcy Robertson (Western)

"Schematic homotopy types of operads"

Time: 14:30

Room: MC 107

The rational homotopy type $X_{\mathbb{Q}}$ of an arbitrary space $X$ has pro-nilpotent homotopy type. As a consequence, pro-algebraic homotopy invariants of the space $X$ are not accessible through the space $X_{\mathbb{Q}}$. In order to develop a substitute of rational homotopy theory for non-nilpotent spaces Toen introduced the notion of a pointed schematic homotopy type over a field $\mathbb{k}$, $(X\times k)^{sch}.$

In his recent study of the pro-nilpotent Grothendieck - Teichm$\mathrm{\ddot{u}}$ller group via operads, Fresse makes use of the rational homotopy type of the little $2$-disks operad $E_2$. As a first step in the extension of Fresse's program to the pro-algebraic case we discuss the existence of a schematization of the little $2$-disks operad.