Geometry and Topology

Speaker: Matthias Franz (Western)

"Describing toric varieties and their equivariant cohomology"

Time: 15:30

Room: MC 108

I will explain how complex and real toric varieties and their non-negative parts can easily be defined topologically. This gives in particular canonical cell decompositions of these spaces.

I will also discuss consequences to the ordinary and equivariant integral cohomology of toric varieties. For example, if the ordinary cohomology is concentrated in even degrees, then the equivariant cohomology can be described by piecewise polynomials. If the toric variety is in addition smooth or compact, then its ordinary cohomology is necessarily torsion-free.

Noncommutative Geometry

Speaker: A. Motadelro (Western)

"holomorphic structure on quantum projective line"

Time: 14:30

Room: MC 106

Abstract: The aim of this talk is to present the notion of holomorphic structure in noncommutative setting. Focusing on quantum projective line we will see that some of the classical structures have perfect analogues here. Also we shall explain a twisted positive Hochschild cocycle related to this complex structure.

Analysis Seminar

Speaker: Tatyana Foth (Western)

"On holomorphic k-differentials on some open Riemann surfaces"

Time: 15:30

Room: MC 108

Let X be a hyperbolic Riemann surface and A be a closed subset of X. We study spaces of integrable, square-integrable and bounded holomorphic k-differentials on X-A. Our main results provide a description of the kernel of the Poincare series map. This is joint work with N. Askaripour.

Pizza Seminar

Speaker: Sheldon Joyner (Western)

"Solving Rubik's cube using group theory"

Time: 17:00

Room: 108

Group theory is the mathematical language of symmetry, and as such has many real world applications, ranging from the study of crystals to fundamental ideas about the workings of the universe. In this talk, we will introduce group theory and see how it is used to create a wonderful algorithm to solve Rubik's cube.

Everyone welcome!

Algebra Seminar

Speaker: Sheldon Joyner (Western)

"The geometry of the functional equation of Riemann's zeta function"

Time: 14:30

Room: MC108

In a seminal 1859 paper, Riemann gave two proofs of the analytic continuation and functional equation of his zeta function. The ideas behind his theta function proof were later developed into a powerful theory of Fourier analysis on number fields, in work of Hecke, Tate and others. In this talk, I will focus instead on the contour integral proof, and based on the ideas therein, will present two infinite families of new proofs of the analytic continuation and functional equation. The proofs are facilitated by geometric data coming from the fact that the polylogarithm generating function is a flat section of the universal unipotent bundle with connection over $\mathbb{P}^{1} \backslash \{0,1,\infty\}$.

Geometry and Topology

Speaker: Ruxandra Moraru (Waterloo)

"Moduli spaces of stable bundles on certain non-Kaehler surfaces"

Time: 15:30

Room: MC 108

In this talk, I will examine the geometry of moduli spaces of stable bundles on manifolds that do not admit Kaehler metrics. In particular, I will show that, in the case of Hopf surfaces, these moduli spaces admit interesting geometric structures such as hypercomplex structures and strong HKT-metrics, as well as algebraic completely integrable systems.

Analysis Seminar

Speaker: Ruxandra Moraru (Waterloo)

"Compact moduli spaces of stable bundles on Kodaira surfaces"

Time: 15:30

Room: MC 108

In this talk, I will examine the geometry of moduli spaces of stable bundles on Kodaira surfaces, which are non-Kaehler compact surfaces that can be realised as torus fibrations over elliptic curves. These moduli spaces are interesting examples of holomorphic symplectic manifolds whose geometry is similar to the geometry of Mukai's moduli spaces on K3 and abelian surfaces.

Colloquium

Speaker: Kenneth R. Davidson (Waterloo)

"Operator algebras and dynamical systems"

Time: 15:30

Room: MC 108

I will discuss the construction of certain nonself-adjoint operator algebras from a discrete dynamical system (namely a space X and one or more maps of X into itself), and discuss how the algebra encodes the system, and how it can be recovered from information about the algebra.

Symplectic Learning Seminar

Speaker: Tatyana Foth (Western)

"Luttinger's surgery and complex structures on $T^2\times D^2$."

Time: 14:30

Room: MC 107

I will describe a result by Eliashberg and Polterovich that allows to construct a family $J_n$ of complex structures on $T^2\times D^2$ with strictly pseudoconvex boundary which are biholomorphically equivalent and homotopic through complex structures but not homotopic through complex structures with strictly pseudoconvex boundary. Note: $T^2\times D^2$ denotes the product of the 2-torus and the closed unit disk in $R^2$. The proof is based on the Lagrangian surgery method of K. Luttinger.

Noncommutative Geometry

Speaker: Masoud Khalkhali (Western)

"Gelfand's theory of commutative Banach algebras 3, Gelfand-Naimark Theorems"

Time: 14:30

Room: MC 106

Analysis Seminar

Speaker: Rasul Shafikov (Western)

"What is boundary value of a holomorphic function?"

Time: 15:30

Room: MC 108

A classical theorem of Fatou states that a bounded holomorphic function in the unit disc $\Delta \subset \mathbb C$ has radial limits almost everywhere on $\partial \Delta$. Ever since, the problem of making sense of boundary values of holomorphic functions (in one or more variables) has been an active area of research, often yielding far-reaching theories (think Hardy spaces). In this talk I will give an overview of two classical approaches to the problem, and will outline the idea of a new construction of boundary values of holomorphic functions for domains with non-smooth boundary.

Algebra Seminar

Speaker: Yunfeng Jiang (University of Utah)

"Counting invariants for $O+O(-2)$-quiver representations"

Time: 14:30

Room: MC 108

In this talk we prove a wall-crossing formula of counting invariants in the derived category of $O+O(-2)$-quiver representations. We verify the GW/DT/PT/NCDT-correspondence for the counting invariants.

Geometry and Topology

Speaker: Aji Dhillon (Western)

"The Essential Dimension of Parabolic Bundles"

Time: 15:30

Room: MC 108

Noncommutative Geometry

Speaker: Masoud Khalkhali (Western)

"NCG Learning Seminar: The unitary dual of the Heisenberg group"

Time: 14:30

Room: MC 106

The Heisenberg group plays a very important role in NCG, quantum mechanics, representation theory, and number theory. I shall give a general introduction to the idea of the unitary dual of a locally compact group and shall then focus on Heisenberg group and a characterization of its unitary dual via Stone-von Neumann theorem. I shall then indicate an application of the Selberg trace formula when one tries to decompose the representation of H on L^2 (\Gamma \H), where \Gamma is the standard integral lattice in H.

Analysis Seminar

Speaker: Rasul Shafikov (Western)

"What is boundary value of a holomorphic function? II"

Time: 15:30

Room: MC 108

A classical theorem of Fatou states that a bounded holomorphic function in the unit disc $\Delta \subset \mathbb C$ has radial limits almost everywhere on $\partial \Delta$. Ever since, the problem of making sense of boundary values of holomorphic functions (in one or more variables) has been an active area of research, often yielding far-reaching theories (think Hardy spaces). In this talk I will give an overview of two classical approaches to the problem, and will outline the idea of a new construction of boundary values of holomorphic functions for domains with non-smooth boundary.

Colloquium

Speaker: Charles Weibel (Rutgers)

"The norm residue is an isomorphism, or the resolution of the Bloch-Kato Conjecture"

Time: 15:30

Room: MC 108

Milnor conjectured in 1970 that each etale cohomology group of a field (mod 2 coefficients) should have a presentation with units as generators and simple quadratic relations (the ring with this presentation is now called the "Milnor K-theory" of the field). This was proven by Voevodsky, but the odd version (mod p coefficients for other primes) has been open until very recently, and had been known as the Bloch-Kato Conjecture.

Using certain norm varieties, constructed by Rost, and techniques from motivic cohomology, we now know that this conjecture is true. This talk will be a non-technical overview of the ingredients that go into the proof, and why this conjecture matters to non-specialists

Algebra Seminar

Speaker: Janusz Adamus (Western)

"On the homological structure of modules over regular local rings"

Time: 14:30

Room: MC108

Homological structure of finite modules over regular local rings is fairly well understood. The classical results date back to Serre, Auslander and Buchsbaum. On the other hand, little is known, in general, about the structure of infinite modules. In this talk, we will consider a class of such modules most important from the geometric point of view, namely those that arise as stalks of coherent sheaves over the source of a morphism with regular target. We will sketch the idea how to generalize the classical theory to the case of those modules, by a kind of fibre dimension reduction argument.

Geometry and Topology

Speaker:

"No seminar"

Time: 15:30

Room: MC 108

Pizza Seminar

Speaker: John Bell (Western)

"Oppositions and Paradoxes in Mathematics and philosophy"

Time: 17:00

Room: MC 108

From antiquity mathematics and philosophy has been beset by a number of oppositions, such as the Continuous and the Discrete, the One and the Many, the Finite and the Infinite, the Whole and the Part, and the Constant and the Variable. These oppositions have on occasion crystallized into paradox and they continue to haunt fundamental thinking to this day. In my talk I'll analyze some of these and describe their impact on the development of mathematics and philosophy.

Colloquium

Speaker: Rajesh Kulkarni (Michigan State)

"Perverse sheaves on compactifications of locally symmetric varieties"

Time: 15:30

Room: MC 108

Algebra Seminar

Speaker: Sam Isaacson (Western)

"Tensor products in homotopical algebra"

Time: 14:30

Room: MC108

In 1969, Quillen introduced the notion of "model category" as an axiomitization of homotopy theory. In the intervening four decades model categories have been proven to be remarkably useful in homotopy theory. In this talk, I will discuss a structure theorem giving a notion of a presentation of a model category, refining a 2001 paper of Dan Dugger; and I will introduce a monoidal structure on the category of model categories that simplifies many "generic" arguments in model category theory.