Noncommutative Geometry

Speaker: TBA (Western)

"NCG Learning Seminar"

Time: 15:00

Room: MC 107

Analysis Seminar

Speaker: Tatyana Foth (Western)

"K\"ahler manifolds, line bundles, and quantization."

Time: 15:30

Room: MC 108

It will be a survey talk, with an overview of some recent results related to complex geometry, geometric quantization, and Toeplitz operators.

Noncommutative Geometry

Speaker: (Western)

"NCG Learning Seminar"

Time: 15:00

Room: MC 107

Colloquium

Speaker: Megumi Harada (McMaster University)

"The topology of Hamiltonian quotients"

Time: 15:30

Room: MC 108

Symplectic geometry lies at the crossroads of many exciting areas of research due to its relationship to geometric

representation theory, combinatorics, and algebraic geometry, among others. As often happens in mathematics, the presence of symmetry in these geometric structures -- in this context, a {\em Hamiltonian G-action} for G a Lie group -- turns out to be crucial in the computation of topological invariants, such as the Betti numbers, the cohomology ring, or the K-theory, of symplectic manifolds which arise as {\em Hamiltonian quotients}. I will give a bird's-eye, motivating overview of this subject. Time permitting, I will give a brief survey of my recent work on this topic, which include generalizations of previous work to hyperk\"ahler geometry, as well as to cases in which the symmetry group is the infinite-dimensional loop group LG of a compact Lie group.

Hodge Theory

Speaker: Priyavrat Deshpande (Western)

"Hermitian Differential Geometry"

Time: 10:00

Room: MC 104

Analysis Seminar

Speaker: André Boivin (Western)

"Uniform approximation on Riemann surfaces - a survey."

Time: 15:30

Room: MC 108

A closed subset E of a Riemann surface R is called a set of holomorphic (resp. meromorphic) approximation if every function continuous on E and holomorphic on Int(E) can be approximated uniformly on E by functions holomorphic (resp. meromorphic) on (all of) R. When R is the complex plane, a complete characterization of the sets of approximation is known. For arbitrary noncompact Riemann surfaces, and E noncompact, the problem is still wide open.

Algebra Seminar

Speaker: Peter Oman (Western)

"Goodwillie calculus and a differential-geometric interpretation to problems in homotopy theory"

Time: 15:00

Room: MC 107

Analysis Seminar

Speaker: Hun Hee Lee (University of Waterloo)

"* CANCELED *"

Time: 15:30

Room: MC 108

Projectivity of certain non-commutative L_p spaces as modules over Fourier algebra.

Dales and Polyakov (2004) investigated projectivity of left L1(G)-modules for locally compact group G. The class of modules include C_0(G) and L^p(G) for 1< p < ∞. They proved that C_0(G) (resp. L^p(G) for 1<p<∞) is projective iff G is compact. In this talk we focus on the dual situation, namely A(G)-modules C^*_r(G) and L^p(VN(G)) for 1<p< ∞. We will show that C^*_r(G) (resp. L^p(VN(G)) for 1<p<∞) is an operator projective left A(G)-module when G is discrete and amenable. Conversely, we can show that C^*_r(G) (resp. L^p(VN(G)) for 2≤ p < ∞) is not operator projective when G is not discrete. Unlike in the case of L1(G)-modules amenability plays an important role here. Indeed, C^*_r(G) (resp. L^p(VN(G)) for 1<p<∞) is not an projective left operator A(G)-module when G is a discrete group containing \mathbb{F}_2, the free group with two generators.

Hodge Theory

Speaker: Enxin Wu (Western)

"Examples of connection and curvature on vector bundles."

Time: 10:00

Room: MC 104

Noncommutative Geometry

Speaker: Farzad Fathizadeh (Western)

"pseudodifferential operators and index theory 1"

Time: 15:00

Room: MC 107

Using heat equation methods, the index of an elliptic operator can be computed by a local formula. In this series of lectures, we will review the necessary analysis for defining the index of an elliptic operator, and derive a local formula for the index.

Analysis Seminar

Speaker: Rasul Shafikov (Western)

"Introductions to CR functions"

Time: 15:30

Room: MC 108

In this three lecture series I will give a general introduction to CR functions. I will start with basic definitions and examples. Then I will give an overview of classical results on holomorphic extension and approximation of CR functions. In the last lecture I will discuss the recent joint work with Chakrabarti on CR functions on singular hypersurfaces.

Noncommutative Geometry

Speaker: Farzad Fathizadeh (Western)

"pseudodifferential operators and index theory 2"

Time: 15:00

Room: MC 107

Using heat equation methods, the index of an elliptic operator can be computed by a local formula. In this series of lectures, we will review the necessary analysis for defining the index of an elliptic operator, and derive a local formula for the index.

Hodge Theory

Speaker: Enxin Wu (Western)

"Examples of connection and curvature on vector bundles. Part II."

Time: 10:00

Room: MC 106

Algebra Seminar

Speaker: Enxin Wu (Western)

"Deformation and Hochschild cohomology of A-infinity algebras with an application"

Time: 15:00

Room: MC 107

In this talk, we will review the deformation and Hochschild cohomology of associative algebras and generalize it to A-infinity algebras. One simple application will be given afterwards. This is based on my extended master thesis in China, which can be downloaded at http://www.math.uwo.ca/~ewu22/notes.html. Slides will be used in this talk.

Noncommutative Geometry

Speaker: Farzad Fathizadeh (Western)

"pseudodifferential operators and index theory 3"

Time: 15:00

Room: MC 107

Using heat equation methods, the index of an elliptic operator can be computed by a local formula. In this series of lectures, we will review the necessary analysis for defining the index of an elliptic operator, and derive a local formula for the index."

Analysis Seminar

Speaker: Rasul Shafikov (Western)

"Introductions to CR functions II"

Time: 15:30

Room: MC 108

Colloquium

Speaker: Joel Kamnitzer (University of Toronto)

"Categorical actions of sl(2) and equivalences of categories"

Time: 14:30

Room: MC 108

Actions of the Lie algebra sl(2) on vector spaces arise naturally in combinatorics, geometry, and algebra. Such an action consists of a sequence of vector spaces with linear maps between them satisfying certain relations.

From this perspective, one can define an action of sl(2) on a category to be a sequence of categories with functors between them satisfying certain relations. Such actions were studied by Chuang-Rouquier in the context of representations of the symmetric group in positive characteristic. More recently, Cautis, Licata, and the speaker studied an action of sl(2) where the categories involved were derived categories of coherent sheaves on cotangent bundles to Grassmannians. Following the ideas of Chuang-Rouquier, we used this sl(2) action to construct an equivalence of derived categories between different cotangent bundles of Grassmannians.

Hodge Theory

Speaker: Richard Gonzales (Western)

"Chern classes of differentiable vector bundles."

Time: 10:00

Room: MC 106