Dept Oral Exam

Speaker: Ivan Kobyzev (Western)

"Algebraic stacks and equivariant K-theory"

Time: 11:00

Room: MC 107

We give a definition of a root stack and describe its most basic properties. We describe the algebraic K-theory of a root stack. Sufficient conditions for a quotient stack to be a root stack are given. When these 2 results are combined immediate applications to equivariant K-theory are obtained. For example, we extend the work of Ellingsgurd and Lonsted to higher dimensions and to higher K-groups.

Noncommutative Geometry

Speaker: (Western)

"Path Integrals 2"

Time: 11:00

Room: MC 106

Homotopy Theory

Speaker: Dan Christensen (Western)

"Computation and data structures in Coq"

Time: 13:30

Room: MC 107

I will give an overview of how to do computations in Coq, including non-trivial recursive computations. I will also describe data structures such as lists and trees, and show how they can be manipulated.

Noncommutative Geometry

Speaker: Ali Fathi (Western)

"Feynman-Kac formula 5"

Time: 11:00

Room: MC 108

Comprehensive Exam Presentation

Speaker: Sergio Chaves (Western)

"Conjugation Spaces"

Time: 14:30

Room: MC 107

Let X be a topological space and \tau an involution of X; \tau induces an action of the group G = { id, \tau} on X. A particular case is when X is a complex manifold and \tau is the complex conjugation; there some algebraic relations between the rings H*(X), H*(X^G) and H*_G(X) occur, where X^G denotes the fixed point subspace and H*_G(X) the G-equivariant cohomology ring of X. Such relations motivate the definition of cohomology frame and allow us to generalize the notion of complex conjugation to another topological spaces. Therefore, we say that a Conjugation Space is a space with involution which admits a cohomology frame. In this talk the notion of conjugation space is introduced, and some properties and examples of such spaces are presented.

Dept Oral Exam

Speaker: Sajad Sadeghi (Western)

"On Logarithmic Sobolev Inequality For the Noncommutative Two Torus and the Scalar Curvature Formula For the Noncommutative Three Torus"

Time: 10:00

Room: MC 106

I will first give an overview of the noncommutative geometry. Then I will discuss

the classic Sobolev type inequalities and also the logarithmic Sobolev inequality and will compare them.

Moreover, one of the main results, which is the logarithmic Sobolev inequality on the noncommutative

two torus (NCT2), will be be proved for a class of elements in NCT2. Afterwards, I will introduce a family of

spectral triples, each of which represents a class of conformaly perturbed metrics on the noncommutative

three torus (NCT3) as a noncommutative compact spin manifold. Then using Connes' pseudodifferential

calculus, I will define the scalar curvature of NCT3 equipped with the mentioned conformaly perturbed

metrics and will compute it by an explicit formula.