Geometry and Topology

Speaker: Jeffrey Morton (Western)

"Extended TQFT by 2-Linearization"

Time: 15:30

Room: MC 108

In this talk, I will describe a 2-functor, called "2-linearization", from spans of groupoids into 2-vector spaces (C-linear abelian categories). Using groupoids representing moduli stacks of flat connections, this gives rise, for every finite group G, to an "extended topological quantum field theory", a 2-functorial invariant for manifolds with corners. I will also discuss how to extend this to compact Lie groups, including measures on stacks, and a generalization of the category of distintegrations (a nice category of measure spaces) to stacks.

Ph.D. Presentation

Speaker: Enxin Wu (Western)

"Some Aspects of Diffeological Spaces"

Time: 15:30

Room: MC 108

Manifolds are very nice objects in modern mathematics. However, the category of manifolds is not that pleasant. Many generalizations of manifolds are proposed around 1980's. Diffeological spaces are one of them, which were first defined by J. Souriau in 1980, and later on systematically developed by P. Iglesias-Zemmour, J. Baez, A. Hoffnung and others. In this talk, some known results on the basic properties of diffeological spaces and some of their differential geometric and topological aspects will be described. Some new results on the general topological aspects and categorical aspects will be presented at the end.

Ph.D. Presentation

Speaker: Tom Prince (Western)

"tba"

Time: 15:30

Room: MC 107

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Stable Homotopy

Speaker: Enxin Wu (Western)

"Freeness of modules over the Steenrod algebra: part 2"

Time: 11:30

Room: MC 107

Colloquium

Speaker: Patrick Brosnan (UBC)

"The zero locus of an admissible normal function"

Time: 15:30

Room: MC 108

I describe recent work with Greg Pearlstein proving that the zero locus of an admissible normal function is algebraic. I will explain why this is a generalization of a result of Cattani, Deligne and Kaplan showing that the Noether-Lefschetz locus is algebraic. I will also explain why the key step in the proof is a boundedness theorem for period maps. In addition, I will spend some time motivating the result and explaining how normal functions arose in Lefschetz's proof the Hodge conjecture for surfaces (the 1-1 theorem) and how they also are related to the Hodge conjecture for arbitrary varieities.

Symplectic Learning Seminar

Speaker: M. VanHoof

"Symplectic Cutting"

Time: 13:30

Room: MC 105C

We will explain the symplectic cutting construction and some of its applications.

Noncommutative Geometry

Speaker: Ivan Dynov (York)

"Introduction to von Neumann algebras I"

Time: 14:30

Room: MC 106

This lecture series on von Neumann algebras consists of four lectures. Von Neumann algebras were discovered by von Neumann (and further developed together with Murray) in the thirties and were intended to give a rigorous explanation behind quantum mechanics. In the first lecture we present the definition of von Neumann algebras and states and give some first properties. In the second lecture, we continue with the first classification of factors (which are building blocks of von Neumann algebras), due to Murray and von Neumann. We end with a generalization of the semi-direct product (as in group theory) to von Neumann algebras, the so-called crossed product. In the third lecture we further explore the crossed product, in particular the famous construction of Krieger, of crossed product of discrete abelian dynamical systems. The final lecture deals with the Tomita-Takesaki theory and the classification of type III factors due to Alain Connes.

Noncommutative Geometry

Speaker: Ivan Dynov (York)

"Introduction to von Neumann algebras II"

Time: 14:30

Room: MC 106

This lecture series on von Neumann algebras consists of four lectures. Von Neumann algebras were discovered by von Neumann (and further developed together with Murray) in the thirties and were intended to give a rigorous explanation behind quantum mechanics. In the first lecture we present the definition of von Neumann algebras and states and give some first properties. In the second lecture, we continue with the first classification of factors (which are building blocks of von Neumann algebras), due to Murray and von Neumann. We end with a generalization of the semi-direct product (as in group theory) to von Neumann algebras, the so-called crossed product. In the third lecture we further explore the crossed product, in particular the famous construction of Krieger, of crossed product of discrete abelian dynamical systems. The final lecture deals with the Tomita-Takesaki theory and the classification of type III factors due to Alain Connes.

Pizza Seminar

Speaker: Emre Coskun (Western)

"An elementary introduction to elliptic curves"

Time: 17:00

Room: MC 108

The theory of elliptic curves is a fascinating field with many connections to algebraic geometry, number theory, complex analysis and even computational problems. In this talk, we introduce these objects in a very elementary manner, describe some of their properties and as an application, we show how they can be used to prove special cases of Fermat's Last Theorem.

Noncommutative Geometry

Speaker: Ivan Dynov (York)

"Introduction to von Neumann algebras III"

Time: 15:00

Room: MC 108

This lecture series on von Neumann algebras consists of four lectures. Von Neumann algebras were discovered by von Neumann (and further developed together with Murray) in the thirties and were intended to give a rigorous explanation behind quantum mechanics. In the first lecture we present the definition of von Neumann algebras and states and give some first properties. In the second lecture, we continue with the first classification of factors (which are building blocks of von Neumann algebras), due to Murray and von Neumann. We end with a generalization of the semi-direct product (as in group theory) to von Neumann algebras, the so-called crossed product. In the third lecture we further explore the crossed product, in particular the famous construction of Krieger, of crossed product of discrete abelian dynamical systems. The final lecture deals with the Tomita-Takesaki theory and the classification of type III factors due to Alain Connes.

Stable Homotopy

Speaker: Enxin Wu (Western)

"Freeness of modules over the Steenrod algebra: part 3"

Time: 11:30

Room: MC 108

Noncommutative Geometry

Speaker: Ivan Dynov (York)

"Introduction to von Neumann algebras IV"

Time: 12:30

Room: MC 106

This lecture series on von Neumann algebras consists of four lectures. Von Neumann algebras were discovered by von Neumann (and further developed together with Murray) in the thirties and were intended to give a rigorous explanation behind quantum mechanics. In the first lecture we present the definition of von Neumann algebras and states and give some first properties. In the second lecture, we continue with the first classification of factors (which are building blocks of von Neumann algebras), due to Murray and von Neumann. We end with a generalization of the semi-direct product (as in group theory) to von Neumann algebras, the so-called crossed product. In the third lecture we further explore the crossed product, in particular the famous construction of Krieger, of crossed product of discrete abelian dynamical systems. The final lecture deals with the Tomita-Takesaki theory and the classification of type III factors due to Alain Connes.

Stable Homotopy

Speaker: David Barnes (Western)

"Sub-Hopf algebras of the Steenrod algebra"

Time: 11:30

Room: MC 107