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30 Geometry and Topology
Geometry and Topology Speaker: Jeffrey Morton (Western) "Extended TQFT by 2-Linearization" Time: 15:30 - 16:30 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. |
1 Ph.D. Presentation
Ph.D. Presentation Speaker: Enxin Wu (Western) "Some Aspects of Diffeological Spaces" Time: 15:30 - 16:30 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. |
2 Ph.D. Presentation
Ph.D. Presentation Speaker: Tom Prince (Western) "tba" Time: 15:30 - 16:30 Room: MC 107 tba |
3 Stable Homotopy
Stable Homotopy Speaker: Enxin Wu (Western) "Freeness of modules over the Steenrod algebra: part 2" Time: 11:30 - 12:30 Room: MC 107 Colloquium
Colloquium Speaker: Patrick Brosnan (UBC) "The zero locus of an admissible normal function" Time: 15:30 - 16:30 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.
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4 Symplectic Learning Seminar
Symplectic Learning Seminar Speaker: M. VanHoof "Symplectic Cutting" Time: 13:30 - 14:30 Room: MC 105C We will explain the symplectic cutting construction and some of its applications. |
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7 Noncommutative Geometry
Noncommutative Geometry Speaker: Ivan Dynov (York) "Introduction to von Neumann algebras I" Time: 14:30 - 15:30 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.
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8 Noncommutative Geometry
Noncommutative Geometry Speaker: Ivan Dynov (York) "Introduction to von Neumann algebras II" Time: 14:30 - 15:30 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
Pizza Seminar Speaker: Emre Coskun (Western) "An elementary introduction to elliptic curves" Time: 17:00 - 18:00 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.
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9 Noncommutative Geometry
Noncommutative Geometry Speaker: Ivan Dynov (York) "Introduction to von Neumann algebras III" Time: 15:00 - 16:00 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.
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10 Stable Homotopy
Stable Homotopy Speaker: Enxin Wu (Western) "Freeness of modules over the Steenrod algebra: part 3" Time: 11:30 - 12:30 Room: MC 108 Noncommutative Geometry
Noncommutative Geometry Speaker: Ivan Dynov (York) "Introduction to von Neumann algebras IV" Time: 12:30 - 13:30 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.
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