Geometry and Combinatorics

Speaker: Avi Steiner (Western)

"Intro to GKZ systems I"

Time: 15:30

Room: MC 108

TBA

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Combinatorics of Feynman diagrams and quantum field theory II"

Time: 11:00

Room: MC 108

Geometry and Topology

Speaker: Nikon Kurnosov (University of Georgia)

"Algebra and geometry of hyperkahler manifolds"

Time: 15:30

Room: MC 107

Hyperkahler manifolds are complex manifolds with a trivial canonical class. They are interesting both for algebraic and differential geometers. I would like to discuss some compact examples, and their geometry as well as the structure of their cohomology ring.

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Combinatorics of Feynman diagrams and quantum field theory III"

Time: 11:00

Room: MC 108

Geometry and Combinatorics

Speaker: Avi Steiner (Western)

"Intro to GKZ systems II"

Time: 15:30

Room: MC 108

TBA

Geometry and Topology

Speaker: Jeff Carlson (Western)

"An 19th-century approach to equivariant complex cobordism"

Time: 15:30

Room: MC 107

Despite its being an important universal object in equivariant homotopy theory, concrete generators-and-relations presentations for the coefficient ring of equivariant complex cobordism with respect to a compact abelian Lie group $G$ are still known only for finite $G$.

For $G$ a torus, Ginzburg--Karshon--Tolman observed that the well-known fixed-point integral localization formula of Atiyah--Bott--Berline--Vergne determines a naive upper bound on this ring, and the geometrically important case of a so-called GKM action, leaning on work of Darby, Carlson--Gamse--Karshon showed this bound is an equality.

The author has recently shown the same for semifree circle actions with isolated fixed points, unexpectedly recovering a 2004 result of Sinha with a new proof that is classical in the literal sense: it would have been accessible in the era of Beethoven. In this talk we will give background and sketch this proof.

Quantum Geometry

Speaker: Elliott Gesteau (Perimeter Institute)

"A new renormalization of Yukawa interactions in the Standard Model from Noncommutative Geometry"

Time: 14:30

Room: MC 108

The Spectral Action principle of Noncommutative Geometry has been extremely successful to understand the mathematical structure of the Standard Model of particle physics. However, as a classical framework, it does not yet encompass the corrections of renormalization, which are crucial to understand the quantized version of any field theory. In this talk, I will describe a first attempt to describe renormalization directly within the setting of Noncommutative Geometry, in the case of Yukawa interactions. In particular, I will show that Wetterich's theory of functional renormalization, when applied to a matrix model inspired from the Dirac operator of the Noncommutative Standard Model, reduces to the usual Feynman diagram approach.

Algebraic Geometry

Speaker: Nicole Lemire (Western)

"Lambda operations"

Time: 15:30

Room: WSC 187

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Combinatorics of Feynman diagrams and quantum field theory IV"

Time: 11:00

Room: MC 108

Colloquium

Speaker: Boris Khesin (Toronto)

"Integrability of pentagram maps and KdV hierarchies"

Time: 15:30

Room: MC 108

We describe pentagram maps on polygons in any dimension, which extend R.Schwartz's definition of the 2D pentagram map. Many of those maps turn out to be discrete integrable dynamical systems, while the corresponding continuous limits of such maps coincide with equations of the KdV hierarchy, generalizing the Boussinesq equation in 2D. We discuss their geometry, Lax forms, and interrelations between several recent pentagram generalizations.

Algebraic Geometry

Speaker: Nicole Lemire (Western)

"Lambda operations"

Time: 15:30

Room: WSC 187

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Combinatorics of Feynman diagrams and quantum field theory V"

Time: 11:00

Room: MC 108

Geometry and Combinatorics

Speaker: Avi Steiner (Western)

"Intro to GKZ systems III *cancelled*"

Time: 15:30

Room: MC 108

TBA

Geometry and Topology

Speaker: Xin Fu (Western)

"Homotopy types of partial quotients for a certain case"

Time: 15:30

Room: MC 107

A moment-angle complex is a space determined by a finite simplicial complex and is allowed a coordinatewise torus action. This space and its quotient provide connections among combinatorial, algebra and topology. In this talk, we look at the topological side. That is, we will determine the homotopy type of the quotient space given by the moment-angle complex corresponding to the k-skeleton of a simplex under the diagonal action.

Colloquium

Speaker: Tom Korner (Cambridge)

"Molehills out of Mountains"

Time: 15:30

Room: MC 108

We construct a hill such that any two points are connected by a path of zero slope (except at the end points). Such a hill cannot be given by a continuously differentiable function but can be given by a once differentiable function.

Quantum Geometry

Speaker: Asghar Ghorbanpour (Western)

"Inner Fluctuations as Gauge Theory for Spectral Triples"

Time: 14:30

Room: MC 108

Originated from the theory of connections on vector bundles over the spin manifolds, inner fluctuations of Dirac operator of spectral triples provide a mechanism through which the gauge fields can be implemented in the noncommutative geometry. In this talk, we shall go over the motivations and constructions that show why inner fluctuations can be interpreted as the gauge fields in the theory of spectral triples and how they generalize the gauge theory for the noncommutative geometries.

Algebraic Geometry

Speaker: Nicole Lemire (Western)

"Lambda operations"

Time: 15:30

Room: MC 108

Geometry and Combinatorics

Speaker: Ahmed Umer Ashraf (Western)

"CSM classes for matroids"

Time: 15:30

Room: MC 108

TBA

Quantum Geometry

Speaker: Masoud Khalkhali (Western)

"Combinatorics of Feynman diagrams and quantum field theory VI"

Time: 11:00

Room: MC 108

Geometry and Topology

Speaker: Avi Steiner (Western)

"Intersection cohomology, characteristic cycles, and affine cones"

Time: 15:30

Room: MC 107

Intersection cohomology, invented by Goresky and MacPherson, is a notion of cohomology for singular spaces which admits generalizations of classical theorems such as Poincare duality and the Lefschetz hyperplane theorem. It is constructed by taking global sections of a certain perverse sheaf called the intersection cohomology complex. This complex is itself an interesting topological invariant, and to study it one often looks at its characteristic cycle. In particular, if X is the affine cone over a projective variety Y, one can look at the multiplicity of this cycle over the vertex of X. I will discuss a conjecture of mine which would describe how this multiplicity changes with the projective embedding of Y, along with some evidence for the conjecture being true coming from the normal toric case.

Algebraic Geometry

Speaker: Nicole Lemire (Western)

"Adam's operations and the Gamma Filtration"

Time: 15:30

Room: WSC 187