Past Junior Geometry and Topology Seminar

14 November 2013
16:00
to
17:30
Jens-Jakob Kratmann Nissen
Abstract
By using the Weil-Gel'fand-Zak transform of Faddeev's quantum dilogarithm, Andersen and Kasheav have proposed a new state-integral model for the Andersen--Kashaev TQFT, where the circle valued state variables live on the edges of oriented levelled shaped triangulations. I will look at a couple of examples which give an idea of how the theories are coupled.
  • Junior Geometry and Topology Seminar
7 November 2013
16:00
to
17:30
Jan Vonk
Abstract
In this talk, I will describe how the eigenvalues of the Atkin operator on overconvergent modular forms might be related to the classical study of the Laplacian on certain manifolds. The goal is to phrase everything geometrically, so as to maximally engage the audience in discussion on possible approaches to study the spectral flow of this operator.
  • Junior Geometry and Topology Seminar
31 October 2013
16:00
to
17:30
Emily Cliff
Abstract
Motivated by the study of PDEs, we introduce the notion of a D-module on a variety X and give the basics of three perspectives on the theory: modules over the sheaf of differential operators on X; quasi-coherent modules with flat connection; and crystals on X. This talk will assume basic knowledge of algebraic geometry (such as rudimentary sheaf theory).
  • Junior Geometry and Topology Seminar
24 October 2013
16:00
to
17:30
Tom Hawes
Abstract
Consider a smooth, complex projective variety X inside P^n and an action of a reductive linear algebraic group G inside GL(n+1,C). On the one hand, we can view this as an algebra-geometric set-up and use geometric invariant theory (GIT) to construct a quotient variety X // G, which parameterises `most' of the closed orbits of X. On the other hand, X is naturally a symplectic manifold, and since G is reductive we can take a maximal real compact Lie subgroup K of G and consider the symplectic reduction of X by K with respect to an appropriate moment map. The Kempf-Ness theorem then says that the results of these two constructions are homeomorphic. In this talk I will define GIT and symplectic reduction and try to sketch the proof of the Kempf-Ness theorem.
  • Junior Geometry and Topology Seminar
17 October 2013
16:00
to
17:30
Jakob Blaavand
Abstract
In the talk we will discuss Quillen's construction of a determinant line bundle associated to a family of Cauchy-Riemann operators. I will first of all try to convince you why this is a cool thing and mention some of the many different applications. The bulk of the talk will be focused on constructing the line bundle, its hermitian metric and calculating the curvature. Hopefully a talk accessible to many.
  • Junior Geometry and Topology Seminar
30 May 2013
12:00
Vittoria Bussi
Abstract
This talk is not a detailed and precise exposition on DAG, but it is conceived more as a kind of advertisement on this theory and some of its interesting new features one should contemplate and try to understand, as they might reveal interesting new insights also on classical objects. We select some of the several motivations for introducing it (non-representability of moduli problem and non-naturality of the obstruction theory), and then we will go through the homotopy theory of simplicial commutative algebras and their cotangent complex. We will introduce the category of derived schemes and we will describe their relation with classical schemes. A good amount of time will be dedicated to examples.
  • Junior Geometry and Topology Seminar
23 May 2013
15:00
Rafael Torres
Abstract
"Among the first successes of the h-cobordism theorem was the classification of simply connected closed 5-manifolds. Dimension five is sufficiently large to be able to implement the tools of surgery theory, yet low enough to allow an explicit classification of the manifolds. These traits make dimension five interesting in terms of existence results of geometric structures, like Riemannian metrics of positive Ricci/nonnegative sectional/positive sectional curvature, Einstein metrics, contact structures, Sasakian structures, among others. The talk will be a limited survey of the five-dimensional symbiosis between topology and geometry"
  • Junior Geometry and Topology Seminar
16 May 2013
15:00
Robert Kropholler
Abstract
I will be taking us on a journey through low dimensional topology, starting in 2 dimensions motivating handles decompositions in a dimension that we can visualize, moving onto to a brief of note of what this means in 3 dimensions and then moving onto the wild world of 4 manifolds. I will be showing a way in which we can actually try and view a 4 manifold before moving onto a way of manipulating these diagrams to give diffeomorphic 4 manifolds. Hopefully, I will have time to go into some ways in which Kirby calculus has been used to show that certain potential exotic 4 spheres are not exotic and some results on stable diffeomorphims of 4 manifolds.
  • Junior Geometry and Topology Seminar

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