Junior Geometry and Topology Seminar
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Thu, 13/10/2011 12:00 |
Maria Buzano |
Junior Geometry and Topology Seminar  |
L3 |
| We will present a class of compact and connected homogeneous spaces such that the Ricci flow of invariant Riemannian metrics develops type I singularities in finite time. We will describe the singular behaviours that we can get, as we approach the singular time, and the Ricci soliton that we obtain by blowing up the solution near the singularity. Finally, we will investigate the existence of ancient solutions when the isotropy representation decomposes into two inequivalent irreducible summands. | |||
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Thu, 20/10/2011 12:00 |
Tom Sutherland |
Junior Geometry and Topology Seminar |
SR2 |
We will describe the space of Bridgeland stability conditions
of the derived category of some CY3 algebras of quivers drawn on the
Riemann sphere. We give a biholomorphic map from the upper-half plane to
the space of stability conditions lifting the period map of a meromorphic
differential on a 1-dimensional family of elliptic curves. The map is
equivariant with respect to the actions of a subgroup of  on the
left by monodromy of the rational elliptic surface and on the right by
autoequivalences of the derived category.
The complement of a divisor in the rational elliptic surface can be
identified with Hitchin's moduli space of connections on the projective
line with prescribed poles of a certain order at marked points. This is
the space of initial conditions of one of the Painleve equations whose
solutions describe isomonodromic deformations of these connections. |
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Thu, 27/10/2011 12:00 |
Heinrich Hartmann |
Junior Geometry and Topology Seminar |
SR2 |
| We will explain Bridgelands results on the stabiltiy manifold of a K3 surface. As an application we will define the stringy Kaehler moduli space of a K3 surface and comment on the mirror symmetry picture. | |||
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Thu, 03/11/2011 12:00 |
Benjamin Volk |
Junior Geometry and Topology Seminar |
SR2 |
We will give an introduction to the theory of d-manifolds, a new class of geometric objects recently/currently invented by Joyce (see http://people.maths.ox.ac.uk/joyce/dmanifolds.html). We will start from scratch, by recalling the definition of a 2-category and talking a bit about  -rings, -schemes and d-spaces before giving the definition of what a d-manifold should be. We will then discuss some properties of d-manifolds, and say some words about d-manifold bordism and its applications. |
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Thu, 10/11/2011 12:00 |
Tim Adamo |
Junior Geometry and Topology Seminar |
SR2 |
| Chern-Simons theory is topological gauge theory in three dimensions that contains an interesting class of operators called Wilson lines/loops, which have connections with both physics and pure mathematics. In particular, it has been shown that computations with Wilson operators in Chern-Simons theory reproduce knot invariants, and are also related to Gauss linking invariants. We will discuss the complex generalizations of these ideas, which are known as holomorphic Chern-Simons theory, Wilson operators, and linking, in the setting of Calabi-Yau three-folds. This will (hopefully) include a definition of all three of these holomorphic analogues as well as an investigation into how these ideas can be translated into simple homological algebra, allowing us to propose the existence of "homological Feynman rules" for computing things like Wilson operators in a holomorphic Chern-Simons theory. If time permits I may say something about physics too. | |||
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Thu, 17/11/2011 12:00 |
Michael Gröchenig |
Junior Geometry and Topology Seminar |
SR2 |
This is the first in a series of  talks about Stable Homotopy Theory. We will motivate the definition of spectra by the Brown Representability Theorem, which allows us to interpret a spectrum as a generalized cohomology theory. Along the way we recall basic notions from homotopy theory, such as suspension, loop spaces and smash products. |
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Thu, 24/11/2011 12:00 |
John Calabrese |
Junior Geometry and Topology Seminar |
SR2 |
| More perspectives on spectra. | |||
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Thu, 01/12/2011 12:00 |
Martin Palmer |
Junior Geometry and Topology Seminar |
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| After recalling some definitions and facts about spectra from the previous two "respectra" talks, I will explain what Thom spectra are, and give many examples. The cohomology theories associated to various different Thom spectra include complex cobordism, stable homotopy groups, ordinary mod-2 homology....... I will then talk about Thom's theorem: the ring of homotopy groups of a Thom spectrum is isomorphic to the corresponding cobordism ring. This allows one to use homotopy-theoretic methods (calculating the homotopy groups of a spectrum) to answer a geometric question (determining cobordism groups of manifolds with some specified structure). If time permits, I'll also describe the structure of some cobordism rings obtained in this way. | |||
