This will discuss the paper of Ricci, Tseytlin & Wolf from 2007.
Colorectal cancer (CRC) is one of the leading causes of cancer-related death worldwide, demanding a response from scientists and clinicians to understand its aetiology and develop effective treatment. CRC is thought to originate via genetic alterations that cause disruption to the cellular dynamics of the crypts of Lieberkűhn, test-tube shaped glands located in both the small and large intestine, which are lined with a monolayer of epithelial cells. It is believed that during colorectal carcinogenesis, dysplastic crypts accumulate mutations that destabilise cell-cell contacts, resulting in crypt buckling and fission. Once weakened, the corrupted structure allows mutated cells to migrate to neighbouring crypts, to break through to the underlying tissue and so aid the growth and malignancy of a tumour. To provide further insight into the tissue-level effects of these genetic mutations, a multi-scale model of the crypt with a realistic, deformable geometry is required. This talk concerns the progress and development of such a model, and its usefulness as a predictive tool to further the understanding of interactions across spatial scales within the context of colorectal cancer.
This will be a review of recent work that obtains amplitudes at strong coupling from certain minimal surfaces in AdS.
Abstract: We will review Kreimer's construction of a Hopf algebra for Feynman graphs, and explore several aspects of this structure including its relationship with renormalization and the (trivial) Hochschild cohomology of the algebra. Although Kreimer's construction is heavily tied with the language of renormalization, we show that it leads naturally to recursion relations resembling the BCFW relations, which can be expressed using twistors in the case of N=4 super-Yang-Mills (where there are no ultra-violet divergences). This could suggest that a similar Hopf algebra structure underlies the supersymmetric recursion relations...
I will discuss what is known about the cohomology of several moduli spaces coming from algebraic and differential geometry. These are: moduli spaces of non-singular curves (= Riemann surfaces) $M_g$, moduli spaces of nodal curves $\overline{M}_g$, moduli spaces of holomorphic line bundles on curves $Hol_g^k \to M_g$, and the universal Picard varieties $Pic^k_g \to M_g$. I will construct characteristic classes on these spaces, talk about their homological stability, and try to explain why the constructed classes are the only stable ones. If there is time I will also talk about the Picard groups of these moduli spaces.
Much of this work is due to other people, but some is joint with J. Ebert.
This talk will largely be a survey and so will gloss over technicalities. After introducing the basics of the theory of the étale fundamental group I will state the theorems and conjectures related to Grothendieck's famous "anabelian" letter to Faltings. The idea is that the geometry and arithmetic of certain varieties is in some sense governed by their non-abelian (anabelian) fundamental group. Time permitting I will discuss current work in this area, particularly the work of Minhyong Kim relating spaces of (Hodge, étale) path torsors to finiteness theorems for rational points on curves leading to a conjectural proof of Faltings' theorem which has been much discussed in recent years.