10:00 to 11:00 Katrin Wendland (Albert-Ludwigs-Universität Freiburg)Vertex Operator Algebras from Calabi-Yau Geometries Vertex operator algebras occur naturally as mathematically well tractable ingredients to conformal field theories (CFTs), capturing in general only a small part of the structure of the latter. The talk will highlight a few examples for which this procedure yields a natural route from Calabi-Yau geometries to vertex operator algebras. Moreover, we will discuss a new technique, developed in joint work with Anne Taormina, which transforms certain CFTs into vertex operator algebras and their admissible modules, thus capturing a major part of the structure of the CFT in terms of a vertex operator algebra. INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Simon Gritschacher (University of Oxford)Coefficients for commutative K-theory Recently, the study of representation spaces has led to the definition of a new cohomology theory, called commutative K-theory. This theory is a refinement of classical topological K-theory. It is defined using vector bundles whose transition functions commute with each other whenever they are simultaneously defined. I will begin the talk by discussing some general properties of the „classifying space for commutativity in a Lie group“ introduced by Adem-Gomez. Specialising to the unitary groups, I will then show that the spectrum for commutative complex K-theory is precisely the ku-group ring of infinite complex projective space. Finally, I will present some results about the real variant of commutative K-theory. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 14:30 Danny Stevenson (University of Adelaide)Pre-sheaves of spaces and the Grothendieck construction in higher geometry The notion of pre-stack in algebraic geometry can be formulated either in terms of categories fibered in groupoids, or else as a functor to the category of groupoids with composites only preserved up to a coherent system of natural isomorphisms.  The device which lets one shift from one perspective to the other is known as the Grothendieck construction' in category theory.  A pre-sheaf in higher geometry is a functor to the ∞-category of ∞-groupoids; in this context keeping track of all the coherent natural isomorphisms between composites becomes particularly acute.  Fortunately there is an analog of the Grothendieck construction in this context, due to Lurie, which lets one straighten out' a pre-sheaf into a certain kind of fibration.  In this talk we will give a new perspective on this straightening procedure which allows for a more conceptual proof of Lurie's straightening theorem. INI 1 14:30 to 15:30 Yang-Hui He (City University, London); (University of Oxford)Calabi-Yau volumes and Reflexive Polytopes We study various geometrical quantities for Calabi-Yau varieties realized as cones over Gorenstein Fano varieties in various dimensions, obtained as toric varieties from reflexive polytopes. One chief inspiration comes from the equivalence of a-maximization and volume-minimization in for Calabi-Yau threefolds, coming from AdS5/CFT4 correspondence in physics. We arrive at explicit combinatorial formulae for many topological quantities and conjecture new bounds to the Sasaki-Einstein volume function with respect to these quantities. Based on joint work with Rak-Kyeong Seong and Shiing-Tung Yau. INI 1 15:30 to 16:00 Afternoon Tea