09:00 to 09:25 Registration 09:25 to 09:30 Welcome from INI Director, Christie Marr 09:30 to 10:30 Divergence and super-divergence cocycles on the Grothendieck-Teichmueller Lie algebra The Grothendieck-Teichmueller Lie algebra grt can be viewed as a Lie subalgebra of derivations of the free Lie algebra in two generators. We use this observation to define two cocycles: the divergence cocycle on grt and the super-divergence cocycle on its even part. The divergence cocycle serves to define the Kashiwara-Vergne Lie algebra which is conjecturally isomorphic to grt. The super-divergence cocycle plays a role in the Rouviere's theory of symmetric spaces, and it is conjectured to be an injective map on the even part of grt. INI 1 10:30 to 11:00 Morning Coffee 11:00 to 12:00 Honorary MZVs and modular forms $\sum_{a>b>c>d>e>0}(-1)^{b+d}/(a^3b^6c^3d^6e^3)$ is an alternating sum with weight 21 and depth 5, yet has a conjectural expression as a Q-linear combination of multiple zeta values (MZVs) that includes a sum of depth 7. The MZV Data Mine [arXiv:0907.2557] contains many other examples of "honorary MZVs", i.e. alternating sums that are reducible to MZVs, sometimes at the expense of an increase of depth by an even integer. This talk concerns the conjecture that the enumeration of MZVs that are not reducible to MZVs of lesser depth, yet are reducible to alternating sums of lesser depth, is generated by an enumeration of modular forms. INI 1 12:15 to 13:15 Lunch at Wolfson Court 13:30 to 14:30 Towards higher dimensional analogues of the torsor of Drinfeld's associators The purpose of this talk is to give a description of the set of homotopy classes of formality quasi-isomorphisms for a Sullivan model of the Little n-discs operads, where we consider any n>1. The Sullivan model of a topological operad combines a commutative dg-algebra structure, reflecting the rational homotopy of the spaces underlying the operad, and a cooperad structure, reflecting the composition structures of the operad. I will explain the definition of an obstruction spectral sequence for the formality of these Sullivan models of operads. I will give a description of the obstruction spectral sequence associated to the little discs operads, and I will explain the connection with the definition of the Drinfeld associators. INI 1 14:30 to 15:00 Afternoon Tea 15:00 to 16:00 Multiple Dedekind Zeta Functions In this paper we define multiple Dedekind zeta values (MDZV), using a new type of iterated integrals, called iterated integrals on a membrane. One should consider them as generalizations of Euler's multiple zeta values to arbitrary number fields. Over imaginary quadratic fields MDZV capture in particular multiple Eisenstein series [ZGK]. We give an analogue of multiple Eisenstein series over real quadratic field. And an alternative definition of values of multiple Eisenstein-Kronecker series [G]. Each of them as a special case of multiple Dedekind zeta values. MDZV are interpolated into functions that we call multiple Dedekind zeta functions (MDZF). We show that MDZF have integral representation and can be written as infinite sums, and have an analytic continuation. Finally, we prove that the multiple residue of a multiple Dedekind zeta function at (1,...,1) is a period. INI 1 16:30 to 17:30 Associators and representations of braids >From their very construction 20 years ago as elements of a torsor for the Grothendieck-Teichmueller group, Drinfeld associators provide representations of the (usual) braid groups. The study of representation-theoretic consequences of this construction reverberate into questions on associators, and provide conjectural views on what to expect from generalizations of associators to other types of braid groups, where the symmetric group is replaced by more general reflection groups. This talk will review some of these questions as well as the state of the art in this area. INI 1 17:30 to 19:00 Wine Reception & Poster session
 09:30 to 10:30 Anatomy of the motivic Lie algebra The motivic Lie algebra is contained in the Grothendieck-Teichmuller Lie algebra, and is isomorphic to the free graded Lie algebra with one generator in every odd degree >1. Using motivic MZV's one can define canonical generators for this algebra, but their arithmetic properties are very mysterious. In this talk, I will explain how elements of the motivic Lie algebra admit a kind of Taylor expansion with a rich internal structure. This is closely connected with the theory of modular forms, universal elliptic motives, and some other unexpected algebraic objects. INI 1 10:30 to 11:00 Morning Coffee 11:00 to 12:00 Motivic Superstring Amplitudes We review the recent advances in open superstring N-point tree-level computations. One basic ingredient is a basis of (N-3)! generalized Gaussian hypergeometric functions (generalized Euler integrals) encoding all string effects through their dependence on the string tension $\alpha'$. The structure of the open superstring amplitudes is analyzed. We find a striking and elegant form, which allows to disentangle its $\alpha'$ power series expansion into several contributions accounting for different classes of multiple zeta values. This form is bolstered by the decomposition of motivic multiple zeta values, i.e. the latter encapsulate the $\alpha'$-expansion of the superstring amplitude. Moreover, a morphism induced by the coproduct maps the $\alpha'$-expansion onto a non-commutative Hopf algebra. This map represents a generalization of the symbol of a transcendental function. In terms of elements of this Hopf algebra the alpha'-expansion assumes a very simple and symmetric form, which carries all the relevant information. INI 1 12:15 to 13:15 Lunch at Wolfson Court 13:30 to 14:30 O Schnetz (Friedrich-Alexander-Universität Erlangen-Nürnberg)Proof of the zig-zag conjecture In quantum field theory primitive Feynman graphs give--via the period map--rise to renormalization scheme independent contribution to the beta function. While the periods of many Feynman graphs are multiple zeta values there exists the distinguished family of zig-zag graphs whose periods were conjectured in 1995 by Broadhurst and Kreimer to be certain rational multiples of odd single zetas. In joint work with F. Brown it was possible in 2012 to prove the zig-zag conjecture using the theory of graphical functions, single valued multiple polylogarithms and a theorem by D. Zagier on multiple zeta values of the form zeta(2,...,2,3,2,...,2). INI 1 14:30 to 15:00 Afternoon Tea 15:00 to 16:00 Polylogarithms, Multiple Zeta Values and Superstring Amplitudes Superstring Theory is one of the most promising candidates for a quantum theory of gravity. Its interactions involve all kinds of multiple zeta values, and I will present how they emerge at the leading order (so-called tree level) of open string scattering amplitudes. The expansion of the underlying generalized Gaussian hypergeometric functions in the string tension gives rise to iterated integrals within the [0,1] interval. I will discuss polylogarithm manipulations required for their systematic reduction to multiple zeta values. INI 1 19:30 to 22:00 Conference Dinner at Corpus Christi College