An effective criterion for Eulerian multizeta values in positive characteristic

Characteristic p multizeta values were initially studied by Thakur, who defined them as analogues of classical multiple zeta values of Euler. In the present paper we establish an effective criterion for Eulerian multizeta values, which characterizes when a multizeta value is a rational multiple of a power of the Carlitz period. The resulting "t-motivic" algorithm can tell whether any given multizeta value is Eulerian or not. We also prove that if zeta_A(s_1,...,s_r) is Eulerian, then zeta_A(s_2,...,s_r) has to be Eulerian. When r=2, this was conjectured (and later on conjectured for arbitrary r) by Lara Rodriguez and Thakur for the zeta-like case from numerical data. Our methods apply equally well to values of Carlitz multiple polylogarithms at algebraic points and zeta-like multizeta values.Comment: 32 page

On F-theory E_6 GUTs

We approach the Minimum Supersymmetric Standard Model (MSSM) from an E_6 GUT by using the spectral cover construction and non-abelian gauge fluxes in F-theory. We start with an E_6 singularity unfolded from an E_8 singularity and obtain E_6 GUTs by using an SU(3) spectral cover. By turning on SU(2) X U(1)^2 gauge fluxes, we obtain a rank 5 model with the gauge group SU(3) X SU(2) X U(1)^2. Based on the well-studied geometric backgrounds in the literature, we demonstrate several models and discuss their phenomenology.Comment: 42 pages, 17 tables; typos corrected, clarifications added, and references adde