Alan Carey, Australian National University, Canberra, Australia, David Ellwood, Clay Mathematics Institute, Cambridge, MA, Sylvie Paycha, Universite Blaise Pascal, Aubiere, France, and Steven Rosenberg, Boston University, MA, Editors

• Introductory articles: An introduction to motivic zeta functions of motives by Y. Andre Algebra for quantum fields by D. Kreimer Pseudodifferential operators and regularized traces by M. Lesch Renormalization in connected graded Hopf algebras: An introduction by D. Manchon Research articles: Fredholm realizations of elliptic symbols on manifolds with boundary II: Fibered boundary by P. Albin and R. Melrose Inversion of series and the cohomology of the moduli spaces $\mathcal{M}^{\delta}_{0,n}$ by J. Bergstrom and F. Brown C*-algebras in tensor categories by P. Bouwknegt, K. C. Hannabuss, and V. Mathai Structural relations of harmonic sums and Mellin transforms at weight $w=6$ by J. Blumlein Hopf subalgebras of rooted trees from Dyson-Schwinger equations by L. Foissy From gauge anomalies to Gerbes and Gerbal actions by J. Mickelsson A microlocal approach to Fefferman's program in conformal and CR geometry by R. Ponge Mirror symmetry for elliptic curves: The A-model (fermionic) counting by M. Roth and N. Yui A symbolic summation approach to find optimal nested sum representations by C. Schneider Logarithmic structures and TQFT by S. Scott Renormalization Hopf algebras for gauge theories and BRST-symmetries by W. D. van Suijlekom