Transcendence in Algebra, Combinatorics, Geometry and Number Theory

Frobenius action on a hypergeometric curve and an algorithm for computing values of Dwork's p-adic hypergeometric functions (Asakura).- A Matrix version of Dwork's Congruences (Beukers).- On the kernel curves associated with walks in the quarter plane (Singer).- A survey on the hypertranscendence of the solutions of the Schröder's, Böttcher's and Abel's equations (Fernandes).- Hodge structures and di?erential operators (Vlasenko).- Beck-type identities for Euler pairs of order (Welch et al.).- Quarter-plane lattice paths with interacting boundaries: the Kreweras and reverse Kreweras models (Xu et al.).- Infinite product formulae for generating functions for sequences of squares (Radu et al.).- A theta identity of Gauss connecting functions from additive and multiplicative number theory (Merca).- Combinatorial quantum ?eld theory and the Jacobian conjecture (Tanasa).- How regular are regular singularities? (Hauser).- Néron desingularization of extensions of valuation rings withan appendix by kestutis cesnavicius (Popescu).- Diagonal Representation of Algebraic Power Series: A Glimpse Behind the Scenes (Yurkevich).- Proof of chudnovskys' hypergeometric series for 1/p using weber modular polynomials (Guillera).-Computing an order-complete basis for m8(n) and applications (Radu et al.).- An algorithm to prove holonomic differential equations for modular forms (Radu et al.).- A case study for ?(4) (zudilin et al.).- Support of an algebraic series as the range of a recursive sequence (bell).- X-coordinates of pell equations in various sequences (luca).- A conditional proof of the leopoldt conjecture for cm fields (mihailescu).- Siegel's problem for e-functions of order 2 (Roques et al.).- Irrationality and Transcendence of Alternating Series Via Continued Fractions (Snowdow).- On the transcendence of critical hecke l-values (sprang).