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Contents 
• Preface .......5
• Participants .......6
• Seminars .......7
• Photo of participants of workshop ``New methods in Hilbert's tenth problem'' .......14
• Program of workshop ``New methods in Hilbert's tenth problem'' .......16
• Program of research workshop .......21
• Photo of participants of research workshop .......24
• Derenthal U., Loughran D. Singular del Pezzo surfaces that are equivariant compactifications .......26
• Dieulefait L. On the modularity of rigid Calabi--Yau threefolds: Epilogue .......44
• Davis M. Representation theorems for r.e. sets and a conjecture related to Poonen's larges subring of $\Bbb{Q}$ .......50
• Zahid J. Non-singular points on Hypersurfaces over $\Bbb F_{q}$ .......55
• Marmon O. A generalization of the Bombieri-Pila determinant method .......63
• Matiyasevich Yu. Towards finite-fold Diophantine representations .......78
• Niedermowwe N. The circle method with weights for the representation of integers by quadratic forms .......91
• Pasten H., Pheidas T., Vidaux X. A survey on B\"uchi's problem: new presentations and open problems .......111
• Poonen B. Curves over every global field violating the local-global principle .......141
• Flicker Yu. Z. Base change for Hilbert eigenvarieties of unitary groups .......148
• Heath-Brown D. R. Bounds for the cubic weyl sum .......199
• Evertse J.-H. On the quantitative subspace theorem .......217
• Reviews .......241

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• Paging 245 pp.

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