By Yves André (auth.), Umberto Zannier (eds.)

Since 2001 the Scuola Normale Superiore di Pisa has geared up the "Colloquio De Giorgi", a sequence of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a basic mathematical viewers, and particularly intended to draw graduate scholars and complicated undergraduate scholars. The lectures are meant to be now not too technical, in fields of vast curiosity. they need to supply an outline of the final subject, almost certainly in a ancient viewpoint, including an outline of newer growth. the assumption of accumulating the fabrics from those lectures and publishing them in annual volumes got here out lately, as a attractiveness in their intrinsic mathematical curiosity, and in addition with the purpose of holding reminiscence of those events.

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A. RUCI NSKI and E. S ZEMER E´ DI, A Dirac-type theorem [24] V. R ODL for 3-uniform hypergraphs, Combin. Probab. Comput. 15 (2006), 229–251. ´ ¨ , A. RUCI NSKI and E. S ZEMER E´ DI, An approximate [25] V. R ODL Dirac-type theorem for k-uniform hypergraphs, Combinatorica 28 (2008), 229–260. ´ ¨ , A. RUCI NSKI and E. S ZEMER E´ DI, Dirac-type conditions [26] V. R ODL for Hamiltonian paths and cycles in 3-uniform hypergraphs, Adv. Math. 227 (2011), 1225–1299. Moduli of algebraic and tropical curves Dan Abramovich Abstract.

K UHN uniform hypergraphs, J. Combin. Theory Ser. B 103 (2013), 291305 ¨ , Minimum codegree threshold for [23] A. L O and K. M ARKSTR OM (K 43 − e)-factors, J. Combin. Theory Ser. A 120 (2013), 708–721. ´ ¨ , A. RUCI NSKI and E. S ZEMER E´ DI, A Dirac-type theorem [24] V. R ODL for 3-uniform hypergraphs, Combin. Probab. Comput. 15 (2006), 229–251. ´ ¨ , A. RUCI NSKI and E. S ZEMER E´ DI, An approximate [25] V. R ODL Dirac-type theorem for k-uniform hypergraphs, Combinatorica 28 (2008), 229–260.

A. D IRAC, Some theorems of abstract graphs, Proc. London Math. Soc. 3 (1952), 69–81. [8] A. H AJNAL and E. S ZEMER E´ DI, Proof of a conjecture of P. Erd˝os, Combinatorial theory and its applications, II, Proc. , Balatonf¨ured, 1969, North-Holland, Amsterdam, 1970, 601–623. ` and M. S CHACHT, Dirac-type results for loose Hamil[9] H. H AN ton cycles in uniform hypergraphs, J. Combin. Theory Ser. B 100 (2010), 332–346. ` , Y. P ERSON and M. S CHACHT, On perfect matchings in [10] H. H AN uniform hypergraphs with large minimum vertex degree SIAM J.

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