Explore cutting-edge developments in arithmetic and Diophantine geometry through this comprehensive conference honoring Emmanuel Ullmo's groundbreaking contributions to the field. Delve into advanced topics including Diophantine geometry, ergodic theory, Hodge theory, and arithmetic dynamics as presented by leading mathematicians from around the world. Examine the arithmetic of power series and applications to irrationality, integral points in Arakelov geometry, and non-hypergeometric local systems. Investigate the dynamical Schinzel-Zassenhaus conjecture, elliptic surfaces and equidistribution, and Baily-Borel compactifications of period images. Study applications of unlikely intersections to integral geometry, contributions to the Zilber-Pink conjecture, and determinant values on irrational lattices. Learn about higher property T and Banach representations, convolution on abelian groups, and quantitative versions of the uniform Mordell conjecture. Discover recent advances in heights of Ceresa and Gross-Schoen cycles, arithmetic volumes of Shimura varieties, and the Bloch-Kato conjecture for symplectic Galois representations. Analyze mod p period maps, Tate locus conjectures, and mixing conjectures with their applications, providing a comprehensive overview of current research directions in this rapidly evolving mathematical field.

Syllabus

Yunqing Tang - The Arithmetic of Power Series and Applications to Irrationality
François Charles - Integral points and affineness in Arakelov geometry
Javier Fresán - Infinitely Many Non-hypergeometric Local Systems
Philipp Habegger - The Dynamical Schinzel-Zassenhaus Conjecture and the Transfinite Diameter (...)
Laura Demarco - Elliptic surfaces, Equidistribution, and Bifurcations
Benjamin Bakker - Baily-Borel Compactifications of Period Images and the b-semiampleness Conjecture
David Urbanik - Applications of Unlikely Intersections to Integral Geometry
Gregorio Baldi - A Tribute to Emmanuel's Contributions to the Zilber–Pink Conjecture
Hee Oh - Determinant Values on Irrational Lattices
Uri Bader - Higher property T, Banach Representations and Applications
Yves Benoist - Convolution and Square on Abelian Groups
Xinyi Yuan - A Quantitative Version of the Uniform Mordell Conjecture
Shouwu Zhang - Heights of Ceresa and Gross-Schoen Cycles
Wei Zhang - Proportionality and the arithmetic volumes of Shimura varieties and the moduli of (...)
Naomi Sweeting - On the Bloch–Kato Conjecture for some four-dimensional symplectic Galois (...)
Fabrizio Andreatta - On two mod p period maps: Ekedahl--Oort and fine Deligne--Lusztig (...)
Anna Cadoret - Tate locus - conjectures and results
Philippe Michel - A split version of the mixing conjecture and applications
Laura Demarco - Elliptic surfaces, Equidistribution, and Bifurcations