Workshop
Registration Deadline:  April 28, 2023 over 1 year ago 

To apply for Funding you must register by:  January 17, 2023 almost 2 years ago 
Parent Program:  

Location:  SLMath: Eisenbud Auditorium 
Show List of Speakers
 Levent Alpöge (Harvard University)
 Irene Bouw (Ulm University)
 Vesselin Dimitrov (Institute for Advanced Study)
 Hélène Esnault (Freie Universität Berlin)
 Ziyang Gao (Leibniz Universität Hannover)
 Mark Kisin (Harvard University)
 Brian Lawrence (University of WisconsinMadison)
 David Masser (Universität Basel)
 Niki Myrto Mavraki (Harvard University)
 Alina Ostafe (University of New South Wales)
 Congling Qiu (Yale University)
 Harry Schmidt (Universität Basel)
 Ananth Shankar (University of WisconsinMadison)
 Salim Tayou (Harvard University)
 Paul Vojta (University of California, Berkeley)
 Xinyi Yuan (Peking University)
 Umberto Zannier (Scuola Normale Superiore)
 ShouWu Zhang (Princeton University)
A central topic in Diophantine Geometry is to understand how the geometry of a variety influences the arithmetic of its algebraic points, and conversely. Conjectures of Bombieri, Lang, and Vojta suggest that rational points of algebraic varieties satisfying suitable approximation conditions, are algebraically degenerate. On the other hand, conjectures on unlikely intersections suggest that algebraic points of special type —e.g. torsion points in semiabelian varieties, special points in Shimura varieties— avoid subvarieties, unless the subvariety itself is also special (in a technical sense).
In recent years, a number of techniques have led to outstanding progress on LangVojta conjectures, such as the Subspace Theorem, padic approaches to finiteness, and modular methods. Similarly, spectacular progress has been achieved on unlikely intersection conjectures thanks to new methods and tools, such as height formulas for special points, connections to model theory, refined counting results, and new theorems of AxShanuel type (bialgebraic geometry).
The goal of this workshop is to create the opportunity for these two groups to interact, to share their techniques, to update on the most recent progress, and to attack the outstanding open questions in the field.
The two directions described above are rather technical and specialized, and it seems necessary to bring together these groups of researchers to explain to each other not only the latest developments in their fields, but also the methods that made possible these breakthroughs. Thus, in this workshop we expect to have lectures explaining the main methods, as well as talks presenting the most recent progress in the subject by the world leading experts.
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
Arithmetic geometry
Arakelov theory
unlikely intersections
rational points
integral points
CM points
Colmez’s conjecture
CM abelian varieties
Vojta’s conjecture
GrothendieckKatz pcurvature conjecture
Faltings height
Chabauty’s method
nonabelian Chabauty
period mappings
BombieriLang conjecture
Lang’s conjecture
Effectivity
Diophantine equations
11G15  Complex multiplication and moduli of abelian varieties [See also 14K22]
11G18  Arithmetic aspects of modular and Shimura varieties [See also 14G35]
14G40  Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
Show Schedule, Notes/Handouts & Videos
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Apr 24, 2023 Monday 



Apr 25, 2023 Tuesday 


Apr 26, 2023 Wednesday 


Apr 27, 2023 Thursday 


Apr 28, 2023 Friday 
