# Mathematical Sciences Research Institute

Home » BGMS Seminar: Polynomial Pell equations and undecidable questions in algebraic geometry

# Seminar

BGMS Seminar: Polynomial Pell equations and undecidable questions in algebraic geometry April 29, 2019 (01:30 PM PDT - 02:30 PM PDT)
Parent Program: Birational Geometry and Moduli Spaces MSRI: Simons Auditorium
Speaker(s) János Kollár (Princeton University)
Description No Description
Video
Abel initiated the  study of  the  polynomial  Pell equation $x^2-g(z)y^2=1$, where  $g(z)$ is a fixed polynomial. We are looking for solutions where $x, y, z$ are also polynomials in a variable  $t$. Then we use these results to exhibit some new  undecidable questions in complex algebraic geometry.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7336928248405457, "perplexity": 4308.066292290689}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313259.30/warc/CC-MAIN-20190817123129-20190817145129-00529.warc.gz"}