What Do Lines, Fermat Surfaces and Sudoku Games Have in Common?

Explore the surprising connections between lines, Fermat surfaces, and sudoku games in this 31-minute conference talk delivered at the 8th edition of the Geometry in Algebra, Algebra in Geometry workshop at IMPA, Rio de Janeiro. Discover how these seemingly disparate mathematical objects share common underlying structures through the lens of algebraic geometry and combinatorics. Learn about the geometric properties that unite linear objects, classical algebraic surfaces, and combinatorial puzzles, revealing deep mathematical relationships that bridge different areas of mathematics. Gain insights into how abstract mathematical concepts can manifest in both pure geometric forms and recreational mathematics, demonstrating the interconnected nature of mathematical structures across diverse fields.