Week of Events
Faster point counting for curves over prime power rings (Maurice Rojas, Texas A&M)
Faster point counting for curves over prime power rings (Maurice Rojas, Texas A&M)
Counting points on algebraic curves over finite fields has numerous applications in communications and cryptology, and has led to some of the most beautiful results in 20th century arithmetic geometry. A natural generalization is to count the number of points over prime power rings, e.g., the integers modulo a prime power. However, the theory behind the latter kind of point […]
Calculus, Real Fewnomials, and P vs NP
Calculus, Real Fewnomials, and P vs NP
We review a beautiful 17th century result by the philosopher Rene Descartes: a univariate real polynomial with t monomial terms has no more than t-1 positive roots. We then see how one can prove a generalization that counts roots of two bivariate polynomials (with few monomial terms), using nothing more than basic calculus. In other […]
GEMS Workshop: Mathematics of Information with Professor Lucas Bang of Harvey Mudd College
GEMS Workshop: Mathematics of Information with Professor Lucas Bang of Harvey Mudd College
TOPIC: The Mathematics of Information We are surrounded by information. Words in books, ones and zeros in computers, mathematical equations, and DNA sequences are all examples of information, but can we say something more about it? In this workshop, we will learn about the mathematics of information, see how it is related to concepts from […]