Kaitlyn Phillipson

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20102019

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math.AG2019

A Faster Solution to Smale's 17th Problem I: Real Binomial Systems

Grigoris Paouris, Kaitlyn Phillipson, J. Maurice Rojas

Suppose $F := (f_{1}, \dots, f_{n})$ is a system of random $n$ -variate polynomials with $f_{i}$ having degree $\leq d_{i}$ and the coefficient of $x_{1}^{a_{1}} \dots x_{n}^{a_{n}}$ in $f_{i}$ being a…

math.AG2010

Fewnomial Systems with Many Roots, and an Adelic Tau Conjecture

Kaitlyn Phillipson, J. Maurice Rojas

Consider a system F of n polynomials in n variables, with a total of n+k distinct exponent vectors, over any local field L. We discuss conjecturally tight bounds on the maximal num…