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Solubility of Systems of Quadratic Forms
We derive an upper bound for the least number of variables needed to
guarantee that a system of t quadratic forms (t>=2) over a field F has a
nontrivial zero. In particular, if F is a local field, then 2t^2+3 variables
insure the existence of a nontrivial zero (2t^2+1 if t is even), while if F=Q_p
with p>=11, then 2t^2-2t+5 variables suffice (2t^2-2t+1 if 3 divides t). The
improvement lies in a more efficient use of information on the solubility of
pairs and triplets of quadratic forms, and the arguments are completely
elementary.Comment: 4 page
Addressing the underrepresentation of women in mathematics conferences
Despite significant improvements over the last few generations, the
discipline of mathematics still counts a disproportionately small number of
women among its practitioners. These women are underrepresented as conference
speakers, even more so than the underrepresentation of women among PhD-earners
as a whole. This underrepresentation is the result of implicit biases present
within all of us, which cause us (on average) to perceive and treat women and
men differently and unfairly. These mutually reinforcing biases begin in
primary school, remain active through university study, and continue to oppose
women's careers through their effects on hiring, evaluation, awarding of
prizes, and inclusion in journal editorial boards and conference organization
committees. Underrepresentation of women as conference speakers is a symptom of
these biases, but it also serves to perpetuate them; therefore, addressing the
inequity at conferences is valuable and necessary for countering this
underrepresentation. We describe in detail the biases against women in
mathematics, knowing that greater awareness of them leads to a better ability
to mitigate them. Finally, we make explicit suggestions for organizing
conferences in ways that are equitable for female mathematicians.Comment: 26 pages. See also "An annotated bibliography of work related to
gender in science" (arXiv:1412.4104
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