Euphemia Haynes was a trailblazer as the first African-American woman to earn a doctorate in mathematics. The Catholic University of America holds a copy of her thesis, entitled “The Determination of Sets of Independent Conditions Characterizing Certain Special Cases of Symmetric Correspondences”, in their archives. 

A short biography: Euphemia Lofton daughter of Dr William Lofton, a dentist, and Lavinia Day Lofton, a kindergarten teacher. She was the valedictorian of M Street High School in 1907 and then graduated from (what is now known as) University of the District of Columbia with distinction and a degree in education in 1909. She was a  mathematics major at Smith College, which she graduated from in 1914. She married Harold Appo Haynes, a teacher in 1917 and earned her master’s degree in education from the University of Chicago in 1930. In 1943 she was awarded her PhD from The Catholic University of America, advised by Professor Aubrey E. Landry. An excellent, more detailed biography can be found at [KSZ] (see also http://www.math.buffalo.edu/mad/PEEPS/haynes.euphemia.lofton.html).

More of her biography is given in the post The Mathematician and the Pope, also available on this blog.

In this blog post, we merely try to explain her title. What is a “symmetric correspondence”?

We refer to Dolgachev’s notes [Do14], section 5.5: A correspondence of degree d between nonsingular curves X and Y is a non-constant morphism to the d-th symmetric product of $Y$. Its graph is denoted . The projection is a finite map of degree $d$, while the projection is a finite map of degree e, say. It defines a correspondence denoted by , called the inverse correspondence. Its graph is the image of under the swap . If d is the degree of T and e is the degree of , we say that $T$ is a correspondence of type (d, e). This correspondence is symmetric if . 

Very roughly speaking, in her thesis, Haynes looks at various special cases of curves and in these cases she derives (technically defined) conditions that characterize the types of symmetric correspondences that arise in those cases.

While a scan of her thesis is archived at Catholic University, I have typed up her thesis in latex. For a digital copy, just email me (wdjoyner@gmail.com).

References

[Do14] I. Dolgachev, Classical Algebraic Geometry: a modern view, Cambridge Univ. Press, 2012.

(at https://mathweb.ucsd.edu/~eizadi/207A-14/CAG.pdf)

[KSZ17] Susan Kelly, Carly Shinners, Katherine Zoroufy, “Euphemia Lofton Haynes: Bringing Education Closer to the “Goal of Perfection“, preprint, 2017 (available at https://arxiv.org/abs/1703.00944). A version of this paper was also published in the Notices of the American Mathematics Society.