Female mathematicians

Google "female mathematicians" and you will get lists of women mathematicians through the ages, historical female mathematicians and famous female mathematicians

Google "male mathematicians" and suddenly the Google page is littered with "the 10 best mathematicians", "list of mathematicians" and my favourite, "The 30 Greatest mathematicians"

A closer look at the "The 30 Greatest mathematicians" link and one of the top 30 is female but it is pretty clear that the majority is male and "mathematician" seems equivalent to "male mathematician" in everyday terms. I therefore want to dedicate this post to those few female mathematicians who I've stumbled across in my short life.

Margarita

Margarita was the person who first introduced me to mathematical proofs and it is from her I learnt the delight of being able to understand the reasoning behind the theorems that is otherwise just learnt by rote. 

In the midst of all the changes to the Mathematics Program at LiTH she was steadfast in making sure that all future young mathematicians would have a good theoretical base to rely on and I can do nothing else than thank for that steadfastness as it so clearly helped me in my future studies. 

Milagros

Modern geometry is not my cup of tea, but I still wanted to mention Milagros in this post. I therefore asked my friend J, who has had the pleasure of knowing her better than I do.

Milagros works on the geometry of Riemann surfaces: their moduli and symmetries. This is a wonderfully rich area, thanks largely to "the miraculous trinity". Namely, the following collections of objects are in a suitable sense the same:

• compact surfaces considered up to angle-preserving maps,
• non-singular complex algebraic curves, and
• complex function fields of transcendence degree one.

This circle of ideas is immensely fruitful, and connects classical topics in geometry and function theory with number theory and theoretical physics. A central concern in modern geometry (and mathematics generally) is to study collections of all possible objects of a certain kind. Such a collection can often be given the structure of a suitably generalized "space" which can then be investigated geometrically. This is then called a moduli space. With various coauthors, Milagros has studied the geometry of moduli spaces of Riemann surfaces with certain extra properties. For example, questions about which kinds of symmetries of the surfaces are compatible with each other translate to questions about the connectedness of "branch loci" in a moduli space.

Some restrict their investigations to contrived objects, narrowly defined so as to admit the application of whatever trick the researcher intends to apply. This can produce PhDs, but is bad mathematics. By contrast, Milagros' work applies a variety of methods to truly natural and important questions. It is mathematics likely to last.

Åsa

When I was doing my thesis for my bachelor I had Åsa as my mentor and those conversations that I had with was very focused on my own work. But a few weeks before I presented my thesis, I had the pleasure of being able to listen to her licentiate presentation. (Licentiate in Sweden is approximately half a doctorate). Her report was called "Dose Plan Optimization in HDR Brachytherapy using Penalties- Properties and Extensions" and a link to her work can be found here. I will try to give a short presentation of it in layman terms.

HDR Branchytherapy is form radiotherapy where the radioactive substance is placed in or near the tumour that is to be treated. Optimization is now generally used when planning where and how long the radioactive substance should be placed.
The difficulty lies in that in this planning you want to make sure that the tumour receives the most radiation and minimizing the radiation to other healthy tissue. This means trying to balance length of time the substance is placed in one place (dwell point) and trying to find several dwell points so that the whole tumour is affected by the radiation. One problem that has been observed with the optimization model is that it would often present results with few dwell points and long time in these spots which would create "hot spots" which is something that you want to avoid.

Her presentation was about analysing the actual optimization model that is being used to find out why the model would give these types of solutions. What she found was that the way linear penalties were used in this optimization model was a cause to the unwanted long dwelling times, and then presented some ways to adapt the model. Now that, is pretty awesome stuff!