Whereas in the early 20th century, physicists would typically turn to mathematicians for technical advice, these later strongly benefitted from the advances of quantum field theory and string theory as can be seen from various standing mathematical conjectures motivated by physics. The links between physics and mathematics have become so strong, that some fields of research have developed at the very threshold between these disciplines, where distinguishing between the mathematical and physical input has become artificial if not impossible. Two meetings that brought together women mathematicians and physicists working in these areas were recently organised, both aimed at identifying new trends of research at the frontier between mathematics, quantum field theory and string theory and exploring how they intertwine.
A first meeting “Women at the Intersection of Mathematics and High Energy Physics” held 6-10 March 2017 at the MITP in Mainz, was organised by Gabriele Honecker (JGU Mainz), Kasia Rejzner (Univ. of York), Katrin Wendland (Univ. Freiburg) and myself.
A second meeting entitled “Women at the intersection of mathematics and theoretical physics” organised  by Elli Pomoni (DESY, Hamburg), Jörg Teichner (DESY, Hamburg) and myself (Univ. Potsdam and Clermont-Auvergne), which gathered some thirty women working at the frontier of mathematics and physics, took place at DESY Hamburg from April 9th to April 12th 2018.
Both meetings triggered interactions across fields in bringing together women mathematicians and theoretical physicists working at the forefront of research topics in mathematical physics. There are still very few women working at the threshold of mathematics and physics, even if some very active distinguished women scientists are opening the way to the younger generation. This regretful scarceness of women working in those interdisciplinary fields forces a broad spectrum of topics when bringing them together. We view this as a strength, for it encourages interactions beyond the ones a scientist is used to with colleagues working in closely related topics. Amongst the speakers in Hamburg were Shabnam Beheshti (Queen Mary, London), Agnese Bissi (Harvard University), Alexandra Castro (Amsterdam University), Johanna Erdmenger (Wurzburg University), Susanne Reffert (University of Bern), Kasia Rejzner (University of York), Claudia Scheimbauer (Oxford University) and and Ulrike Tillmann (Oxford University).

In view of the diversity of the audience, the talks of the workshop in Hamburg entailed a substantial pedagogical component. These were delivered with the goal to teach each other, stimulate interactions and to foster possible collaborations between the participants, as well as to motivate the younger generation to enter these fields of research. Beyond their scientific impact, we also hope this type of workshop can offer an opportunity to envisage new patterns of sharing research in an inclusive manner with ethics geared by generosity rather than exclusively by excellence criteria that follow today’s excellence scheme oriented trend.
During an informal evaluation of the meeting in Hamburg, participants made useful suggestions to keep in mind for future mathematical physics meetings for women, such as to encourage small projects between participants of “Women and mathematical physics” meetings in a similar way to the “Women and topology” meetings and to organise interdisciplinary discussions during the meeting on topics that reach out across fields such as (to name a couple of examples) duality, locality, (super) symmetry, etc.

In the second workshop in Hamburg, we furthermore organised two roundtable discussions related to women/gender issues in mathematical physics, trying to pinpoint the problems specific to such interdisciplinary fields of research and to search for possible solutions/actions specifically aimed at the younger generations. The aim was to

1. discuss the particular case of mathematical physics regarding the under-representation of women in fields of research at the intersection of mathematics and theoretical physics,
2. try to identify mechanisms which underlie this situation,
3. gather some ideas for the situation to evolve.

Here is a brief summary of the main issues addressed during the discussions. Let us first list the general problems identified during the discussions:

• female students are not taken seriously by some professors who are still very prejudiced regarding their actual scientific competence and young female professors are not taken seriously by some students who are still very prejudiced regarding the competence of women scientists. In their collaborative research experience, women often find it difficult to impose their point of view and feel they are not taken seriously;
• we miss a critical mass of women which would enable to attract more women;
• women have to do more to get a recognition comparable to their male colleagues;
• leaking pipeline: the proportion of women tends to decrease as one climbs up in the hierarchy;
• women professors are asked to take part in various committees, which takes up time from research;
• women professors are asked to act as a role model doing teaching for undergraduates, which takes up time from their research;
• in grant evaluations, women can be evaluated (anonymously) differently from men;
• dual career, two-body problem.

Among the issues raised during the discussion were problems specific to areas at the threshold between mathematics, theoretical physics and mathematical physics such as
the lack of female role models in theoretical physics, very few women physicists (interestingly, Lisa Meitner didn’t benefit from the recognition received by Otto Hahn who got the Nobel prize);
the fact that topics in mathematical physics are often risky and new, so there is no set path to follow as a young researcher. In mathematical topics, like topology, one sees more women at conferences (some 30 %), in topics like axiomatic quantum field theory, hardly any.

Here are further observations collected during the discussions:

• a critical mass of women in a department or institute (this was the case in Amsterdam) has an influence on professional practices;
• diversity is not only for women’s sake; in the long run, it is beneficial for any department or scientific institution;
• women discuss their professional practices more often than men, due to their specific situation as part of a minority; the fruit of such discussions can be useful for the whole community;
• the gender issue is everyone’s problem, we’re all part of it, we all contribute to the problem. For example, the two body problem is both men and women’s problems, it should not be considered as the woman’s sole problem;
• women tend to be not as visible as men.

Possible concrete actions that were suggested are to:

• raise awareness of PhD advisers whose role is central, in giving encouragements and self-confidence so as to help the PhD student find a job and build up a network;
• foster students whether male or female, which essential, sponsoring female postdocs and mentorship schemes play an important role;
• convince decision makers that diversity is beneficial in the long run, not only for women but for the whole department or institute;
• envisage research excellence in a more collaborative form:
  • evaluating not so much individual achievements as the collective potential of a team,
  • taking into account various aspects of the candidate’s career beyond the traditional publication records.
• counterbalance the extra work induced by women’s implication in various committees (sabbatical?);
• raise students’ awareness concerning their behaviour towards their female peers;
• develop better networking for women working across fields within the broad area of mathematical physics e.g.
  • create a dedicated email list to send out announcements for conferences and advertisements for positions in mathematics/ theoretical physics,
  • organise such interdisciplinary meetings for women scientists.
• establish a dual career network on the university or city level (it is more about help than financial support);
• offer partners of candidates offered jobs free access to advice at the university careers office;
• create a prominent chair for a female guest professorship;
• active scouting at all levels, not looking for the best people in a specific topic but for the best people within a pool of topics;
• women should dare speak up and ask questions in seminars;
• meetings with only women speakers and a majority of women in the audience are more inclusive in terms of the atmosphere they generate between speakers and audience;
• go through a training scheme on gender issues in order to get tenured;
• involve and engage male colleagues in the discussion and improve awareness of our male colleagues.

A summary of the panel discussions shared on the EWM network triggered interesting comments after the meeting:
Are researchers as likely to pick up and run with a new idea that a woman came up with as they would be to run with an idea come up with by a man?  If this is not the case, then “men come up with the most influential new ideas” becomes a self-fulfilling prophecy and one can wonder whether this is why women often chose by preference to work in established areas that the community has already decided are interesting;
Going through a training scheme on gender issues in order to get tenured was strongly approved by some. As a matter of fact, in Oxford, even for interviewing prospective candidates for the undergraduate course, the academic staff need to undergo some training sessions (about gender and disability issues, e.g.).
The unbalance in the representation of women in the different fields of mathematics has long been observed and particularly regarding mathematical physics. A recent paper addresses these or related issues. This topic is also at the center of the project “A Global Approach to the Gender Gap in Mathematical, Computing, and Natural Sciences: How to Measure It, How to Reduce It?”

All these discussions speak for the need to bring together women academics working at the threshold of mathematics and theoretical physics, as they offer an opportunity for them to share their experiences, their knowledge and gain in visibility. Such meetings encourage

• networking at the crossroads of mathematics and physics;
• young women to enter the (rather risky) realm of mathematical physics in the broad sense of the word;
• interactions between mathematicians and physicists in exchanging ideas across disciplines, an opportunity we rarely have in our everyday scientific work.

Following the meetings in Mainz in 2017 and in Hamburg in 2018, Kasia Rejzner (York), Xenia de la Ossa (Oxford), Susanne Reffert (Bern) , Anne Taormina (Durham) and myself are planning to organise the third meeting of this kind, possibly in Bern, Switzerland.

Sylvie Paycha