Laura Colmenarejo

Visiting Assistant Professor
UMass Amherst (US)


Laura was born in Madrid, Spain, where she grew up and studied a major in Mathematics because she did not want to spend many years at the university studying Medicine. Quickly it became obvious that she had fallen in love with mathematics and that she wanted to know more. Then, thanks to her mentor, Adolfo Quiros, Laura decided to pursue a Ph.D. After working with Orlando Villamayor in her master thesis about blow-ups, Laura moved to Sevilla (Spain) to continue with her studies. In Sevilla, Laura discovered the area of algebraic combinatorics and became fascinated by the beauty of the formulas and structures. Laura obtained her Ph.D. in 2016 at the Universidad de Sevilla, under the supervision of Emmanuel Briand and Mercedes H. Rosas Celis. Since then, Laura has been working in different universities around the world, such as York U in Toronto (Canada) and the Max Planck Institute for Mathematics in Leipzig (Germany). Nowadays, Laura is Marshall H. Stone Visiting Assistant Professor at UMass Amherst (US). Laura enjoys working with combinatorial objects and trying to understand structures defined by them. In her free time, Laura enjoys traveling and discovering new coffee places and restaurants whenever she is. If she was not to work in Academia, Laura would open her cafe or pursue a career as a chef in some restaurant. Laura also enjoys reading non-math books and watching movies. Her favorite sport is swimming and she usually trains after work. Living abroad is fun and hard at the same time. Fortunately, Laura counts with the unconditional support of her family and friends back in Madrid, and she always spends Christmas and her birthday with them.

Laura's research has its starting point in the intersection of algebraic combinatorics and representation theory of finite groups and expands to other areas from there, such as algebraic geometry, physics, or stochastic analysis. Concretely, she is interested in getting a better understanding of the combinatorial structures appearing in other areas and that are interesting on their own. For instance, the symmetric functions as a way to understand character theory for the symmetric group and the general linear group, the combinatorial properties of the Bruhat order as a tool to describe the multiplication of the Schubert classes in the cohomology ring of the Grassmannian or the invariants in the shuffle algebra that gives us the description of the invariants for multidimensional series in stochastic analysis. Combinatorial objects and structures appear in many areas, providing a new approach and perspective to look at the problems.

Laura enjoys talking and collaborating with other researchers, and many of her projects happened because a colleague shared a nice formula or identity with her. Nowadays, Laura is working on chromatic polynomials trying to prove some positivity problems with Greta Panova and Alejandro H. Morales, and she is also working on understanding signatures of paths and the combinatorics behind them as a project with Joscha Diehl and Miruna-Stefana Sorea.

As part of her research, Laura also enjoys working with undergraduate students. This summer, Laura is working with her REU student, Christo Keller, on parking functions and the statistics arising from diagonal harmonics. She is also a research leader for a team in the Advancing Inquiry/Inclusion in Mathematics Undergraduate Program organized by Pamela E. Harris.

Laura enjoys teaching as much as research and considers that the goal must be guiding and helping students in their learning path.

Laura considers that everyone is a lifelong student for whom the learning path generally goes through three distinct stages. The initial stage is mostly computational, and students must reproduce the techniques learned in class to solve similar exercises and memorize core definitions of mathematics. The next stage is the comprehension state, where students can explain new techniques to each other as well as creatively solve new types of exercises. To achieve this, students develop connections between concepts and derive results. The final state requires a substantial jump to the abstraction of mathematics. This is the new dimension stage since the students are more engaged with the knowledge and theory behind their results. Students now dare to explore new areas of mathematics.While in the classroom, Laura tries to engage with the students and carefully navigate them in different stages. She is open to improvising the lectures guided by the enthusiasm of the students and is always prepared to pique the students' interest with intriguing questions. Laura also tries to make sure that students are comfortable asking and answering questions. Laura is aware of the difficulties for many students due to her own experience, and so she emphasizes the importance of being present during class and having an active role as students.

For Laura, it is also important to keep working on her teaching skills and so these days she is attending seminars and workshops about online teaching and she is excited to practice all the new techniques she is learning in the coming semester.

From the beginning of her career as a mathematician, Laura has counted with incredible mentors that encourage her to keep working and pursue her dreams. From them, Laura has learned how important it is to have your support network at work and in your personal life. That's why, as a mentor, Laura enjoys spending time with her mentees not only talking about math and career paths but also talking about personal experiences and doing other activities. She also learns a lot from her mentees, who help her to be a better mentor and mathematician.

As a female mathematician and immigrant, Laura shares her experiences with her students and colleagues. She also participates as a panelist in discussions with undergraduate and graduate students or at conferences. Laura considers it essential to talk about the challenges in Academia, especially these days with online teaching and a very competitive job market. Laura also knows the importance of role models and so, she participates in activities with female and underrepresented minorities organized by the AWM student chapter at UMass Amherst.

Due to the lack of travel for conferences, at the beginning of the quarantine, Laura focused her attention on organizing online activities to keep the community active and connected. She organized the conference AlCoVE (Algebraic Combinatorics Virtual Expedition), together with Maria Gillespie, Oliver Pechenik, and Liam Solus. The conference counted with an incredible list of speakers and poster presenters, and there were social activities such as an escape room, a scavenger hunt, and poll questions during the coffee breaks. The conference was a success and the participants were very enthusiastic about social activities.

Laura is also willing to get more engaged in other service activities once she becomes an assistant professor.

I grew up in Spain, and we do not learn much about American history other than the main wars. Knowing about Hispanic Heritage Month has made me read and learn more about the Hispanic Americans, and understand the relevance of bringing our cultures into every aspect of our lives, including research and teaching. Moreover, as an immigrant in the US, I connect with other Hispanic and Latino communities differently, making me feel at home when I'm thousands of kilometers far from my hometown. This helps me to embrace my culture and share it whenever I can.