Lie group representations, discretization, and Gelfand pairs
The theory of Lie groups and their representations has played a fundamental role in a variety of fields within analysis, geometry, number theory and probability theory. The focus of this conference was the role played by Lie groups in recent developments in functional and harmonic analysis. Guided by the organizers, participants explored current research questions in the areas of admissible representations, Coorbit theory and Gelfand pairs.
"The largest difference was 'passive vs active.' By actually working on an open problem with other participants, all of the other material became more relevant. The length of the conference and the opportunity for socializing also sets it apart from other conferences. I left with not just new research collaborators, but friends!"
Character Varieties: Experiments and New Frontiers
June 5– 11, 2016
Organizers: Sean Lawton, George Mason University; Christopher Manon, George Mason University; Adam Sikora, State University of New York at Buffalo
There has been intense interest and activity in the study of character varieties (aka moduli spaces of representations) in recent years. The study of these spaces intersects a wide range of mathematics and physics. In particular, they are central to the study of moduli theory and serve as non-trivial yet tractable working examples in algebraic geometry, topology, and dynamics. This focused workshop emphasized examples, computations, and visualizations. After briefly introducing participants to the general theory of these spaces, we focused on important areas that demand more attention, and how they relate: (1) quantization, (2) tropicalization, and (3) arithmetic structure.
"MRC gave us hands-on experience with plenty [of] opportunities for discussion and exchanging information/knowledge."
The fact that I was basically given a research project and encouraged to work on it was amazing!!!"
June 12 – 18, 2016
Organizers: Mathias Drton, University of Washington; Elizabeth Gross, San Jose State University; Serkan Hosten, San Francisco State University; David Kahle, Baylor University; Sonja Petrovic, Illinois Institute of Technology
Algebraic statistics lies at the intersection of algebraic geometry and statistics. Expanding tremendously in recent years, non-traditional new tools, methods and computational approaches are in demand due to the development of new data acquisition technologies. Algebraic statistics answers this call. The field draws from commutative algebra, computational geometry, discrete mathematics and algebraic geometry to address pressing issues in statistics, such as parameter estimation, model fitting challenges, simulation and model selection methods. The workshop focused on a number of topics: likelihood geometry, parameter identifiability, network models, statistical software, and phylogenetics/tree-based Markov models.
From an article in Illinois Institute of Technology "Illinois Tech Today"
“The workshop was a huge success,” said Petrovic. “It created an environment where career-long research relationships could be built. It introduced a new wave of young researchers to the field of algebraic statistics by engaging them with exciting research problems. It also provided opportunities for participants to obtain information and advice on topics vital for a junior researcher, such as publishing, presenting, and grant writing.” --Sonja Petrovic co-organizer of 2016 MRC was also a participant in the first MRC in 2008.
Mathematics in Physiology and Medicine
June 19 – 25, 2016
Organizers: Dan Beard, University of Michigan; Brian Carlson, University of Michigan; Adam Mahdi, University of Oxford; Mette Olufsen, North Carolina State University; Johnny Ottesen, Roskilde University
This workshop focused on mathematical interactions in systems physiology and systems biology. This fast-growing area of research has been shown to have a two-fold benefit. Mathematical methods are instrumental for attacking open problems in the area of physiological and biological modeling, spanning from molecular to whole-organism scales. On the other hand, the challenges that arise in the process often lead to interesting theoretical problems which require the development of new mathematical and computational approaches.
The workshop included an introduction on how to set up multi-scale computations from the cellular to the system levels. The workshop concentrated on three projects all focusing on how to use modeling for data analysis and to examine physiological hypotheses. The three projects used modeling to study blood-flow regulation, energy metabolism and inflammation. Mathematically these projects were studied using dynamical systems-type models combined with methodologies for parameter estimation and uncertainty quantification.
"The focus on young mathematicians was very welcome. I now know 20 mathematicians who will have almost parallel career paths. That was probably the best networking opportunity I have had."
"I really felt like the AMS did a good job of building community in our field."
Photo courtesy of Wei Wei Chen - MRC 2016
The American Mathematical Society's Mathematics Research Communities program builds social and collaborative networks to inspire and sustain mathematicians who are just beginning their research careers—those who are close to finishing their doctorates or have recently finished. The structured program engages and guides all participants as they start their careers. The program includes:
* One-week summer conference for each topic
* Special Sessions at the national meeting
* Discussion networks by research topic
* Longitudinal study of early career mathematicians
* Funding for additional collaborations
Those accepted into this program receive support for the summer conference, and will be partially supported for their participation in the Joint Mathematics Meetings which follow in January. The summer conferences of the MRC were held in the breathtaking mountain setting of the Snowbird Resort, Utah, where participants can enjoy the natural beauty and a collegial atmosphere. This program is supported by a grant from the National Science Foundation.
For information on the 2017 MRC sessions and how to apply.
--- Robin Hagan Aguiar