I am a postdoctoral lecturer in mathematics at Washington University in St. Louis (WUSTL) since August 2019.
My research interests are free analysis, free algebras and free skew fields, noncommutative function theory and operator theory. Currently my research goals are to use function theoretic ideas to study objects from noncommutative algebra.
Before coming to WUSTL, I was a PhD student at the University of Florida in Gainesville.
Syllabi:
Math318 Syllabus - Spring 2021
Math4111 Syllabus - Spring 2021
maugat at WUSTL dot edu
Department of Mathematics and Statistics
Washington University in St. Louis
University of Florida - May 2019
Thesis: The free Grothendieck theorem
University of Florida - May 2011
Thesis: On Tilings of C^n
The Free List of Open Problems (FLOP) is a public list of unsolved or unexplored problems/conjectures/ideas in the field of free analysis. The items in the list should provide some background in the problem, perhaps some ideas of what might work or what doesn't work, and references to related material. If an open problem is solved, then a link to the solution should be provided and connections to other problems or generalizations can be added.
Why FLOP?While free analysis can trace its roots back to the 1970's, the field is relatively new and is growing at an impressive rate. Having a collection of important or interesting unsolved problems could help the field grow in exciting new directions.
For established members of the field the FLOP provides opportunities for new research and collaboration. Starting a project is much easier when you already know the state of the art and potential collaborators. On the other hand, if you have been working on a problem for a while and haven't cracked it yet, putting the problem on the FLOP gives you a good place to pick up the problem later as well as giving others a chance to contribute.
Graduate students and fledgling members of the community also benefit greatly from FLOP. Having a robust list of open problems with references, explanations and basic ideas of attack helps folks to gain a foothold on research in the field.
One more reason to FLOP is that it is an easy way to advertise the field. Is there a graduate student that is interested in free analysis? FLOP them! Giving the student a robust resource for starting work on open problems can help them to choose free analysis. Is there a colleague that has expressed interest in free analysis but doesn't know where to start? FLOP them! They may see a project that interests them or an idea that they are already familiar with. The FLOP is a great way to show off the health of the field is and how rapidly it is evolving.
The idea of the FLOP is to connect people and ideas.
How do I FLOP?Contribute! The FLOP depends completely on contributions from members of the field and it will only be successful if it is large & robust enough to actually be useful. Feel free to add problems, explanations, references, etc.
Right now the FLOP is on github and it can be publically edited or added to. I tried to keep the files modular so that entries can be added and edited easily. If you have any suggestions for how to organize the FLOP or where to host it, please let me know.