Frederic Latremoliere
Professor
303-871-2693 (Office)
https://fredericlatremoliere.com
http://www.math.du.edu/~frederic
Clarence M. Knudson Hall, 2390 S. York St. Denver, CO 80210
What I do
I am a pure mathematician who explores quantum hypertopologies defined using analogues of the Gromov-Hausdorff distance in noncommutative geometry and their applications to mathematical physics.Specialization(s)
mathematics, Physics, functional analysis, Geometry of metric spaces, C*-algebras, Noncommutative geometry, Statistics, Probability theory, computer science, economics.
Professional Biography
I am a full professor of Mathematics. My research is concerned with noncommutative metric geometry, and in particular, the study of various topologies induced by analogues of the Gromov-Hausdorff distance on such classes as locally compact quantum metric spaces, C*-correspondences, C*-dynamical systems, and metric spectral triples. I hope to see this work applied to mathematical physics, using these topologies to study matrix models approximations of physical models, and even the geometry of the space of possibly noncommutative space-times.
I received most of my education in France, where I was awarded the title of Statisticien-Economiste from the Ecole Nationale de l'Administration Economique (now, statistical engineer), and a Maitrise in pure mathematics from the Université Pierre et Marie Curie (Paris 6). I then obtained a M.A. in statistics and a PhD in mathematics at U.C. Berkeley under Dr. M. A. Rieffel.
I was a postdoctoral fellow at the University of Toronto, and became a tenure-track assistant professor in mathematics at the University of Denver in 2007. I obtained tenure in 2012 and I became full professor in 2016.
I received most of my education in France, where I was awarded the title of Statisticien-Economiste from the Ecole Nationale de l'Administration Economique (now, statistical engineer), and a Maitrise in pure mathematics from the Université Pierre et Marie Curie (Paris 6). I then obtained a M.A. in statistics and a PhD in mathematics at U.C. Berkeley under Dr. M. A. Rieffel.
I was a postdoctoral fellow at the University of Toronto, and became a tenure-track assistant professor in mathematics at the University of Denver in 2007. I obtained tenure in 2012 and I became full professor in 2016.
Degree(s)
- Ph.D., Mathematics, University of California, Berkeley, 2004
- Candidate in Philosophy, Mathematics, University of California, Berkeley, 2001
- MA, Mathematical Statistics, University of California, Berkeley, 1999
- MS, Mathematical Economics and Statistics, Ecole Nationale de la Statistique et de l'Administration Economique, 1998
- MS, Mathematics, Universite Pierre et Marie Curie - Paris 6, 1997
- BS, Mathematics, Universite Pierre et Marie Curie - Paris 6, 1996
- Mathematiques Superieures et Speciales, Mathematics and Physics, Classes Preparatoires Scientifiques, Pasteur, 1995
Research
Our research aims at providing a new analytical framework based on metric geometry for the study of certain
noncommutative analogues of Lipschitz algebras, motivated by approximations problems from mathematical physics, and by the exploration of the metric aspects of noncommutative geometry. To this end, we have developed an analogue of the Gromov-Hausdorff distance between quantum compact metric spaces, applied it to obtain various new continuity and approximation results for quantum metric spaces, discovered analogues of important results in metric geometry such as Gromov compactness theorem, showed new applications of our metric to group actions and approximations of symmetries in noncommutative geometry, and open a new area of inquiry by proposing a new metric on Hilbert modules, appropriately augmented with metric data, and on spectral triples. These later developments are new even in the classical setting, and show the potential of the interaction between functional analysis and metric geometry at the core of our work.
The motivations for our research area are rooted in problems in mathematical physics, and include:
* the constructions of finite-dimensional approximations of quantum models,
* furthering our understanding of the metric aspects of noncommutative geometry,
* discovering new methods for the study of C*-algebras inspired by metric geometry.
At its core, our research continues to bring the profound ideas of analysis to new realms: in our case, by creating a geometric space out of collections of C*-algebras which may describe quantum space-time.
noncommutative analogues of Lipschitz algebras, motivated by approximations problems from mathematical physics, and by the exploration of the metric aspects of noncommutative geometry. To this end, we have developed an analogue of the Gromov-Hausdorff distance between quantum compact metric spaces, applied it to obtain various new continuity and approximation results for quantum metric spaces, discovered analogues of important results in metric geometry such as Gromov compactness theorem, showed new applications of our metric to group actions and approximations of symmetries in noncommutative geometry, and open a new area of inquiry by proposing a new metric on Hilbert modules, appropriately augmented with metric data, and on spectral triples. These later developments are new even in the classical setting, and show the potential of the interaction between functional analysis and metric geometry at the core of our work.
The motivations for our research area are rooted in problems in mathematical physics, and include:
* the constructions of finite-dimensional approximations of quantum models,
* furthering our understanding of the metric aspects of noncommutative geometry,
* discovering new methods for the study of C*-algebras inspired by metric geometry.
At its core, our research continues to bring the profound ideas of analysis to new realms: in our case, by creating a geometric space out of collections of C*-algebras which may describe quantum space-time.
Areas of Research
Mathematics
Physics
Functional analysis
Geometry of metric spaces
C*-algebras
Noncommutative geometry.
Key Projects
- Collaborative Research: GPOTS Special Meetings 2009/2010
- West Coast Operator Algebra 2014
Featured Publications
. (2013). Quantum Locally Compact Metric Spaces. Journal of Functional Analysis, 264(1), 362-402.
. (2015). The Dual Gromov-Hausdorff Propinquity. Journal de Mathematiques Pures et Appliquees, 103(2), 303--351.
Presentations
. (2018). The spectral propinquity. Operator Algebra Seminar. Tokyo: Tokyo University.
. (2018). The Gromov-Hausdorff Propinquity. Operator Algebra Seminar. Kyoto University: Kyoto University.
. (2018). The . New Geometry of Quantum Dynamics. Warsaw: Polish Science Academy.
. (2014). The Quantum Propinquity. East Coast Operator Algebra Seminar. Toronto, ON: Fields Institute, University of Toronto and York University.
. (2016). A Gromov-Hausdorff Distance for Hilbert Modules. Noncommutative Geometry Seminar. California: Caltech.
Awards
- Ulam Professorship, University of Colorado, Boulder
