Resume

• 2013

  Abstract: Motivated by the quest for an analogue of the Gromov-Hausdorff distance in noncommutative geometry which is well-behaved with respect to C*-algebraic structures

  we propose a complete metric on the class of Leibniz quantum compact metric spaces

  named the dual Gromov-Hausdorff propinquity

  which resolves several important issues raised by recent research in noncommutative metric geometry: our new metric makes *-isomorphism a necessary condition for distance zero

  is well-adapted to Leibniz seminorms

  and --- very importantly --- is complete

  unlike the quantum propinquity which we introduced earlier. Thus our new metric provides a new tool for noncommutative metric geometry which offers a solution to several important problems in the field and is designed to allow for the generalizations of techniques from metric geometry to C*-algebra theory. \n\nFrédéric Latrémolière

  Journal de Mathématiques Pures et Appliquées 103 ( 2015 ) 2

  303--351

  The Dual Gromov-Hausdorff Propinquity

  Konrad Aguilar

  We construct quantum metric structures on unital AF algebras with a faithful tracial state

  and prove that for such metrics

  AF algebras are limits of their defining inductive sequences of finite dimensional C*-algebras for the quantum propinquity. We then study the geometry

  for the quantum propinquity

  of three natural classes of AF algebras equipped with our quantum metrics: the UHF algebras

  the Effr{\\\"o}s-Shen AF algebras associated with continued fraction expansions of irrationals

  and the Cantor space

  on which our construction recovers traditional ultrametrics. We also exhibit several compact classes of AF algebras for the quantum propinquity and show continuity of our family of Lip-norms on a fixed AF algebra. Our work thus brings AF algebras into the realm of noncommutative metric geometry.\n

  Abstract: Quantum tori are limits of finite dimensional C*-algebras for the quantum Gromov-Hausdorff propinquity

  a metric defined by the author as a strengthening of Rieffel's quantum Gromov-Hausdorff designed to retain the C*-algebraic structure. In this paper

  we propose a proof of the continuity of the family of quantum and fuzzy tori which relies on explicit representations of the C*-algebras rather than on more abstract arguments

  in a manner which takes full advantage of the notion of bridge defining the quantum propinquity.

  Convergence of Fuzzy Tori and Quantum Tori for the quantum Gromov-Hausdorff Propinquity: an explicit approach

  My project consists in developing quantum analogues of metric spaces and the Gromov-Hausdorff distance

  then to expand of these constructions with the goal to provide:\n1) a formal framework to define approximations in mathematical physics using geometry

  \n2) help introduce techniques from metric geometry into noncommutative geometry

  \n3) define an additional approach for the study of the interactions between C*-algebra theory and geometry of singular spaces.

  Latremoliere

  Frederic

  Latremoliere

  University of Colorado Boulder

  University of Cincinnati

  University of Toronto

  University of Denver

  Boulder

  CO

  Ulam visiting professor

  University of Colorado Boulder

  Universitt if Denver

  * Research (Noncommutative metric geometry

  functional analysis)\n* Teaching (5 classes / year

  from calculus to graduate level)\n* Mentoring / Advising: advise PhD students

  undergraduate majors in mathematics

  first year undergraduate students\n* Service: serve or chair various committees in the department

  division or university.

  Full Professor of Mathematics

  University of Denver

  University of Denver (Colorado

  United States)

  Tenured associate professor of mathematics: I am a mathematician

  carrying out research in pure mathematics by constructing a theory of quantum metric geometry and regularly publishing my results in numerous research papers in high reputation mathematical journals. I have been invited to several international conferences to present my research. \n\nI also teach five quarter classes a year

  at all levels from calculus to graduate classes for our Ph.D. program. I supervise two PhD students for their research toward their Ph.D. thesis. I am an academic advisor for about twenty to thirty undergraduate students. Last

  I am very active in service to my university and department: I am currently the undergraduate coordinator for the department of Mathematics at DU

  and the faculty senate representative for my department as well. I also organize conferences (including GPOTS 2010

  WCOAS 2014) and I am a reviewer for various publications.

  Associate Professor of Mathematics

  University of Denver

  As a visiting assistant professor at the University of Cincinnati

  I carried out research in functional analysis and taught six quarter classes.

  Visiting Assistant Professor

  Cincinnati

  Ohio Area

  University of Cincinnati

  As a postdoctoral fellow in Mathematics at the University of Toronto (main campus)

  I carried out research in functional analysis and taught one to two classes per semester.

  Postdoctoral Fellow

  Toronto

  Canada Area

  University of Toronto

  Tenure-track assistant professor of mathematics. I carried out research in pure mathematics

  taught five quarter classes in mathematics at all levels from calculus to graduate school

  and was active in service (hiring committees

  IT representative

  Chair of IT committee for the Natural Science and Mathematics Division

  organizer of a large conference at my campus --- GPOTS 2010).

  Assistant Professor of Mathematics

  United States

  University of Denver

• 1999

  Doctor of Philosophy (Ph.D.)

  Ph.D. dissertation in noncommutative metric geometry

  titled \"Finite Dimensional Approximations of Quantum Tori for the Quantum Gromov-Hausdorff Distance\". Advisor: M. A. Rieffel.\n\nThe topic of my research is at the interface between mathematical physics (in particular

  quantum physics)

  geometry of metric spaces and functional analysis. I proved that quantum tori are limits of matrix algebras for a new metric introduced by Rieffel

  which generalizes the Gromov-Hausdorff distance to quantum spaces. This was a step in developping a rigorous framework for certain type of approximations in physics. Since then

  I have developped a more robust generalization of Gromov-Hausdorff distance and I continue to explore quantum metric geometry

  with an interest on its applications to physics.

  Mathematics

  University of California

  Berkeley

• 1998

  French

  English

  Master of Arts (M.A.)

  Obtained as a Ph.D. student in probability by passing the qualifying examinations for the Ph.D. (A+ in the probability exam). I later transferred to a Ph.D. in pure mathematics.

  Statistics

  University of California

  Berkeley

• 1996

  Maitrise de Mathematiques et Applications Fondamentales

  Equivalent to a Master in Sciences in pure Mathematics. Classes included differential geometry

  dynamical system theory

  functional analysis and advanced complex analysis. I did this degree in addition to being a full time student at the ENSAE.

  Mathematics

  Université Pierre et Marie Curie (Paris VI)

  Mention: Bien

• 1995

  Statisticien - Economiste (Equivalent to a MS)

  Admitted to the ENSAE via the Mathematics competition after Math Sup / Spe (35 students admitted). The ENSAE is a grande ecole specializing in training \"statistical engineers\" who often chose a career in finance. It is a very competitive

  very academically rigorous

  and very prized degree to obtain.\n\nCourses include (among many other): stochastic calculus with applications to finance

  econometrics

  mathematical statistics

  applied statistics (using SAS)

  microeconomics (including Von-Neumann-Morgenstern and applications to the theory of insurance)

  macroeconomics (mathematically based)

  computer programming

  demography

  and many more. All the classes are very heavily based on mathematics

  as students must pass an advanced mathematics competition to enter this school.

  Statistics

  Economics.

  Member of the \"Forum\"

  helped with Gala organization.

  Ensae ParisTech

  Licence de Mathematiques Pures

  Equivalent to a Bachelor in Mathematics (classes: measure theory and Lebesgues Integration; Topology and advanced differential calculus; ring and fields theory

  algorithmics). I did this degree in addition to being a full time student in first year at the ENSAE.

  Mathematics

  Université Pierre et Marie Curie (Paris VI)

  Mention: Bien

• Dr. Frederic Latremoliere

  PhD Web Page VI

  My home page contains all my research publications

  an updated CV

  the web sites for conferences I have organized

  and the many documents associated with my current teaching.

  JavaScript

  Quantum Theory

  Java

  HTML5

  C++

  CUDA

  Geometry

  LaTeX

  C

  OpenGL

  Probability Theory

  XSLT

  SAS Programming

  Functional Analysis

  XML

  Programming

  Differential Geometry

  Computer Science

  Statistics

  Mathematics

  The Quantum Gromov-Hausdorff Propinquity

  Abstract: We introduce the quantum Gromov-Hausdorff propinquity

  a new distance between quantum compact metric spaces

  which extends the Gromov-Hausdorff distance to noncommutative geometry and strengthens Rieffel's quantum Gromov-Hausdorff distance and Rieffel's proximity by making *-isomorphism a necessary condition for distance zero

  while being well adapted to Leibniz seminorms. This work offers a natural solution to the long-standing problem of finding a framework for the development of a theory of Leibniz Lip-norms over C*-algebras. \n\n(49 pages)

  The Quantum Gromov-Hausdorff Propinquity

  Quantum metric spaces and the Gromov-Hausdorff propinquity

  Convergence of Cauchy Sequences for the covariant Gromov-Hausdorff propinquity

  We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation

  when this group is endowed with a natural length function.\n

  Curved Quantum Tori as Leibniz quantum compact metric spaces

  Judith Packer

  Noncommutative Solenoids and their projective modules

  We characterize Lipschitz morphisms between quantum compact metric spaces as those *-morphisms which preserve the domain of certain noncommutative analogues of Lipschitz seminorms

  namely lower semi-continuous Lip-norms. As a corollary

  lower semi-continuous Lip-norms with a shared domain are in fact equivalent. We then note that when a family of lower semi-continuous Lip-norms are uniformly equivalent

  then they give rise to totally bounded classes of quantum compact metric spaces

  and we apply this observation to several examples of perturbations of quantum metric spaces.\n

  Equivalence of Quantum Metrics with common domains

  A compactness theorem for the dual Gromov-Hausdorff Propinquity

  Judith Packer

  Explicit Construction of Equivalence Bimodules between Noncommutative Solenoids

  A Topographic Gromov-Hausdorff Quantum Hypertopology for Proper Quantum Metric Spaces

  Judith. J. Packer

  We prove that noncommutative solenoids are limits

  in the sense of the Gromov-Hausdorff propinquity

  of quantum tori. From this observation

  we prove that noncommutative solenoids can be approximated by finite dimensional quantum compact metric spaces

  and that they form a continuous family of quantum compact metric spaces over the space of multipliers of the solenoid

  properly metrized.\n

  Noncommutative Solenoids and the Gromov-Hausdorff propinquity

  Abstract: The dual Gromov-Hausdorff propinquity is a generalization of the Gromov-Hausdorff distance to the class of Leibniz quantum compact metric spaces

  designed to be well-behaved with respect to C*-algebraic structures. In this paper

  we present a variant of the dual propinquity for which the triangle inequality is established without the recourse to the notion of journeys

  or finite paths of tunnels. Since the triangle inequality has been a challenge to establish within the setting of Leibniz quantum compact metric spaces for quite some time

  and since journeys can be a complicated tool

  this new form of the dual propinquity is a significant theoretical and practical improvement. On the other hand

  our new metric is equivalent to the dual propinquity

  and thus inherits all its properties. (16 pages)

  The Triangle Inequality and the Dual Gromov-Hausdorff Propinquity