Welcome to Trieu Le's homepage

(picture taken by Nate Iverson)

Dept. of Mathematics and Statistics
University of Toledo
Toledo, OH 43606

Curriculum Vitae (pdf)
My full name in Vietnamese is Lê Long Triều. I received my Ph.D. in Mathematics from the University at Buffalo in 2007 under the direction of Prof. Jingbo Xia. I spent the year 2007-2008 as a postdoctoral fellow at the University of Toronto and the Fields Institute under the supervision of Prof. George Elliott. During 2008-2009, I was a postdoctoral fellow at the University of Waterloo under the supervision of Prof. Ken Davidson. I've been at the University of Toledo since 2009.
Email: trieu (dot) le (number 2) (at) utoledo (dot) edu

I've taught a variety of courses from introductory undergraduate to graduate courses. Below is a list of courses that I have taught at UT and elsewhere.
For students: take a Calculus 1 Quiz.

MATH 4820/5820 (Intro to Real Analysis I) and MATH 6800/8800 (Real Analysis I).

Spring 2026: MATH 2860 (Elementary Differential Equations) and MATH 6800/8800 (Real Analysis II).
Fall 2025: MATH 1850-001 (Calculus I for Mathematicians/Scientists/Educators) and MATH 6800/8800 (Real Analysis I).
Spring 2025: MATH 2860 (Elementary Differential Equations) and MATH 6810/8810 (Real Analysis II).
Fall 2024: MATH 1850-001 (Calculus I for Mathematicians/Scientists/Educators) and MATH 6800/8800 (Real Analysis I).
Spring 2024: .
Fall 2023: MATH 1850-001 (Calculus I for Mathematicians/Scientists/Educators) and MATH 6980/8980 (Topics in Mathematical Science).
Spring 2023: MATH 1850 (Calculus I) and MATH 4880/5880 (Complex Variable).
Fall 2022: MATH 1850 (Calculus I) and MATH 3190 (Intro to Mathematical Analysis).
Spring 2022: MATH 4830/5830 (Intro to Real Analysis II) and MATH 6980/8980 (Topics in Mathematical Science).
Fall 2021: MATH 1850 (Calculus I) and MATH 4820/5820 (Intro to Real Analysis I).
Spring 2021: MATH 2860 (Elementary Differential Equations) and MATH 4830/5830 (Intro to Real Analysis II).
Fall 2020: MATH 2860 (Elementary Differential Equations) and MATH 4820/5820 (Intro to Real Analysis I).
Spring 2020: MATH 4880/5880 (Complex Variables) and MATH 6980/8980 (Topics in Mathematical Science: Intro to Operator Theory).
Spring 2019: MATH 2860 (Elementary Differential Equations) and MATH 6830/8830 (Functional Analysis II).
Fall 2018: MATH 2860 (Elementary Differential Equations) and MATH 6820/8820 (Functional Analysis I).
Spring 2018: MATH 2860 (Elementary Differential Equations) and MATH 4830/5830 (Intro Real Analysis II).
Fall 2017: MATH 2860 (Elementary Differential Equations) and MATH 4820/5820 (Intro to Real Analysis I).
Spring 2017: MATH 2860 (Elementary Differential Equations) and MATH 6810/8810 (Real Analysis II).
Fall 2016: MATH 2860 (Elementary Differential Equations) and MATH 6800/8800 (Real Analysis I).
Spring 2016: MATH 6810/8810 (Real Analysis II).
Fall 2015: MATH 2850 (Multivariable Calculus) and MATH 6800/8800 (Real Analysis I).
Spring 2015: MATH 1200, MATH 1850, MATH 4460 (Introduction to Topology II).
Fall 2014: MATH 1200 (Mathematical Modelling), MATH 1860, MATH 1980 (Trig Review), MATH 4450 (Introduction to Topology I).
Spring 2014: MATH 1840, MATH 1860, MATH 2860.
Fall 2013: MATH 1320, MATH 1850, MATH 1830, MATH 2450 and MATH 1980.
Spring 2013: MATH 1850 and MATH 1860 (Single Variable Calculus I and II) I was the coordinator for MATH 1860.
Fall 2012: MATH 1320 (College Algebra), MATH 1850 (Single Variable Calculus I) I was the coordinator for MATH 1850.
Spring 2012: MATH 1860 (Single Variable Calculus II), MATH 3860 (Elementary Differential Equations).
Fall 2011: MATH 1320 (College Algebra), MATH 1860 (Single Variable Calculus II).
Spring 2011: MATH 1270 (Calculus for Business with Applications II), MATH 1860 (Single Variable Calculus II) and MATH 3860 (Elementary Differential Equations).
Fall 2010: MATH 1750 and MATH 1760 (Calculus for the life sciences with applications I and II).
Spring 2010: MATH 1830 (Calculus I for Mathematicans, Scientists and Educators) and MATH 1270 (Calculus for Business with Applications II).
Fall 2009: MATH 1850 (Single Variable Calculus I) and MATH 1270 (Calculus for Business with Applications II).

Winter 2009: coordinator for MATH137 (Calculus I for Honours Math), University of Waterloo
Fall 2008: tutorial instructors for MATH135 (Algeba for Honours Math) and MATH137 (Calculus I for Honours Math), University of Waterloo
Fall 2007 and Spring 2008: MAT135Y Calculus, University of Toronto
Spring 2007: MTH 131 Mathematical Analysis for Management, University at Buffalo
Fall 2006: MTH 131 Mathematical Analysis for Management, University at Buffalo
Summer 2005: MTH 241 College Calculus 3, University at Buffalo

Research Statement (pdf)
My research interests are in the fields of Operator Theory and Operator Algebras. More specifically, I am interested in Toeplitz, Hankel, composition operators, weighted composition operators on Hilbert spaces of analytic function spaces such as Bergman, Hardy and Segal-Bargmann (Fock) spaces. I am also interested in dilation theory, frame theory and its applications, and reproducing kernel methods in Machine Learning. Click here for my publications.
Our research group in Complex Analysis and Operator Theory.
Recent papers (click a title to see the coressponding abstract. Click an abstract to hide it):

On compactness of products of Toeplitz operators (pdf) (with Tomas Miguel Rodriguez and Sonmez Sahutoglu), Complex Anal. Oper. Theory 19 (2025), no. 1, Paper No. 2; arXiv:2401.04869

We study compactness of product of Toeplitz operators with symbols continuous on the closure of the polydisc in terms of behavior of the symbols on the boundary. For certain classes of symbols $f$ and $g$, we show that $T_fT_g$ is compact if and only if $fg$ vanishes on the boundary. We provide examples to show that for more general symbols, the vanishing of $fg$ on the whole polydisc might not imply the compactness of $T_fT_g$. On the other hand, the reverse direction is closely related to the zero product problem for Toeplitz operators on the unit disc, which is still open.

I'm one of the organizers of the Complex Analysis and Operator Theory seminar. Click here for our seminar page.

Last updated: September 14, 2026. This webpage uses the bootstrap framework.