Welcome to Dr. Dong’s homepage

I am a Boas Assistant Professor at the Department of Mathematics, Northwestern University. I obtained my Ph.D. in math from the University of Illinois at Urbana-Champaign.

Office: 312 Lunt Hall; E-mail: dong@northwestern.edu

Research:

I am interested in machine learning, harmonic analysis and its applications. Google Scholar; Mathematical Reviews 

Articles:

  • Analysis of hyperspectral data by means of transport models and machine learning (with W.~Czaja, P-E.~Jabin and F.~Njeunje), IEEE International Geoscience and Remote Sensing Symposium, Waikoloa, HI, USA, 2020, pp. 3680-3683
  • Transport Model for Feature Extraction (with W.~Czaja, P-E.~Jabin and F.~Njeunje), SIAM J. Math. Data Sci. 3 (2021), no. 1, 321–341
  • Special cases of power decay in multilinear oscillatory integrals (with D. Maldague and D. Villano), Appl. Anal. 101 (2022), no. 15, 5517–5527.
  • A Hormander type theorem in finite fields, Finite Fields Appl. , 59 (2019), 22-31.
  • Improved estimates for polynomial Roth type theorems in finite fields (with X. Li and W. Sawin),  J. Anal. Math. 141 (2020), no. 2, 689–705.
  • Quasi pieces of the bilinear Hilbert transform incorporated into a paraproduct, J. Geom. Anal. 29 (2019), no. 1, 224–246.
  • On bilinear Hilbert transform along two polynomials, Proc. Amer. Math. Soc., 147 (2019), 4245-4258
  • Full range boundedness of bilinear Hilbert transform along certain nonlinear polynomials, Math. Inequal. Appl. 22 (2019), no. 1, 151–156
  • Discrete bilinear Radon transforms along arithmetic functions with many common values (with X. Meng), Bull. Lond. Math. Soc. 50 (2018), no. 1, 132–142.
  • On a discrete bilinear singular operator, C. R. Math. Acad. Sci. Paris 355 (2017), no. 5, 538–542.
  • On a hybrid of bilinear Hilbert transform and paraproduct (with X. Li), Acta Math. Sin. (Engl. Ser.) 34 (2018), no. 1, 29–41.
  • Irrational factor of order k and its connections with k-free integers (with X. Meng), Acta Math. Hungar. 144 (2014), no. 2, 353-366.

Teaching

Northwestern University:

  • Winter 2023: MATH 368-0, Introduction to Optimization; MATH 306-0, Combinatorics and Discrete Mathematics
  • Fall 2022: MATH 220-2, Single-Variable Integral Calculus; MATH 314-0, Probability and Statistics for Econometrics
  • Spring 2022: MATH 310-3, Probability and Stochastic Processes

  • Winter 2022: MATH 228-1, Multivariable Differential Calculus for Engineering

  • Spring 2021: MATH 310-3, Probability and Stochastic Processes
  • Winter 2021: MATH 306-0, Combinatorics and Discrete Mathematics
  • Fall 2020: MATH 228-1, Multivariable Differential Calculus for Engineering

University of Maryland, College Park:

  • Spring 2020: MATH 858L, Selected Topics in Analysis: Mathematical Methods in Machine Learning)
  • Fall 2019: STAT 420, Theory and Methods of Statistics
  • Spring 2019: MATH 401, Applications of Linear Algebra
  • Fall 2018: MATH 241 H, Calculus III Honors – Introduction to Multivariable Calculus

University of Illinois at Urbana-Champaign:

  • Spring: 2018: Grader for MATH 541 (Graduate Functional Analysis), MATH 417 (Abstract Algebra I), MATH 418 (Abstract Algebra II)
  • Fall 2017: Grader for MATH 540 (Graduate Real Analysis) and MATH 447 (Real Variables )
  • Spring 2017: TA for MATH 415 (Linear Algebra), 5 sections
  • Fall 2016: Grader for MATH 540 (Graduate Real Analysis), MATH 461 (Probability), MATH 285 (Differential Equations)
  • Spring 2016: Grader for MATH 540 (Graduate Real Analysis), MATH 225 (Matrix Theory)
  • Fall 2015: Instructor for MATH 124 (Finite Math), 2 sections
  • Spring 2015: TA for MATH 231 (Calculus II), 2 sections
  • Fall 2014: Grader for MATH 540 (Graduate Real Analysis), MATH 285 (Differential Equations)
  • Spring 2014: Netmath TA for MATH 461 (Probability)
  • Fall 2013: TA for Merit MATH 241 (Calculus III)
  • Spring 2013: TA for MATH 241 (Calculus III), 2 sections
  • Fall 2012: TA for MATH 221 (Calculus I), 2 sections
  • Summer 2012: Instructor for MATH 103 (College Algebra)
  • Spring 2012: TA for MATH 133 (Calculus II)
  • Fall 2011: TA for MATH 103 (College Algebra)