Teaching

Go to Canvas for current course information. Here is Atlas for Umich users.

Random Matrix Theory Reading Group: In W26, I ran a reading group on random matrix theory with 12 students, meeting once a week. Students read and presented on various topics, and came from a range of programs, including MATH and AIM PhD and MLB, EECS PhD, and undergraduate.

MATH 395 and 396 (Honors Analysis I and II): Previously, these courses were typically taught by a single professor and covered analysis on manifolds along with additional topics of the instructor’s choosing. In ’26–27, we plan to decouple them. In F26, I will cover multivariable analysis, including standard topics up to vector calculus such as Stokes’ theorem, as well as other fundamental analysis concepts such as point-set topology and spaces of functions. In W27, Professor Chelkak will teach 396, which will feature Fourier analysis as one of the main topics. The overall goal of this experiment in the ’26–27 academic year is to provide students with a rigorous foundation while introducing them to a broader range of analysis topics.

MATH 602 (Real Analysis II) and 603 (Functional Analysis): Previously, MATH 602 was Functional Analysis. The course is now split into two: MATH 602, which covers advanced real analysis, and MATH 603, which covers functional analysis in greater depth than the old 602. Graduate analysis courses offered in the math department include 596 (Complex Analysis I), 597 (Real Analysis I), 602 (Real Analysis II), 603 (Functional Analysis), 604 (Complex Analysis II), and 650 (Fourier Analysis). Of these, 596, 597, and 602 are offered every year, while the others are typically offered every other year. Analysis students may also be interested in 625, 626 (Probability I & II), and 656, 657 (PDE I & II) as well.

MATH 551, Introduction to Real Analysis: This is a course I helped introduce starting in Winter 2021. It covers Lebesgue measure theory and a few other topics in real analysis, aimed at advanced math undergraduates, master’s students, and AIM and non-math PhD students. There is some overlap with MATH 597, the alpha course for MATH PhD students, but MATH 551 proceeds at a gentler pace and focuses on measures on Rⁿ rather than on general spaces. As prerequisites, students should have a solid background in advanced calculus (MATH 295, 297, or 451) and linear algebra (MATH 217 or 296).

  • 2026 Fall: Math 395, Honors Analysis I
  • 2026 Winter: Math 603, Functional Analysis
  • 2025 Fall: Math 596, Analysis I (Complex)
  • 2024 Winter: Math 710, Topics course in analysis; Random Matrix Theory
  • 2023 Fall: Math 596, Analysis I (Complex)
  • 2023 Winter: MATH 396, Honors Analysis II
  • 2022 Fall: MATH 395, Honors Analysis I
  • 2022 Winter: Math 597, Analysis II (Real)
  • 2022 Winter: MATH 551, Introduction to Real Analysis
  • 2021 Fall: MATH 285, Honors Multivariable & Vector Calculus
  • 2021 Winter: MATH 551, Introduction to Real Analysis
  • 2020 Fall: Math/Stats 425, Introduction to Probability (2 sections)
  • 2020 Winter: Math 710, Topics course in analysis; Random Matrix Theory
  • 2019 Fall: Math 285, Honors Multivariable Calculus (2 sections)
  • 2019 Winter: Math 525, Probability Theory (2 sections)
  • 2018 Fall: Math 709, Topics in Analysis (Integrable Probability)
  • 2018 Winter: Math 597, Analysis II (Real)
  • 2016 Fall: Math 709, Topics in Analysis (Exactly solvable models in probability and statistical physics)
  • 2016 Fall: Math 596, Analysis I (Complex)
  • 2016 Winter: Math 597, Analysis II (Real)
  • 2015 Fall: Math 625, Probability and Random Processes I
  • 2015 Winter: Math 710, Topics in Analysis (Random Matrix Theory )
  • 2014 Fall: Math 596, Analysis I (Complex)
  • 2014 Winter: Math 215, Calculus III (2 sections)
  • 2013 Winter: Math 215, Calculus III (2 sections)
  • 2012 Fall: Math 596, Analysis I (Complex)
  • 2012 Winter: Math 316, Differential Equations (2 sections)
  • 2011 Fall: Math 650, Fourier Analysis
  • 2010 Fall: Math/Stats 526 Discrete State Stochastic Processes (3 sections)
  • 2009 Fall: Math 709, Topics in Analysis (Random Matrix Theory)
  • 2009 Winter: Math/Stats 526 Discrete State Stochastic Processes (2 sections)
  • 2008 Fall: Math 596 Analysis I (complex)
  • 2008 Fall: Math/Stats 425 Introduction to Probability
  • 2008 Winter: Math/Stats 425 Introduction to Probability
  • 2008 Winter: Math 597 Analysis II (real)
  • 2007 Fall: Math 602 Real Analysis II (Functional Analysis)
  • 2006 Winter: Math/Stat 526 Discrete State Stochastic Processes
  • 2005 Fall: Math/Stat 525 Probability
  • 2004 Winter: Math 609 Toplics in Analysis (Random permutations and random matrices)
  • 2003 Fall: Math 555 Complex Variables and Applications

Advising

Ph.D. students
MLB students
  • 2026 Ammar Eltigani: Faculty advisor for Marjorie Lee Browne Final Report
Undergrad mentoring
  • 2026 Rishi Dadlani (Upenn) and Shaotian Sun: REU
  • 2023 Justin Liu: Independent study
  • 2021 Ron Nissim (NYU): REU
  • 2017 Han Wu: REU
  • 2016 Guanting Chen: Reading course
  • 2016 Yu Sheng: Reading course
  • 2011 Asad Lodhia (UC Davis): REU
  • 2006 Anthony Fader: REU
  • 2005 Robert Hines: REU