Congratulations to Pure Mathematics PhD candidate Jacob Campbell and recent Computer Science master’s graduate Mahbod Majid, the 2023 recipients of the Faculty of Mathematics Graduate Research Excellence Awards. The prestigious recognition comes with a $5,000 cash prize and is conferred annually to two graduate students in the Faculty of Mathematics who have authored or co-authored an outstanding research paper.

## Jacob Campbell

Jacob
Campbell
is
a
PhD
candidate
in
Pure
Mathematics
who
is
finishing
his
final
semester
of
graduate
education
before
beginning
a
postdoctoral
position
in
the
Department
of
Mathematics
at
the
University
of
Virginia.
In
2021
and
2022,
he
published
two
papers
and
posted
the
preprint
of
a
third:
"Finite
free
convolutions
via
Weingarten
calculus,"
(with
Zhi
Yin,
research
fellow
at
Harbin
Institute
of
Technology)
“A
Central
Limit
Theorem
for
Star-Generators
of
S_{¥},
Which
Relates
to
Traceless
CCR-GUE
Matrices,”
(with
Claus
Köstler,
lecturer
in
Mathematical
Sciences
at
University
College
Cork,
Ireland,
and
Alexandru
Nica,
professor
of
Pure
Mathematics
at
Waterloo
and
Campbell’s
advisor)
and
“Commutators
in
finite
free
probability,
I”
(preprint,
as
sole
author).

In the paper published with Köstler and Nica, the authors found a novel random matrix model for a certain family of probability distributions related to characters of symmetric groups. In the two other papers, the authors used techniques from combinatorial representation theory to study sums, products, and commutators of random matrices, in the context of the new theory of "finite free probability."

Campbell emphasizes the importance of collaboration to pure math research: “solving problems that other people are interested in” is a driver for his work. The area of inquiry that Campbell investigated, explains his Alexandru Nica, his advisor and a professor of Pure Mathematics, ”has been studied since the 1970s, but he recently found new interpretations within the framework.”

## Mahbod Majid

Majid,
who
is
currently
a
first-year
PhD
student
in
the
Machine
Learning
Department
at
Carnegie
Mellon
University’s
School
of
Computer
Science,
received
the
award
in
recognition
of
the
paper
“Efficient
Mean
Estimation
with
Pure
Differential
Privacy
via
a
Sum-of-Squares
Exponential
Mechanism.”
This
paper,
which
he
co-authored
with
his
graduate
advisor
Professor
Gautam
Kamath
and
Professor
Samuel
Hopkins
at
MIT,
was
presented
at
STOC
2022,
the
54^{th}
ACM
Symposium
of
Theory
of
Computing,
one
of
two
top
conferences
in
theoretical
computer
science.

Mahbod’s paper solved a core problem in private statistical estimation, one that has plagued researchers for years: how do you estimate the mean in a distribution or population efficiently and accurately while also preserving the privacy of sensitive data? “Previously developed algorithms had achieved two out of three of these goals at any given time,” explains Kamath, “but Mahbod’s elegant solution satisfies all three simultaneously. It is not only a nearly-optimal solution for the most fundamental statistical task under strong privacy constraints, but it also closes a long-standing gap in our understanding of private multivariate statistics.”