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Qi Xu has coauthored six papers on partial differential equations, focusing on fluid dynamics and the time evolution of solutions. In geophysics, he has solved a difficult mathematical problem concerning the primitive equations of ocean dynamics coupled with an elastic ice sheet, establishing estimates that account for the interaction between ocean currents and the moving ice. He has also obtained the first local well-posedness result for an elastic body immersed in an inviscid fluid, showing that, under suitable conditions, the coupled motion exists and is uniquely determined for a short time. Another direction of his work explores how the conditions imposed where fluid enters and leaves a region determine the flow inside. He has obtained the surprising result that the same boundary conditions can produce a unique flow or infinitely many different flows, depending on the regularity required of the solutions. In a separate paper, he establishes analytic regularity up to the boundary for a fundamental equation used in fluid mechanics.

His two most recent papers contribute to the longstanding study of uniqueness and decay: can a solution that is initially nonzero disappear completely, and how quickly can it approach zero? He establishes precise limits on this decay for heat-type equations and shows that adding a transport term can make solutions fade much faster.

Every summer, SLMath organizes several summer graduate schools (usually two weeks each), some of which are held at SLMath and others at partner institutions around the world. Attending one of these schools can be a very motivating and exciting experience for a student; participants have often said that it was the first experience where they felt like real mathematicians, interacting with other students and mathematicians in their field.

For more information: https://www.slmath.org/summer-schools

Internal applications are due by November 15 

Your demographic information is requested by SLMath and will not affect our selection of nominees for this program. 

The Spring Graduate Exams registration form is now open! The Mathematics Graduate Exams will be offered between January 6-8, 2027.

You can change your selections up until December 1, 2026.

We have now created a form for students approaching their Oral Qualifying Exam. The form will outline the steps for signing up for the oral exam and provide the student services team with the information needed to complete the required paperwork. 

The Department of Mathematics is pleased to offer the following awards annually. Students must complete this form and identify the award they are being nominated for, the name of the faculty member nominating them, CV, and Teaching or Research Statement. 

Research Awards

Teaching Awards

Students must be nominated by their faculty advisor for a Research Award or an instructor for a Teaching Award. 

Faculty members should be asked to email nomination letters to PhD Student Services Advisor, Alexis Teodoro at ateodoro@usc.edu. Additional documents should be submitted by the student to this form. All materials must be submitted by November 1. 

The Rockwell Dennis Hunt Scholastic Award honors USC graduate students whose undergraduate degree is from USC. The $5,000 award is bestowed at the USC Honors Convocation. Applicants must meet the following criteria:

Competitive candidates will demonstrate the following:

Applications are due through the Graduate School by Monday, November 16, 2026 at 11:59pm.

The online application can be found by clicking here.

One letter of recommendation must be included with the online application by Monday, November 16, 2026 at 11:59pm.

To recognize our current PhD students’ academic professional development, The Graduate School will provide USC PhD Achievement Awards for students with exceptional academic profiles. Six awards of $5,000 will be made to students from across the university. Each recipient’s primary faculty advisor will receive a $500 USC Graduate School PhD Mentoring award. 

Current students from every PhD program at USC are eligible. Students must be registered to receive the award.  Ideally students will be registered in spring 2027, but if they are graduating in December other arrangements for processing the award will need to be made.  The award is for exceptional achievement as a USC PhD student. The student’s overall profile as a doctoral candidate may include such elements as significant publications as the sole or primary author; major awards in a broadly conceived field; and other markers of excellence appropriate to the student’s field.

The application for the award includes the following: 

Submissions will be reviewed by an interdisciplinary faculty committee. Recipients of the USC PhD Achievement Awards will be invited to the USC Academic Honors Convocation and will lead the column of PhD graduates at the university commencement.

Students will not apply to the Graduate School directly, but are expected to submit application materials to Alexis Teodoro, PhD Student Services Advisor, at ateodoro@usc.edu no later than Sunday, November 1st at 11:59pm. Please note that programs may only nominate one candidate per program.

The Dornsife PhD Academy will be hosting their next academic event, Preparing for Qualifying Exams: Strategies for Success.

Qualifying exams are a major milestone on the path to doctoral candidacy. Designed for second- and third-year Ph.D. students, this session will provide practical guidance on preparing for qualifying exams, developing effective study strategies, managing the process, and setting yourself up for success. 

Tuesday, October 13, 2026
DML 240 + Zoom
5:30-7:00pm

Qualifying exams are a major milestone on the path to doctoral candidacy. Hear from senior Ph.D. candidates who will provide practical guidance on preparing for qualifying exams, developing effective strategies, managing the process, and setting yourself up for success! 

Refreshments and dinner (pizza) will be served. Please register to confirm your attendance.

For those who plan to join on Zoom, please join the Zoom link below by 6:00pm.

Zoom Meeting Link
Meeting ID: 998 6958 2054
Passcode: 033859

P.S. This event counts towards attendance for the Ph.D. Academy Scholarship and Research Fund.

The Dornsife PhD Academy will be hosting their next academic event, Crafting Your Ph.D. Elevator Pitch.

This interactive workshop designed for first-year PhD students will give you the chance to practice your elevator pitches. The goal is to craft an effective elevator pitch that communicates your research, interests, and goals to a variety of audiences. Whether you're introducing yourself at a conference, networking event, or casual conversation, this session aims to help you make a memorable first impression.

Tuesday, October 20, 2026
DML 240 
5:30-7:00pm

Refreshments and dinner (pizza) will be served. Please register to confirm your attendance.

P.S. This event counts towards attendance for the Ph.D. Academy Scholarship and Research Fund.

Due to the format of this event, it is in person only (no Zoom).