Research Roundup

We will regularly announce newly posted articles and newly accepted articles within the group.  We are proud to announce the following updates from the past few months.

Arunima Bhattacharya, Assistant Professor

    • Newly posted: J. Bernstein and A. Bhattacharya, The CR-volume of horizontal submanifolds of spheres.
    • Upcoming Invited Talk: European Congress of Mathematicians: Satellite Conference on Analysis and PDE, Portugal (July 2024)
    • Upcoming Invited Talk: Partial Differential Equations and Convexity, (special session of AMS sectional meeting), San Francisco (May 2024)
    • Upcoming Invited Talk: PDEs in Complex Geometry: Thematic program, Centre de Recherches Mathématiques (CRM), Montréal, Canada, (April 15, 2024)
    • Upcoming Invited Talk: PDE seminar, Indiana University (April 1, 2024)
    • Upcoming Invited Talk: Geometric Analysis Colloquium, Fields Institute, Toronto, Canada (February, 2024)
    • Presentation: Ideas Seminar, Department of Statistics and Operations Research, UNC-Chapel Hill (November 9, 2023)
    • Presentation: Geometry-Topology seminar, North Carolina State University (August 25, 2023)

Maddie Brown, Graduate Student

Yaiza Canzani, Associate Professor

    • Award: Hettleman Prize, UNC
    • Upcoming Invited Talk: 13th Ohio River Analysis Meeting  (March 16-17, 2024)
    • Presentation: 8th Coloquio Uruguayo de Matematica (December 19-21, 2023)

Andrew Lyons, Graduate Student

Jeremy Marzuola, Professor

Casey Rodriguez, Assistant Professor

    • Newly posted and accepted: C. Rodriguez, A midsurface elasticity model for a thin, nonlinear gradient elastic plate, Int. J. Eng. Sci., to appear.
    • Upcoming Invited Talk: PDE Seminar, Georgia Tech (March 26, 2024)
    • Upcoming Invited Talk: Great Lakes Mathematical Physics Meeting (GLaMP), Michigan State University (June 7-9, 2024)
    • Presentation: Colloquium, Virginia Tech (December 1, 2023)

Jeremy Wall, Graduate Student

    • Presentation: Fall 2023 TAGMaC at NCSU (Isoperimetric Inequalities and Function Bounds)
    • Upcoming Event: Helping run the Spring 2024 TAGMaC at UNC-CH.

Jian Wang, Postdoctoral Fellow

Mark Williams, Professor

Research Roundup

We will regularly announce newly posted articles and newly accepted articles within the group.  We are proud to announce the following updates from the past few months.

Arunima Bhattacharya, Assistant Professor

Yaiza Canzani, Associate Professor

Jeremy Marzuola, Professor

Casey Rodriguez, Assistant Professor

James Rowan, Postdoctoral Fellow

Timothy Van Hoose, Graduate Student

Jian Wang, Postdoctoral Fellow

New grants in the group

Congratulations to RTG faculty members Arunima Bhattacharya, Jeremy Marzuola, and Casey Rodriguez on their new grants that were awarded!

  • Arunima was awarded a Travel Support for Mathematicians grant from the Simons Foundation.  The project is titled “Nonlinear PDEs in Lagrangian Geometry” and will run 9/1/2023-8/31/2028.
  • Jeremy’s grant from the National Science Foundation will support the project “Spectral theory and applications for models with localized or boundary defects” from 7/2023-6/2026.
  • Casey’s successful application was titled “Collaborative Research: Strain-limiting Cosserat Rods with Applications to Modeling Biological Fibers” and earned funding from the National Science Foundation for the period 8/1/2023-7/31/2026.

Girls Talk Math

The RTG is excited to welcome the Girls Talk Math program back to campus.  This summer camp was started by two alumni, including Katrina Morgan who is beginning a new faculty position at Temple University and has returned for this year’s camp.  Each year a number of high school students are hosted and dig into challenging problems.  See https://girlstalkmath.com for more info and to follow them on social media.

Congratulations to Michael Taylor

We congratulate Michael Taylor on his retirement after 36 years at UNC.  Michael is a 1970 PhD from Berkeley (with Cordes) and came to UNC in 1987.  Amongst his many accolades, he is an ICM speaker and an elected member of the American Academy of Arts & Sciences.  He has made many notable contributions with the fields of analysis and PDE.  He is the author of more than a dozen books including some absolute classics in microlocal analysis and an elegant and famous three volume set on Partial Differential Equations in addition to his classroom texts on analysis, linear algebra, complex analysis, ODE, and measure theory.

The members of the RTG are deeply grateful to Michael for his mentorship, generous sharing of ideas, and enthusiasm for all things in mathematics.

Derrick Nowak dissertation defense

Congratulations to Dr. Derrick Nowak!  Derrick successfully defended his dissertation “Local smoothing of the Schrödinger equation on a multi-warped product with degenerate trapping on Thursday, May 11.  Congratulations also goes to Hans Christianson, who was Derrick’s thesis advisor.

Research Roundup

We will regularly announce newly posted articles and newly accepted articles within the group.  We are proud to announce the following updates from the past few months.

Arunima Bhattacharya, Assistant Professor

    • Presentation: Geometry and Topology Seminar, Duke University (March 20, 2023)
    • Presentation: Continuum Mechanics Seminar, University of Nebraska-Lincoln (March 30, 2023)
    • Upcoming invited talk: Geometric Analysis Seminar, University of Oregon (May 16, 2023)
    • Upcoming invited talk: Differential Geometry/PDE Seminar, University of Washington (May 17, 2023)
    • Upcoming invited talk: Birthday Conference for Mikhail Safonov, Seoul, South Korea (June 20, 2023)
    • Newly accepted: A. Bhattacharya, J. Chen, and M. Warren: Regularity of Hamiltonian stationary equations in symplectic manifolds, Adv. Math., to appear.
    • Newly accepted: A. Bhattacharya, The Dirichlet problem for the Lagrangian mean curvature equation, Analysis & PDE, to appear.

Benjamin Bechtold, Graduate Student

    • Successfully completed the Departmental Oral Exam (February 2023)

Madelyne Brown, Graduate Student

Yaiza Canzani, Associate Professor

Hans Christianson, Professor

Casey Rodriguez, Assistant Professor

Jian Wang, Postdoctoral Fellow

2023 Undergraduate Research Cohort

With graduation approaching, we want to congratulate our graduating class of undergraduate researchers.

  • Ameer Qaquish has been working with Hans Christianson and will return to UNC in the biostatistics graduate program.
  • David Snider studied with Mark Williams and recently defended his honors thesis “Nonlinear geometric optics for pulses with nonlinear phases”.  He will enrolled in the graduate program in statistics at Columbia University in the fall.
  • Xiao-Ming Porter and Yizhou Gu have worked with Jason Metcalfe.  They presented their research at the 2023 UNC Celebration of Undergraduate Research.
    • Xiao-Ming will graduate with honors with a thesis titled “Local energy estimates for damped waves”.  Xiao-Ming will enroll in the graduate program in mathematics at the National University of Singapore.
    • Yizhou will enroll at the University of Michigan in statistics.  She was one of this year’s recipients of the Archibald Henderson Mathematics Medal and received recognition at the 2023 Chancellor’s Awards Ceremony.

We are extremely proud of these students, provide deep congratulations on their graduations, and wish them much luck in their new endeavors.