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The annual Phillip and Ruth Hettleman Prizes for Artistic and Scholarly Achievement have been awarded to five promising faculty members who exemplify groundbreaking and innovative research along with future career promise. These coveted awards, established in 1986 by the late Phillip Hettleman, a proud alumnus of the Carolina class of 1921, and his wife Ruth, shine a spotlight on exceptional junior faculty members who embody a commitment to groundbreaking research and hold the promise of a brilliant future.

Among those gracing this year’s recipient list is our very own Professor Yaiza Canzani. Her work transcends boundaries, connecting microlocal analysis, partial differential equations, probability, geometry, and dynamical systems. On the national stage, her scholarship shines bright, having earned accolades including a prestigious Alfred P. Sloan Fellowship, the Sadosky Research Prize in Analysis, and a National Science Foundation CAREER grant.

The winners will illuminate their groundbreaking research during University Research Week: October 24, from 3 to 5 p.m., at the School of Social Work’s Tate-Turner-Kuralt Auditorium. The full announcement for the prize can be found here. Congratulations Yaiza!

During University Research Week, members of the research group will host an informal meet-up where students can delve into the exciting world of research and the pursuit of advanced degrees in mathematics.

• Date: October 26
• Time: 2-3 PM
• Location: PH 365

Students can get insights, ask questions, and explore the possibilities in this dynamic field! The official University Research Week link for this event can be found here.

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, Minimal surfaces and Colding-Minicozzi Entropy in the Complex Hyperbolic Space.
  • Newly posted: A. Bhattacharya and A. Skorobogatova, Variational integrals on Hessian spaces: partial regularity for critical points.
  • Newly accepted: A. Bhattacharya and R. Shankar, Regularity for convex viscosity solutions of Lagrangian mean curvature equation, Crelle’s Journal, to appear.
  • Upcoming Invited Talk: European Congress of Mathematicians: Satellite Conference on Analysis and PDE, Portugal (July 2024)
  • Upcoming Invited Talk: PDEs in Complex Geometry: Thematic program, Centre de Recherches Mathématiques (CRM), Montréal, Canada, (April 2024)
  • Upcoming Invited Talk: PDE seminar, Indiana University (Spring, 2024)
  • Upcoming Invited Talk: Geometry-Topology seminar, North Carolina State University (August 25, 2023)
  • Presentation: Colloquium, Tata Institute of Fundamental Research, Mumbai, India (August 3, 2023)
  • Presentation: Geometric Analysis Seminar, University of Oregon (May 16, 2023)
  • Presentation: Birthday Conference for Mikhail Safonov, Seoul, South Korea (June 20, 2023)

Yaiza Canzani, Associate Professor

• • Newly accepted: Y. Canzani and J. Galkowski:  Geodesic Beams in Eigenfunction Analysis.  Synthesis Lectures on Mathematics & Statistics.  Springer Nature. (2023)

Jeremy Marzuola, Professor

• • Newly posted: T. Alazard, J. L. Marzuola, and J. Wang: Damping for fractional wave equations and applications to water waves.
  • Presentation: ESI Program on Spectral Theory and Mathematical Relativity, Vienna, June 5-July 28, 2023

Casey Rodriguez, Assistant Professor

• • Newly accepted: K. R. Rajagopal and C. Rodriguez: Special Cosserat rods with rate-dependent evolving natural configurations.
  • Upcoming Invited Talk: Birthday Conference in Honor of Carlos E. Kenig, Melbourne, Australia (December 10-15, 2023)

James Rowan, Postdoctoral Fellow

• • Presentation:  MSRI program Mathematical Problems in Fluid Dynamics, part 2.

Timothy Van Hoose, Graduate Student

• • Newly posted: T. Van Hoose:  Modified Scattering for the Schrödinger-Bopp-Podolsky equation.

Jian Wang, Postdoctoral Fellow

• • Newly posted: T. Alazard, J. L. Marzuola, and J. Wang: Damping for fractional wave equations and applications to water waves.
  • Mini-course: The mathematics of internal wave attractors, Tsinghua University (June 2023)
  • Presentation: Spectral Geometry Senimar, University of Science and Technology of China (July 7, 2023)

We congratulate PI Yaiza Canzani and her co-author Jeff Galkowski on the publication of their new book: Geodesic beams in eigenfunction analysis.  Yaiza and Jeff have pioneered many uses of geodesic beams to better understand the behavior of eigenfunctions of the Laplacian.  It is exciting to see a recap of their achievements in text form.

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.

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.

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.

The most recent Community Spotlight from MSRI / the Simons Lauer Mathematical Sciences Institute has featured RTG faculty member Arunima Bhattacharya.  You can read the article and learn more about Arunima here.  Congratulations to Arunima!

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

• • Newly accepted: M. Brown: On the growth of generalized Fourier coefficients of restricted eigenfunctions.  Comm. PDE, to appear.
  • Elected President of UNC’s Graduate Math Associate (GMA) for the 2023-24 academic year.

Yaiza Canzani, Associate Professor

• • Newly accepted: Y. Canzani and J. Toth:  Lower bounds for eigenfunction restrictions in lacunary regions.  Communications in Mathematical Physics, to appear.

Hans Christianson, Professor

• • Newly posted: H. Christianson, J. Wang, and R. P. T. Wang: Control estimates for 0th order pseudodifferential operators.
  • Presentation: Tsinghua-Fudan joint online seminar on microlocal analysis (April 28, 2023)

Casey Rodriguez, Assistant Professor

• • Newly posted: C. Rodriguez, Elastic solids with strain-gradient elastic boundary surfaces.
  • Newly posted: K. R. Rajagopal and C. Rodriguez, Special Cosserat rods with rate-dependent evolving natural configurations.
  • Upcoming invited talk: 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications, UNC-Wilmington (May 31-June 4, 2023).

Jian Wang, Postdoctoral Fellow

• • Newly posted: H. Christianson, J. Wang, and R. P. T. Wang: Control estimates for 0th order pseudodifferential operators.
  • Presentation: Analysis and PDE Seminar, University of California at Berkeley (April 10, 2023)
  • Upcoming invited talk: Analysis Seminar, Northwestern University (May 15, 2023).

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.