Category: Uncategorized

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 appeared: A. Bhattacharya, M. Warren, and D. Weser, A Liouville type theorem for ancient Lagrangian Mean Curvature flows, Communications in Partial Differential Equations (2025), 1–12
  • Newly appeared: A. Bhattacharya and A. Skorobogatova, Variational integrals on Hessian spaces: partial regularity for critical points, Nonlinear Analysis 255 (2025), 113760
  • Newly accepted: J. Bernstein and A. Bhattacharya, The CR-volume of horizontal submanifolds of spheres,  International Mathematics Research Notices
  • Upcoming invited talk: Colloquium, TIFR Center for Applicable Mathematics, Bengaluru, India, February 2025
  • Upcoming invited talk: PDE seminar, Brown University, August 2025
  • Upcoming invited talk: Nonlinear Elliptic PDEs and Geometry, AMS sectional meeting, University of Denver, August 2025

Yaiza Canzani, Professor

• • Award: Board of Governors’ Award for Excellence in Teaching
  • Newly accepted: Y. Canzani, J. Galkowski, and B. Keeler.  Asymptotics for the spectral function on Zoll manifolds. Journal of Spectral Theory.
  • Invited talk: Geometric Spectral Theory and Applications Program Conference, March 23-27, 2026. (ISAAC Newton Institute; Cambridge, UK)
  • Conference organization:  Member at Large on the Joint Math Meetings Program Committee

Hans Christianson, Professor

• • Newly posted: Hans Christianson and John Toth, Small-scale mass estimates for Laplace eigenfunctions on compact C² manifolds with boundary

Govanni Granados, Postdoc

• • Award: SIAM Postdoctoral Support
  • Upcoming Invited Talk: SIAM Conference on Computational Science and Engineering, Fort Worth, TX (March 5, 2025)

Hanna Kim, Postdoc

• • Newly posted:  Hanna N. Kim and Richard S. Laugesen, Two disks maximize the third Robin eigenvalue: positive parameters

Jeremy Marzuola, Professor

• • Newly Posted:  Greg Berkolaiko, Yaiza Canzani, Graham Cox, Peter Kuchment and Jeremy L.  Marzuola, Stability of Spectral Partitions with Corners
  • Newly Accepted:  T. Alazard, J. L. Marzuola, and J. Wang: Damping for fractional wave equations and applications to water waves.  Accepted to Journal de Mathematiques Pures et Appliqués (2024).
  • Newly posted:  Roy H. Goodman, Grace Conte, and Jeremy L. Marzuola QGLab: A MatLab Package for Computations on Quantum Graphs.  Accepted to SIAM Journal of Scientific Computation.
  • Newly Appeared:  Greg Berkolaiko, Yaiza Canzani, Graham Cox and Jeremy L. Marzuola.  Homology of spectral minimal partitions, Journal of the London Mathematical Society, Vol. 111, No. 1 (2025), Paper No. e70065.
  • Upcoming Workshop:  Interpretable Algorithms for High-Dimensional Data Sets: Analysis, Computation, Machine Learning, Optimization, and Statistics, ICERM, Providence, RI, May 12 – 16, 2025

Jason Metcalfe, Professor

• • Newly Posted:  Marvin Koonce and Jason Metcalfe, The sharp lifespan for a system of multiple speed wave equations:  Radial case.
  • Conference organization:  JAMI 2025 – The interplay of harmonic analysis, eigenfunctions of the Laplacian, and dispersive partial differential equations.  May 19-24, 2025

Casey Rodriguez, Assistant Professor

• • Newly posted: V. Prusa, K. R. Rajagopal, C. Rodriguez, L. Trnka, and M. Vejvoda. Modeling metamaterials by second-order rate-type constitutive relations between only the macroscopic stress and strain.
  • Newly accepted: D. Cichra, V. Prusa, K. R. Rajagopal, C. Rodriguez, and M. Vejvoda. The conclusion that metamaterials could have negative mass is a consequence of improper constitutive characterisation. Math. Mech. Solids, to appear.
  • Newly appeared: K. R. Rajagopal and C. Rodriguez. A mathematical justification for nonlinear constitutive relations between stress and linearized strain. Z. Angew. Math. Phys., 75, 210 (2024).
  • Upcoming Invited Talk: PDE Seminar at Vanderbilt University
  • Presentation: Blackwell-Tapia Conference, ICERM, Brown University (November 15-16, 2024)

Daniel Weser, Postdoc

• • Newly appeared: A. Bhattacharya, M. Warren, and D. Weser, A Liouville type theorem for ancient Lagrangian mean curvature flows. Communications in Partial Differential Equations, 50(1–2), 118–129 (2025).

Mark Williams, Professor

• • Newly appeared:  Jian Wang and Mark Williams, Transport of nonlinear oscillations along rays that graze a convex obstacle to any order, Annals of PDE, 11:7 (2025).

  • Newly posted: Jian Wang and Mark Williams, Convex waves grazing convex obstacles to high order, 40 pages, arXiv:2412.11926

The RTG is proud to share that two of its members were recognized with 2025 UNC University Teaching Awards.  Please join us in congratulating Yaiza Canzani, who is the Board of Governor’s Award Recipient for Excellence in Teaching, and Andrew Lyons, who has earned a Tanner Award for Excellence in Undergraduate Teaching by Graduate Teaching Assistants.  You can find wonderful citations for these awards on the CFE website.

Congratulations to Yaiza and Andrew for these apt recognitions for your teaching prowess!

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: A. Bhattacharya and J. Wall,  A priori estimates for singularities of the Lagrangian mean curvature flow with supercritical phase
  • Newly posted: A. Bhattacharya, M. Warren, and D. Weser, A Liouville type theorem for ancient Lagrangian Mean Curvature flows
  • Newly accepted: A. Bhattacharya and R. Shankar, Optimal regularity for Lagrangian mean curvature type equations, Archive for Rational Mechanics and Analysis
  • Newly accepted: A. Bhattacharya, C. Mooney, and R. Shankar, Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase, American Journal of Mathematics
  • Newly accepted: A. Bhattacharya and J. Wall,  Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian mean curvature flow, Calculus of Variations and PDE, 63:201 (2024)
  • Upcoming invited talk: Differential Equations and Nonlinear Analysis Seminar, North Carolina State University, April 2025
  • Upcoming invited talk: GAP (Geometry, Algebra, Physics) Seminar, Penn State University, Spring 2025
  • Upcoming invited talk: Differential Geometry Seminar, National Taiwan Normal University, Taipei, Spring 2025

Yaiza Canzani, Professor

• • Award: Graduate Assistance in Areas of National Need Grant P200A240148, Department of Education (2024-2027).
  • Newly accepted: T. Beck, Y. Canzani, and J. Marzuola. Uniform upper bounds on Courant sharp Neumann eigenvalues of chain domains. The Journal of Geometric Analysis. 34, no. 9, pp 262. (2024)
  • Upcoming Invited Talk: Mini-course Lecturer: Great Lakes Mathematical Physics Meeting (Kentucky, USA), June 6-8, 2025

Hans Christianson, Professor

• • Newly accepted: Hans Christianson and Daniel Pezzi, Energy Distribution for Dirichlet Eigenfunctions on Right Triangles, J. Differential Equations, Vol. 407 (2024), 153–180.
  • Upcoming invited talk: Johns Hopkins Analysis Seminar (28 October 2024)

Govanni Granados, Postdoc

• • Participant: Gene Golub SIAM Summer School, Escuela Politécnica Nacional, Ecuador (July 22 – August 2, 2024)
  • Talk: M.E. Taylor Analysis & PDE Seminar, UNC-Chapel Hill (September 4, 2024)
  • Upcoming Invited Talk: SIAM Central States Section Conference, University of Missouri-Kansas City (October 5, 2024)
  • Upcoming Invited Talk: Baby Inverse Problems Seminar, via Zoom (October 15, 2024)

Hanna Kim, Postdoc

• • Upcoming presentation: Spectral Theory and Differential Equations, November 4-7, 2024

Jeremy Marzuola, Professor

• • Newly appeared:  Tom Beck, Yaiza Canzani, and Jeremy L. Marzuola, Uniform Upper Bounds on Courant Sharp Neumann Eigenvalues of Chain Domains, Journal of Geometric Analysis, Vol. 34, No. 262 (2024).
  • Newly accepted:  Tom Beck, Marichi Gupta and Jeremy L. Marzuola, Nodal Set Openings on Perturbed Rectangular Domains, To appear in Annales Henri Poincare.
  • Newly posted:  Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola, Peter J. Mucha, and Braxton Osting, Targeting influence in a harmonic opinion model.

Casey Rodriguez, Assistant Professor

• • Newly posted: D. Cichra, V. Prusa, K. R. Rajagopal, C. Rodriguez, and M. Vejvoda. The conclusion that metamaterials could have negative mass is a consequence of improper constitutive characterisation.
  • Newly posted: R. Bustamante, K. R. Rajagopal, and C. Rodriguez. Piecewise linear constitutive relations for stretch-limited elastic strings.
  • Newly accepted: K. R. Rajagopal and C. Rodriguez. A mathematical justification for nonlinear constitutive relations between stress and linearized strain. Z. Angew. Math. Phys., to appear.
  • Newly appeared: C. Rodriguez. Elastic solids with strain-gradient elastic boundary surfaces. J. Elast., 156 (2024), p. 769-797.
  • Upcoming Invited Talk: Blackwell-Tapia Conference, ICERM, Brown University (November 15-16, 2024)
  • Presentation: Modelling, PDE Analysis and Computational Mathematics in Material Sciences, Charles University, Prague, Czech Republic (September 22-27, 2024)
  • Presentation: International Conference on Nonlinear Solid Mechanics, Facoltà di Ingegneria e Architettura, University of Cagliari, Italy (June 11-14, 2024)

James Rowan, Postdoc

• • Newly posted: J. Rowan and L. Wan, Two-dimensional solitary water waves with constant vorticity, Part II: the deep capillary case.
  • Upcoming invited talk: AMS Fall Western Sectional Meeting 2024 (26-27 October 2024)

Jeremy Wall, Graduate Student

• • Newly appeared: Hessian estimates for the Lagrangian mean curvature flow, Calc. Var. (2024) Vol 63-201
  • Newly posted: A. Bhattacharya and J. Wall, A Priori Estimates for Singularities of the Lagrangian Mean Curvature Flow with Supercritical Phase

Daniel Weser, Postdoc

• • Newly posted: Arunima Bhattacharya, Micah Warren and Daniel Weser, A Liouville type theorem for ancient Lagrangian mean curvature flows
  • Newly appeared: Matias G. Delgadino and Daniel Weser, A Heintze-Karcher inequality with free boundaries and applications to capillarity theory. Journal of Functional Analysis, Vol. 287, No. 9 (2024).

Mark Williams, Professor

• • Newly appeared:  Reflection of conormal pulse solutions to large variable-coefficient semilinear hyperbolic systems, Journal of Differential Equations, vol. 401, (2024), 93-147.
  • Newly posted : Transport of nonlinear oscillations along rays that graze a convex obstacle to any order, with Jian Wang, submitted. arXiv:2309.05910
  • Invited Talk: Progress in nonlinear geometric optics, Knox College, June 2024
  • Conference Organized: Conference on the occasion of the retirement of Dennis Schneider, Knox College, June 2024

We congratulate the following RTG Undergraduate Researchers on their upcoming induction into Phi Beta Kappa.

• Malaika Shroff
• Joseph Stellman
• Joseph Yordy

They will be recognized in a ceremony on October 30, 2024.  We are proud of their accomplishments!

With the fall semester underway, we want to highlight a few of the happenings with the RTG.

• We congratulate Assistant Professor Arunima Bhattacharya who was awarded a new NSF grant DMS-2350290, “Fully Nonlinear Equations and Minimal Submanifolds in Lagrangian Geometry”, which will provide her $234,951 in funding over the next three years!
• We congratulate Professor Yaiza Canzani on her promotion to full professor, which was effect July 1!
• Our former undergraduate researcher, Marleigh Purgar-McDonald, just began her graduate studies at Texas A&M.  We wish Marleigh luck with this new endeavor.
• We similarly wish our former postdoc, Jian Wang, luck with his new position at the Institut des Hautes Études Scientifiques at the Université Paris-Saclay.
• We welcome two new postdocs to the group:  Hanna Kim and Govanni Granados!  We are looking forward to working with you.
• We are proud to announce that Jason Metcalfe was recently awarded a 2024 Faculty Mentoring Award from the Carolina Women’s Leadership Council for faculty to junior faculty mentoring.
• Undergraduate researcher Jonah Boan is amongst the inaugural class of Kennedy Scholars within the Department.  These are possible due to a generous contribution from Dr. Daniel Kennedy in support of undergraduate research.  Jonah will be investingating the isoperimetric problem, a geometric question going back to the ancient Greeks that seeks to identify the shape that maximizes area for a given perimeter. His research focuses on a variant of the problem related to the eigenvalues of the Laplacian, and they will gather numerical data using the finite element method on real projective space.  Congratulations, Jonah!

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.

Benjamin Bechtold, Graduate Student

• • Presentation: Spring 2024 TAGMaC at UNC

Arunima Bhattacharya, Assistant Professor

• • Newly posted: A. Bhattacharya and J. Wall,  Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian mean curvature flow
  • Newly accepted: J. Bernstein and A. Bhattacharya, Minimal surfaces and Colding-Minicozzi entropy in the complex hyperbolic space, Geometriae Dedicata, 218 (2024), no. 3, 61.
  • Upcoming invited mini course: Tata Institute of Fundamental Research, India, January 2025.
  • Upcoming plenary talk:  European Congress of Mathematics, Satellite conference, Coimbra, Portugal.  July 2024.

Maddie Brown, Graduate Student

• • Presentation: Spring 2024 TAGMaC at UNC

Hans Christianson, Professor

• • Newly posted: H. Christianson and J. Toth, Small-Scale Mass Estimates for Neumann Eigenfunctions: Piecewise Smooth Planar Domains
  • Newly posted: H. Christianson and J. Toth, Quantum Flux and Quantum Ergodicity for Cross Sections
  • Upcoming invited talk: Microlocal Analysis and Quantum Dynamics 2024 (24-28 June 2024)

Andrew Lyons, Graduate Student

• • Presentation: Spring 2024 TAGMaC at UNC

Jeremy Marzuola, Professor

• • Newly appeared:  Kiril Datchev, Jeremy L. Marzuola and Jared Wunsch, Newton polygons and resonances of multiple delta-potentials. Trans. Amer. Math. Soc., Vol. 377, No. 3 (2024), 2009-2025.
  • Newly appeared:  Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola, Peter J. Mucha, and Braxton Osting, Escape times for subgraph detection and graph partitioning. SIAM J. Matrix Anal., Vol. 45, No. 1 (2024), 685-711.
  • Upcoming Invited Talk:  Conference on Mathematical and Statistical Tools for High Dimensional Data on Compressive Networks, Casa Matematica Oaxaca, May 29, 2024
  • Upcoming Invited Talk: 81st Fujihara Seminar (Mathematical Aspects for Interfaces and Free Boundaries), Sapporo, Japan, June 3rd, 2024
  • Upcoming Invited Talk:  Workshop on Metric Networks, Frankfurt, Germany,  July 18th, 2024

Casey Rodriguez, Assistant Professor

• • Newly accepted: C. Rodriguez, Elastic solids with strain-gradient elastic boundary surfaces, J. Elast., to appear
  • Upcoming Invited Talk: International Conference on Nonlinear Solid Mechanics, Facoltà di Ingegneria e Architettura, University of Cagliari, Italy (June 11-14 2024)

Jeremy Wall, Graduate Student

• • Presentation: Spring 2024 TaGMaC at UNC
  • Presentation: M. E. Taylor Analysis and PDE Seminar, UNC-CH (April 17, 2024)
  • Newly Posted: Arunima Bhattacharya and J. Wall, Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian Mean Curvature Flow

Timothy Van Hoose, Graduate Student

• • Presentation: Spring 2024 TAGMaC at UNC

Congratulations to Maddie Brown who successfully defended her dissertation, “Fourier Coefficients of Restricted Eigenfunctions”.  It is a beautiful result and was a masterful presentation.  Maddie worked with Yaiza Canzani and Jeff Galkowski, and we also congratulate them. Maddie will be leaving for a postdoctoral position at the University of Auckland, after which she will join Oberlin College & Conservatory as an Assistant Professor.

We are proud of Maddie, wish her luck, and will miss her.

Congratulations to RTG faculty member and co-PI Casey Rodriguez!  Casey is one of the 2024 recipients of the Goodman-Petersen Award for Excellence in Teaching.

The Goodman-Petersen Awards were established thanks to a donation from UNC Mathematics Alumni Jennifer Johnson and Janos Kollar, and they are given annually by the Department to faculty for excellence in the teaching of mathematics to undergraduates.  The awards are named after two of our Emeritus Faculty members, Professors Sue Goodman and Karl Petersen, both of whom showed incredible devotion to undergraduate education throughout their careers.

The RTG is privileged and proud to have Casey in the group.  He has mastered the art of delivering deeply rigorous material in digestible ways and using humor to keep students engaged.

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

• • Presentation: Fall 2023 TAGMaC at NCSU

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

• • Newly posted: A. Lyons: Nodal sets of Laplacian Eigenfunctions with an eigenvalue of multiplicity 2.
  • Presentation: Fall 2023 TAGMaC at NCSU

Jeremy Marzuola, Professor

• • Newly posted:  Roy H. Goodman, Grace Conte, and Jeremy L. Marzuola QGLab: A MatLab Package for Computations on Quantum Graphs
  • Newly accepted:  Kiril Datchev, Jeremy L. Marzuola and Jared Wunsch, Newton polygons and resonances of multiple delta-potentials.  Trans. Amer. Math. Soc., to appear.
  • Newly accepted:  Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola, Peter J. Mucha, and Braxton Osting, Escape times for subgraph detection and graph partitioning. SIAM J. Matrix Anal., to appear.
  • Upcoming Invited Talk:  Georgia Tech PDE Seminar (March 12, 2024)
  • Upcoming Invited Talk: Berkeley PDE Seminar (March 15, 2024)
  • Presentation: George Mason University Applied & Computational Mathematics Seminar (September 29, 2023)

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

• • Newly posted: J. Wang and M. Williams: Transport of nonlinear oscillations along rays that graze a convex obstacle to any order
  • Newly accepted: H. Christianson, J. Wang, and R. P. T. Wang, Control estimates for 0th-order pseudodifferential operators, International Mathematics Research Notices, published online.
  • Newly accepted: S. Dyatlov, J. Wang, and M. Zworski, Mathematics of internal waves in a 2D aquarium, to appear in Analysis & PDE.
  • Upcoming Invited Talk: Colloquium, the University of Melbourne (February 6, 2024)
  • Upcoming Invited Talk: Colloquium, Texas A&M University (January 25, 2024)
  • Upcoming Invited Talk: Colloquium, the University of Pittsburgh (January 23, 2024)
  • Presentation: PDE Seminar, Laboratoire de Mathématiques d’Orsay (November 23, 2023)
  • Presentation: Microlocal Analysis Seminar (online), Tsinghua University and Fudan University (November 14, 2023)
  • Presentation: M. E. Taylor Analysis and PDE Seminar, UNC (November 1, 2023)

Mark Williams, Professor

• • Newly posted: J. Wang and M. Williams: Transport of nonlinear oscillations along rays that graze a convex obstacle to any order

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!