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: 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