To speak at the seminar, contact Chunhua Shan at firstname.lastname@example.org or any of us.
Current students:Xueliang Lu
(advisors: Arsie and Shan)
Daniel Liu, undergraduate research
Past students:2014 Dr. Ramesh Karki, PhD thesis: Sobolev gradient semi-flows and applications to nonlinear problems (advisor: Arsie), now Assistant Professor at Indiana University East.
2015 Dr. Krishna Pokharel, PhD thesis: An Isospectral Flow for Complex Upper Hessenberg Matrices (advisor: Arsie), now Assistant Professor at Young Harris College.
2012 Matthew Osborne, honors thesis (advisor: Arsie), now PhD student at Ohio State University.
2012 Dr. Douglas Oliver, M.Sc. thesis: Analysis of a Pseudo-Harmonic Tubular Bell (advisor: Arsie), now at Taylor University, Indiana.
- Alessandro Arsie :
Integrable systems, Differential Eqs (Ordinary, Partial and Functional), Mathematical Physics, Aspects of functional and real analysis related to DEs.
- (preprint) D. Oliver and A. Arsie, Effects ofWeighting the Ends of a Tubular Bell on Modular Frequencies.
- (preprint) R. Aceska, A. Arsie and R. Karki, On near-optimal time samplings for initial data best approximation.
- (preprint) A. Arsie and P. Lorenzoni, F-manifolds, multi-flat structures and Painlevé transcendents
- A. Arsie and P. Lorenzoni, Flat F-manifolds, Miura invariants and integrable systems of conservation laws to appear in Journal of Integrable Systems, Oxford University Press, 2018
- A. Arsie, P. Lorenzoni, Complex reflection groups, logarithmic connections and bi-flat F-manifolds, Lett.Math.Phys, 43 pages, 2017
- A. Mansour, D. Offin, A. Arsie, Extensions to Chen's minimizing equal mass parallelogram solutions , 18 pages, Taiwanese J. Math. Volume 21, Number 6, 1437-1453, 2017
- A. Arsie, P. Lorenzoni and A. Moro, Integrable viscous conservation laws , Nonlinearity, Volume 28, Number 6, 48 pages, 2015
- A. Arsie, K. Pokharel, A normalizing isospectral flow on complex Hessenberg matrices , Journal of Mathematical Analysis and Applications, Volume 432, Issue 2, 787-805, 2015
- A. Arsie, P. Lorenzoni, A. Moro, On integrable conservation laws, Proc. R. Soc. A, 2014
- A. Arsie, P. Lorenzoni, Purely non-local Hamiltonian formalism, Kohno connections and $\vee$-systems, J. Math. Phys. 55, 113510, 2014
- A. Arsie and Ch. Ebenbauer, A Hessenberg-Jacobi isospectral flow , Nonlinear Differential Equations and Applications (NoDEA), Birkaeuser, vol. 21, 2 , 2014
- Jeongoo Chen: Lie symmetries and differential invariants arising in problems of mathematical physics and differential geometry
- J. Cheh, On local congruence of immersions in homogeneous or nonhomogeneous spaces SIGMA (Symmetry, Integrability, and Geometry: Methods and Applications) 9, 2013
- J. Cheh, P.J. Olver, J. Pohjanpelto, Algorithms for Differential Invariants of Symmetry Groups of Differential Equations, Foundations of Computational Mathematics, 2008
- J. Cheh, P.J. Olver, and J. Pohjanpelto, Maurer–Cartan equations for Lie symmetry pseudogroups of differential equations, Journal of Mathematical Physics, 46, 2005
- Biao Ou: Partial differential equations, applied analysis
- W. Chen, C. Li, B. Ou, Positive regular solutions to a singular integral equation, Int. J. Pure Appl. Math. 52, 4, 2009
- W. Chen, C. Li, B. Ou, Classification of solutions for a system of integral equations, Communications in Partial Differential Equations, 2005
- Chunhua Shan : Differential equations, dynamical systems, and mathematical biology
- M. Li, W. Liu, C. Shan, Y. Yi, Turning points and relaxation oscillation cycles in epidemic models, SIAM J. Appl. Math., 2016
- C. Shan, Y. Yi, H. Zhu, Nilpotent singularities and dynamics in an SIR type of compartmental model with hospital resources, Journal of Differential Equations, 2016
- A. Abdelrazec, J. Belair, C. Shan and H. Zhu, Modeling the spread and control of dengue with limited public health resources, Math. Biosci. 271, 136-145, 2016
- C. Rousseau, C. Shan and H. Zhu, Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems, Qual. Theor. Dyn. Syst. 15, 237-256, 2016
- Ekaterina Shemyakova :
Algebraic, geometric and symbolic methods for partial differential operators
- (preprint) E. Shemyakova, Th. Voronov, Differential operators on the algebra of densities and factorization of the generalized Sturm-Liouville operator
- (preprint) E. Shemyakova, Factorization of Darboux Transformations of Arbitrary Order for Two-dimensional Schroedinger operator
- S. Li (undergraduate student), E. Shemyakova, Th. Voronov, Differential operators on the superline, Berezinians, and Darboux transformations, Lett.Math.Phys, 2017
- D. Hobby, E. Shemyakova, Classification of Multidimensional Darboux Transformations: First Order and Continued Type, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 2017
- E. Shemyakova, An algorithm for construction of orbits of Darboux transformations of type I for third order hyperbolic operators of two variables, Programming and Computer Software, special issue Computer Algebra, (Russian Academy of Science, eds. S. Abramov, S.Tsarev), 2016
- E. Shemyakova, Invertible Darboux Transformations of Type I , Programming and Computer Software, special issue Computer Algebra, (Russian Academy of Science, eds. S. Abramov, S.Tsarev), 2015.
- S. Hill (undergraduate student), E. Shemyakova, Th. Voronov, Darboux transformations for differential operators on the superline ,
Russian Mathematical Surveys, (6), pp. 207-208, 70, 2015
EVENTS:October 20-21, 2018 Special session "Advances on Analytical and Geometric Aspects of Differential Equations" at the AMS meeting at the University of Michigan. Organizers: Alessandro Arsie, Chunhua Shan, Ekaterina Shemyakova.
April 21-22, 2018 Special session "Dynamical systems, Geometric Structures and Special Functions, I" at the AMS meeting at Northeastern University, Boston, MA. Organizers: Alessandro Arsie and Oksana Bihun (University of Colorado, Colorado Springs)
January 10-13, 2018 Special Session "Dynamical Systems with Applications to Mathematical Biology" at Joint Mathematics Meetings, San Diego, CA. Organizers: Guihong Fan (Columbus State University), Jing Li (California State University Northridge) and Chunhua Shan.