**Our seminar on Differential Equations and Nonlinear Analysis:**we usually meet Tuesdays, 4:00 - 5:00pm in UH 4170, see details here

To speak at the seminar, contact Chunhua Shan at chunhua.shan@utoledo.edu or any of us.

#### Current students:

Xueliang Lu(advisors: Ou)

Paduma Samarawickrama-Kuruppuge

(advisors: Arsie)

Chanaka Kottegoda

(advisors: Arsie and Shan)

Daniel Liu, undergraduate research

(advisors: Shemyakova)

#### 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.

#### Faculty:

- 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 PainlevĂ© 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,
Maurerâ€“Cartan equations for Lie symmetry pseudogroups of differential equations,
Journal of Mathematical Physics,
**46**, 2005

- J. Cheh,
On local congruence of immersions in homogeneous or nonhomogeneous spaces
SIGMA (Symmetry, Integrability, and Geometry: Methods and Applications)
- 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

- W. Chen, C. Li, B. Ou, Positive regular solutions to a singular integral equation, Int. J. Pure Appl. Math. 52,
- 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

- (preprint) E. Shemyakova, Th. Voronov,

#### 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.