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

Meetra Nouri
(advisor: Ou)

Xueliang Lu
(advisor: Ou)

Chanaka Kottegoda
(advisors: Arsie and Shan)

undergraduate research projects:

Alex Peterson (Spring 2020) (advisor: Shemyakova)

Robinson Czajkowski (Fall 2019 -- Spring 2020) (advisor: Shemyakova)

Jacob Imre (Fall 2019 -- Spring 2020) (advisor: Shemyakova)

PhD thesis On the Reducibility of Systems of Quasi-Periodic Linear Functional Differential Equations , (advisor: Arsie),

now a senior lecturer at Department of Mathematics, University of Colombo, Sri Lanka

** 2018 ** Daniel Liu, undergraduate research project on the families of factorizations of differential operators acting on the algebra of densities, (advisor: Shemyakova),

now studies chemistry at
University of Michigan

** 2015** Dr. Krishna Pokharel, PhD thesis:
An Isospectral Flow for Complex Upper Hessenberg Matrices (advisor: Arsie),

now Assistant Professor at Young Harris College.

** 2014** Dr. Ramesh Karki, PhD thesis: Sobolev gradient semi-flows and applications to nonlinear problems (advisor: Arsie),
now Assistant Professor at Indiana University East.

** 2012 ** Matthew Osborne, honors thesis (advisor: Arsie),

now a 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) A. Arsie, A. Buryak, P. Lorenzoni, P. Rossi Semisimple flat F-manifolds in higher genus
- (preprint) R. Aceska, A. Arsie and R. Karki, On near-optimal time samplings for initial data best approximation
- A. Arsie and Paduma Samarawickrama-Kuruppuge, On the reducibility of systems of analytic quasi-periodic linear functional differential equations, Journal of Mathematical Analysis and Applications, 2019.
- D. Oliver and A. Arsie, Effects of Weighting the Ends of a Tubular Bell on Modular Frequencies, Journal of Mathematics and Music, 15 pages, 2019.
- A. Arsie and P. Lorenzoni, F-manifolds, multi-flat structures and Painlevé transcendents, 69 pages, to appear in Asian Journal of Mathematics
- A. Arsie and P. Lorenzoni, Flat F-manifolds, Miura invariants and integrable systems of conservation laws , Journal of Integrable Systems, Volume 3, Issue 1, 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

- 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

- C. Shan, G. Fan and H. Zhu, Periodic Phenomena and Driving Mechanisms in Transmission of West Nile Virus with Maturation Time, J. Dynam. Differential Equations, 2019.
- C. Shan and Q. Huang, Direct and Indirect Effects of Contaminants on Two Competing Species in a Polluted Aquatic Environment, J. Math. Biol. 78 (2019), 739-766.
- X. Zhang, C. Shan, Z. Jin and H. Zhu, Complex Dynamics of Epidemic Models on Adaptive Networks, J. Differential Equations 266 (2019), 803-832.
- 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, J. Differential Equations (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 :
Geometry, Topology, Mathematical Physics, Computational Mathematics.
Algebraic theory of differential operators. Supergeometry

- (preprint) E. Shemyakova, Th. Voronov,
*On super Plücker embedding and possible application to cluster algebras*. - E. Shemyakova,
*Factorization of Darboux Transformations of Arbitrary Order for Two-dimensional Schroedinger operator*, Illinois J. of Math., 2019 - E. Shemyakova, Th. Voronov,
*Differential operators on the algebra of densities and factorization of the generalized Sturm-Liouville operator*, Lett.Math.Phys, 2019 - 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,

March 30 - April 3, 2020 FIELDS workshop "Supergeometry and bracket structures in mathematics and physics", the Fields Institute, Canada. Organizers: Ekaterina Shemyakova, Alexander Odesski (Brock, Canada), Theodore Voronov (Manchester, UK).

September 14-15, 2019 Special Session " Supergeometry, Poisson Brackets, and Homotopy Structures" at the AMS meeting at U. of Wisconsin-Madison, Madison, WI. Organizers: Ekaterina Shemyakova, Theodore Voronov (Manchester, UK).

July 21-25, 2019 Special Session on "Recent Advances on Vector-borne Diseases'', Annual Society on Mathematical Biology Meeting, University of Montreal, Montreal, Canada. Organizers: Guihing Fan (Columbus State University), Rongsong Liu (University of Wyoming), and Chunhua Shan.

October 20-21, 2018 Special session "Advances on Analytical and Geometric Aspects of Differential Equations" at the AMS meeting at the University of Michigan, Ann Arbor. 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.

2017 - 2020 Ekaterina Shemyakova (PI) (amended to David Hobby as PI, and Shemyakova as co-PI, because of the change of the affiliation by Shemyakova) RUI: Algebraic, Differential-Geometric, and Computational Aspects of Darboux Transformations in Classical and Super Settings, NSF, DMS, Geometric Analysis program. $118,374.00

summer 2017 Alessandro Arsie. INDAM Stipend grants (sponsored by the GNFM - Italian National Group for Mathematical Physics) for collaborative work with Prof. P. Lorenzoni. INDAM is the National Institute for Higher Mathematics in Rome.

summer 2015 Alessandro Arsie. INDAM Stipend grants (sponsored by the GNFM - Italian National Group for Mathematical Physics) for collaborative work with Prof. P. Lorenzoni. INDAM is the National Institute for Higher Mathematics in Rome.

2015-2016 Alessandro Arsie (co-PI), Judy Lambert (PI), Doug Oliver, Sekhar Pindiprolu, Tod Shockey, William B. Weber, Jr. (co-PIs). Ohio Board of Regents, Improving Teaching Quality State Grants Program, New Learning Standards in Math and Science through a Technology Lens in NW Ohio.

2011-2012 Alessandro Arsie (PI), Tod Shockey (co-PI), Willam B. Weber (co-PI), Mark Templin (co-PI). The Woodward High School Mathematics and Science Partnership Project, Phase III.

2010-2011 Alessandro Arsie (PI), Tod Shockey (co-PI), Willam B. Weber (co-PI), Mark Templin (co-PI). The Woodward High School Mathematics and Science Partnership Project, Phase II.

2010-2011 Alessandro Arsie (PI), Dynamical Systems of Lax type, Integrability and Applications, Summer URAF, internal grant.

2010-2011 Alessandro Arsie (PI), Integrable PDEs of hydrodynamic type and bi-Hamiltonian deformations, Visiting scholar grant, internal grant to invite at UT Prof. Paolo Lorenzoni.