Seminar
on Differential Equations and Nonlinear Analysis
Organizers: 
Alessandro
Arsie (alessandro dot arsie at utoledo dot edu) 

Chunhua
Shan (chunhua dot shan at
utoledo dot edu) Ekaterina
Shemyakova (ekaterina dot
shemyakova at utoledo dot
edu) 
Time: 
Tuesday,
4:005:00PM 
Location: 
UH
2210 
● 
All are welcome to attend. 
● 
If you
would like to present your work or an interesting paper you have read, please
contact us. 
● 
If you have any suggestions on this seminar, please also let us
know. Thanks. 
Spring Semester, 2019
Talk: 
Dynamics
of the $\lambda \tan z^2 $ family (II) 
Speaker: 
Dr. Santanu Nandi,
Visiting Assistant Professor, The University of Toledo 
Date: 
4:005:00PM, Tuesday, April 16, 2019 
Abstract: 
In my second talk,
I'll discuss some topological properties of the dynamical plane ($z$plane)
and a combinatorial structure of the parameter plane (\lambdaplane) of $
\lambda \tan z^2.$ In the dynamical plane,
I'll prove that there is no Herman ring and the Julia set is a Cantor
set for the map when the parameter is in the central capture
component. Julia set is connected for the maps when the parameters are
in other hyperbolic components. In the parameter plane, I'll show that the
capture components are simply connected and there are always four hyperbolic
shell components attached to a virtual center. The capture components and the
periodic shell components of the period greater than one are
bounded. 
Talk: 
Dynamics
of the $\lambda \tan z^2 $ family (I) 
Speaker: 
Dr. Santanu Nandi,
Visiting Assistant Professor, The University of Toledo 
Date: 
4:005:00PM, Tuesday, April 9, 2019 
Abstract: 
In my first talk, I'll give an
introduction to complex dynamics. I'll give a short description of the
dynamics of the quadratic polynomials in the complex plane and Mandelbrot
set. My work is a motivation to study the dynamics of the family of meromorphic maps, in particular, the dynamics of the
$\lambda \tan z $ family where $ \lambda $ is a parameter in the complex
plane. I'll review some important results to describe the combinatorial
structure of both the dynamical plane($z$plane) and
the parameter plane(zplane) of this family. 
Talk: 
A
generalized Floquet theory result for analytic
linear delay differential equations 
Speaker: 
Paduma Eranga, The University of Toledo 
Date: 
4:005:00PM, Tuesday, April 2, 2019 
Abstract: 
In
the classical Floquet Theory, there exists a smooth
change of variables that reduces a given linear periodic system to a linear
system with constant coefficients. In this talk, I discuss a generalized Floquet theory result for analytic linear delay
differential equations. I provide a simpler proof of the asymptotic
reducibility that bypasses the method of accelerated convergence and it is
instead based on more transparent KAMtype estimates. 
Talk: 
Using
symmetries to solve differential equations 
Speaker: 
Professor Ryad Ghanam, Virginia Commonwealth University
at Qatar 
Date: 
4:005:00PM, Tuesday, March 12, 2019 
Abstract: 
In this talk we will show how Lie symmetries
play a major role in solving differential equations. We will talk about the
origin of symmetries, how to calculate them and use them to solve
differential equations. 
Talk: 
Ideal
Fluid Flow Past A Body In Space 
Speaker: 
Xueliang Lu, The University of Toledo 
Date: 
4:005:00PM, Tuesday, Feb. 26, 2019 
Abstract: 
This talk is about the problem of an irrotational and incompressible flow around a body in
space. The basic existence is proved by formulating the
problem into a variational problem. It is
also shown that the solution is unique, and
that the maximum speed is attained on the body's boundary. 
Talk: 
Topological
degree theory and boundary value problems (I) 
Speaker: 
Meetra Nouri, The University of Toledo 
Date: 
4:005:00PM, Tuesday, Feb.12, 2019 
Abstract: 
I will review Rafael Ortega's lectures on
topological degree theory and boundary value problems. I will discuss few
elementary examples and then I will talk about topologica
degree in R and R^2, in order to generalize Bolzano's theorem to higher
dimensions (Poincare'Miranda theorem) and to pave the way for dealing with
less elementary examples. 
Talk: 
BogdanovTakens bifurcation of codimension
2 
Speaker: 
Chanaka Kottegoda,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, Feb.5, 2019 
Abstract: 
In this talk I will introduce the concepts of
structural stability and bifurcation of a vector field. Especially I will
talk about BogdanovTakens bifurcation of codimension
2, all possible topological structures we can see from this bifurcation and
the proof of it. Finally I will talk about the preypredator model and the
existence of BogdanovTakens bifurcation in this
model. 
Fall Semester, 2018
Talk: 
Turkowski's 1990 paper on
6dimensional Lie algebras and beyond 
Speaker: 
Professor Gerard Thompson, The University of Toledo 
Date: 
4:005:00PM, Tuesday, Nov. 27, 2018 
Abstract: 
I will review Turkowski's 1990 paper on 6dimensional solvable Lie algebras,
which leaves quite a few details. I will provide a few structure theorems and
discuss the prospects for extending the results to 7 dimensions. 
Talk: 
Sheaves
and Algebraic Geometry 
Speaker: 
Professor Alessandro Arsie, The University
of Toledo 
Date: 
4:005:00PM, Tuesday, Nov. 20, 2018 
Abstract: 
I will start introducing sheaves (and
possibly their cohomology) and some basic ideas in
algebraic geometry (using tools from complex analysis rather than commutative
algebra) using my graduate school notes. 
Talk: 
Connection
from mediating maps of pullbacks 
Speaker: 
Professor Geoffrey Martin, The University of Toledo 
Date: 
4:005:00PM, Tuesday, Nov. 13, 2018 
Abstract: 
This will be a somewhat elementary talk on an
approach to connection theory I have found useful. The approach makes
constructions more functorial. I give some simple
applications and if I will I can show why the second structure equation is
rightly call the second structure equation. 
Talk: 
Regularized
Solutions for Backward Heat Equation with TimeDependent Veritable
Coefficient 
Speaker: 
Dr. Sujeewa Hapuarachchi, Visiting Assistant Professor, The
University of Toledo 
Date: 
4:005:00PM, Tuesday, Nov. 6, 2018 
Abstract: 
Backward heat equation with timedependent
variable coefficient is severely ill‐posed in the sense of Hadamard,
so we need regularization. We consider Backward heat equation with timedependent
variable coefficient, and by small perturbing, we obtain an approximation
problem. We show this approximation problem is well‐posed with small parameter. Also, we show
this approximation system converges to the original problem when parameter
goes to zero. Here, we use modified‐quasi boundary value method to regularize
this problem. 
Talk: 
Classification and the dynamics of surface mapping classes on Teichmuller space 
Speaker: 
Professor Funda Gultepe, The University
of Toledo 
Date: 
4:005:00PM, Tuesday, October 30, 2018 
Abstract: 
In this introductory
talk, I will discuss the NielsenThurston classificiation
of surface mapping classes in analogy with classification of isometries of the
upper half plane. If time permits, I will also talk about their dynamical
behavior on the Teichmuller space and give sketch
of proof of the classification theorem. This will be a selfcontained talk, previous knowledge is helpful but not required to follow. 
Talk: 
Introduction to Mapping class group of a surface 
Speaker: 
Professor Funda Gultepe, The University
of Toledo 
Date: 
4:005:00PM, Tuesday, October 23, 2018 
Abstract: 
Study on the mapping
class group goes back to works of Dehn and Nielsen
in 1920's. During 1970's, Thurston gave this study a geometric flavor
and used it to understand hyperbolic 3 manifolds. Today mapping
class group is used in many areas to understand topological and geometric
properties of 3 manifolds as well as to solve moduli problems related to
curves. As a consequence, it is one of the main topics of the geometric group
theory. I will give a basic introduction to this group which will include
first examples. The talk will be expository and will not assume background in
the area. 
Talk: 
New
approaches to integrable hierarchies of topological
type (II) 
Speaker: 
Professor Alessandro Arsie,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, October 9, 2018 
Abstract: 
I will survey a large class of systems of
partial differential equations which on one hand appear in classical problems
in mathematical physics and on the other hand provide an efficient tool for
description of enumerative invariants in algebraic geometry. Particular
attention will be paid to new approaches to these systems. 
Talk: 
New
approaches to integrable hierarchies of topological
type (I) 
Speaker: 
Professor Alessandro Arsie,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, September 25, 2018 
Abstract: 
I will survey a large class of systems of
partial differential equations which on one hand appear in classical problems
in mathematical physics and on the other hand provide an efficient tool for description
of enumerative invariants in algebraic geometry. Particular attention will be
paid to new approaches to these systems. 
Talk: 
Stable
curves, Moduli Spaces and Cohomological
Field Theories 
Speaker: 
Professor Alessandro Arsie,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, September 11, 2018 
Abstract: 
I will review the notion of stable curves and
their moduli spaces. I will also introduce axiomatically Cohomological Field Theories following Manin and Kontsevich and I will
provide some examples. 
Spring Semester, 2018
Talk: 
Relativistic
Treatment of Confined Hydrogen Atoms via Numerical Approximations 
Speaker: 
Jacob Noon, The
University of Toledo 
Date: 
4:005:00PM, Tuesday, April 10, 2018 
Abstract: 
The study of particles and atoms confined to spherically
symmetric regions have been used to illustrate the differences between
classical and quantum systems since Erwin Schrodinger famous equation was
published in 1926. Paul Dirac later added his own equation, the Dirac
Equation (1928), which integrated the quantum principles that had been
developing in the decades prior to Schrodinger equation with the principles
of Einstein Special Theory of Relativity. The literature on Hydrogen atoms confined to spherically
symmetric regions (using the Schrodinger equation) is abundant, with
consensus on the results. To the best of our knowledge there exists no
relativistic treatment to this problem (i.e., using the Dirac equation). Some
reasons for this are the complexity of the Dirac equation, its solutions, and
problems that arise when trying to satisfy the boundary conditions. 
Talk: 
A revisit to the
Jordan canonical form for a complex square matrix 
Speaker: 
Professor Biao Ou, The University of Toledo 
Date: 
4:005:00PM, Tuesday, March 13, 2018 
Abstract: 
I will first look at the canonical form of two by two and three
by three matrices via a rank one matrix. Next, I look at the process in which
we see the Jordan canonical form by first applying a much easier Schur's theorem and then considering a system of linear
differential equations. I will also apply the Jordan canonical form to a
sequence of numbers satisfying a linear iterative equation. 
Talk: 
Factorization of differential operators on the algebra of densities on
the line (II) 
Speaker: 
Professor Ekaterina Shemyakova, The University of Toledo 
Date: 
4:005:00PM, Tuesday, February 20, 2018 
Abstract: 
I shall show that for differential
operators on the algebra of densities on the line (unlike the familiar
setting) there are obstructions for factorization. I shall analyze
these obstructions. In particular, for the "generalized SturmLiouville" operators acting on the algebra of
densities on the line, I shall show our criterion of factorizabily
in terms of solution of the classical SturmLiouville
equation. I shall also show the possibility of an incomplete
factorization. 
Talk: 
Factorization of differential operators on the algebra of densities on
the line (I) 
Speaker: 
Professor Ekaterina Shemyakova, The University of Toledo 
Date: 
4:005:00PM, Tuesday, February 13, 2018 
Abstract: 
I shall speak about my new work where I explore factorization
problem for differential operators on the algebra of densities. This work is
a starting point for one of the directions of my research program, namely
study of differential operators acting on geometric quantities and their Darboux transformations in classical and super setting. 
Talk: 
Flat $F$manifolds, Miura invariants and integrable
systems of conservation laws 
Speaker: 
Professor Alessandro Arsie,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, February 6, 2018 
Abstract: 
In this talk, I will present the extension to the case of
systems of integrable conservation laws of some of
the results proved for scalar equations in Arsie,
Moro, Lorenzoni (Integrable
viscous conservation laws, Nonlinearity 2015) and in Arsie,
Moro, Lorenzoni (On Integrable
Conservation Laws, Proceedings of the Royal Society A, 2014). 
Fall Semester, 2017
Talk: 
Lie symmetries of the
canonical Lie group connection 
Speaker: 
Professor Gerard Thompson, The University of Toledo 
Date: 
4:005:00PM, Tuesday, December 5, 2017 
Abstract: 
It is well known that any Lie group carries a canonical
symmetric although usually not metric linear connection  Cartan's
socalled "0"connection. In this talk we investigate Lie
symmetries of the canonical connection. We shall focus particularly on the codimension one abelian nilradical
case for which many symmetries and first integrals
may be written down explicitly. 
Talk: 
Hopf bifurcation of planar
systems 
Speaker: 
Chanaka Kottegoda,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, November 28, 2017 
Abstract: 
In this talk, we will review the Hopf
bifurcations of planar systems. The definition of Hopf
bifurcation and the Hopf bifurcation Theorem will
be introduced. As an application, periodic solutions of Selkov
model will be studied. 
Talk: 
Representation
homology of spaces 
Speaker: 
Professor Yuri Berest, Cornell
University 
Date: 
4:005:00PM, Thursday, November 16, 2017 
Abstract: 
Let $ G $ be an affine algebraic group defined over a field $ k $.
For any (discrete) group $ \pi $, the set of all representations of $ \pi $
in $ G $ has a natural structure of an algebraic variety (more precisely,
affine kscheme) called the representation variety $ Rep_G(\pi) $. If $ X $ is a
(based) topological space, the representation variety of its fundamental
group $ Rep_G[π_1(X)] $ is an important geometric invariant of $X$
that plays a role in many areas of mathematics. In this talk, I will present
a natural homological extension of this construction, called representation
homology, that takes into account a higher homotopy
information on $ X $ and has good functorial
properties. The representation homology turns out to be computable (in terms
of known invariants) in a number of interesting cases (simplyconnected
spaces, Riemann surfaces, link complements, lens spaces,
...), some of which I will examine in detail. Time permitting, I will
also explain the relation of representation homology to other homology
theories associated with spaces, such as higher Hochschild
homology, $ S^1$equivariant homology of free loop
spaces and the (stable) homology of automorphism
groups of the free groups $ F_n $. 
Talk: 
Lie Symmetries of
Differential Equations (II) 
Speaker: 
Dr. Jeongoo Cheh, The University of Toledo 
Date: 
4:005:00PM, Tuesday, November 7, 2017 
Abstract: 
It is well known to most students that differential equations
are usually studied with tools provided by some kind of analysis  real analysis,
complex analysis, functional analysis, harmonic analysis, etc.. A very different approach is to treat differential
equations as submanifolds of jet bundles and employ
geometric tools to study their symmetries. In fact, it was this geometric
approach to differential equations that led historically to the genesis of
the vast central industry of Lie groups and Lie algebras. In this
introductory talk into the area, we will start by recalling a few necessary
basics on manifolds and group actions, proceed to
define Lie (point) symmetries of differential equations, construct symmetry
algebras and symmetry groups, and then conclude with specific examples
including an application to the HopfCole
transformation. 
Talk: 
Lie Symmetries of
Differential Equations (I) 
Speaker: 
Dr. Jeongoo Cheh, The University of Toledo 
Date: 
4:005:00PM, Tuesday, October 31, 2017 
Abstract: 
It is well known to most students that differential equations are
usually studied with tools provided by some kind of analysis  real
analysis, complex analysis, functional analysis, harmonic analysis, etc.. A very different approach is to treat differential
equations as submanifolds of jet bundles and employ
geometric tools to study their symmetries. In fact, it was this geometric
approach to differential equations that led historically to the genesis of
the vast central industry of Lie groups and Lie algebras. In this
introductory talk into the area, we will start by recalling a few necessary
basics on manifolds and group actions, proceed to
define Lie (point) symmetries of differential equations, construct symmetry
algebras and symmetry groups, and then conclude with specific examples
including an application to the HopfCole
transformation. 
Talk: 
Coﬁnite graphs and their proﬁnite completions 
Speaker: 
Dr. Amrita Acharyya, The University of Toledo 
Date: 
4:005:00PM, Tuesday, October 24, 2017 
Abstract: 
We generalize the idea of coﬁnite
groups due to B. Hartley. First we deﬁne coﬁnite
spaces. Then, as a special situation, we study coﬁnite
graphs and their uniform completions. The idea of constructing a coﬁnite graph starts with deﬁning a uniform
topological graph $\Gamma$, in an appropriate
fashion. We endow abstract graphs with uniformities corresponding to
separating ﬁlter bases of equivalence relations with ﬁnitely
many equivalence classes over $\Gamma$. It is established that for any coﬁnite graph there exists a unique Profinite completion. 
Talk: 
Integrable structures of dispersionless systems and differential geometry 
Speaker: 
Professor Alexandre
Odesski, Brock University, Canada 
Date: 
4:005:00PM, Tuesday, October 12, 2017 
Abstract: 
We develop the theory of Whitham type
hierarchies integrable by hydrodynamic reductions
as a theory of certain differentialgeometric objects. As an application we
construct GibbonsTsarev systems associated to
moduli space of algebraic curves of arbitrary genus and prove that the
universal Whitham hierarchy is integrable
by hydrodynamic reductions. 
Talk: 
Recovery of initial
conditions for some classes of PDEs using discrete time samplings (II) 
Speaker: 
Professor Alessandro Arsie,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, October 3, 2017 
Abstract: 
I will present some results about using discrete time samplings
to recover in an optimal way and in suitable functional spaces the initial
conditions for some classes of linear evolutive PDEs,
using discrete time samplings at a fixed location. We will also provide some
insights about a question posed by DeVore (Texas
A&M) and Zuazua (Basque Foundation for Science)
about the dependence of the optimal sampling strategy on the details of the spectrum
of a linear operator. It turns out that for the class of PDEs we analyzed,
the dependence of the optimal strategy on the spectrum is really weak. If
time allows, I will talk about some open problems involving nonlinear PDEs
(both in the integrable and nonintegrable
cases) and linear nonautonomous evolutionary PDEs. This
is a joint paper with Roza Aceska
(Ball State University) and Ramesh Karki (Indiana
University East). 
Talk: 
Recovery of initial
conditions for some classes of PDEs using discrete time samplings (I) 
Speaker: 
Professor Alessandro Arsie,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, September
26, 2017 
Abstract: 
I will present some results about using discrete
time samplings to recover in an optimal way and in suitable functional spaces
the initial conditions for some classes of linear evolutive
PDEs, using discrete time samplings at a fixed location. We will also provide
some insights about a question posed by DeVore
(Texas A&M) and Zuazua (Basque Foundation for
Science) about the dependence of the optimal sampling strategy on the details
of the spectrum of a linear operator. It turns out that for the class of PDEs
we analyzed, the dependence of the optimal strategy on the spectrum is really
weak. If time allows, I will talk about some open problems involving
nonlinear PDEs (both in the integrable and nonintegrable cases) and linear nonautonomous evolutionary
PDEs. This is a joint paper with Roza Aceska (Ball State University) and Ramesh Karki (Indiana University East). 
Talk: 
A Reducibility Theorem
for Smooth Quasi periodic Linear Systems 
Speaker: 
Paduma Eranga,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, September
5, 2017 
Abstract: 
In this talk, I'll explain an iterative procedure for finding
a change of variables to reduce a quasiperiodic linear system into an
autonomous system worked done by G.C. O'Brien. This process called the accelerated
convergence method. A quasi periodic linear system is a linear system of
ordinary differential equations \begin{align*}
x' & = Ax + P(\varphi)x \\ \varphi'
& = \omega , \end{align*} where $x \in \mathbb{R}^n,
\varphi \in \mathbb{R}^m,
\, A $ is a constant $n\times n$ matrix, $\omega $ is a constant
vector in $\mathbb{R}^m. $ P(\varphi)$ is periodic in $\varphi_i$
with period $2\pi$ for $i =1, \dots, m$. In
this discussion, we are going to obtain a quasiperiodic transformation which
transform above system into the system with constant coefficients. 
Spring Semester, 2017
Talk: 
Analysis of a
PseudoHarmonic Tubular Bell 
Speaker: 
Dr. Douglas Oliver, The University of
Toledo 
Date: 
4:005:00PM, Tuesday, April 18, 2017 
Abstract: 
Tubular bells, or
chimes are used for ambient sounds as well as serious music. Unlike most wind
or stringed instruments, a tubular bell does not have a harmonic set of
overtones. The lack of harmonious overtones
creates a problem with using tubular bells for serious music: there is not
unanimity regarding the pitch, or musical note associated with a particular
tubular bell. The EulerBernoulli model for vibrating thin beams was used to
derive a mathematical model for vibrations of a tubular bell. Using this
model, an analysis of the natural frequencies of a modified tubular bell was
presented. One or more ends of the tubular bell were weighted with a mass.
This mass changes the boundary conditions, and hence the ratio of the natural
frequencies of the tubular bell. Values for the ratio of the mass of weight(s) to the mass of the
tube were identified such that the ratio of the frequency of the first
overtone to the second overtone was 2. Under these conditions, these
overtones are one octave apart. The frequency ratios predicted by the model
have been compared with experimental results of a frequency analysis of the
sound produced by two physical tubes. The experimental results were in good
agreement with the theoretical predictions. 
Talk: 
The Lavrentiev Phenomenon 
Speaker: 
Dr. Dean A. Carlson, Mathematical Reviews, American Mathematical
Society, Ann Arbor, MI 
Date: 
4:005:00PM, Tuesday,
April 4, 2017 
Abstract: 
In 1926 M. Lavrentiev gave an example of
a free problem in the calculus of variations for which the infimum over the
class of functions in $W^{1,1}[t_1,t_2]$ satisfying prescribed end point
conditions was strictly less than the infimum over the dense subset $W^{1,\infty}[t_1,t_2]$ of admissible functions in
$W^{1,1}[t_1,t_2]$. This property is now referred to as the Lavrentiev phenomenon. After Lavrentiev's
discovery L.~Tonelli and
B. Mania gave sufficient conditions under which this phenomenon does not
arise. After these results, the study of the Lavrentiev
phenomenon lay dormant until the 1980s when a series of papers by Ball and Mizel and by Clarke and Vinter
gave a number of new examples for which the Lavrentiev
phenomenon occurred. Also in 1979, T. S. Angell showed that the Lavrentiev phenomenon did not occur if the integrands
satisfy a certain analytic property known as property (D). Moreover, he
showed that the conditions of Tonelli and Mania insured that the analytic
property (D) was satisfied. In this talk we will begin by presenting B.~Mania's elementary example to illustrate that the
phenomenon exists and discuss Angell's property (D) to give a general theorem
that avoids Lavrentiev's phenomenon and show
briefly that some more recent results can be viewed as corollaries to
Angell's result in that the conditions assumed imply property (D). 
Talk: 
Some classes of
nonlinear integral operators and existence results via Schauder's
fixed point theorem 
Speaker: 
Professor Alessandro
Arsie, The University of Toledo 
Date: 
4:005:00PM, Tuesday,
March 28, 2017 
Abstract: 
I will discuss three examples of nonlinear
integral operators that are completely continuous on some spaces of
continuous functions (they are Volterra integral
operators, Fredholm integral
operators and integral operators with delay). By means of Schauder's
fixed point theorem, I will discuss existence of continuous solutions for the
integral equations associated to these operators. 
Talk: 
Mathematical Modelling
for Parametric Resonance 
Speaker: 
Dr. Zhiwei Chen, The University of
Toledo 
Date: 
4:005:00PM, Tuesday,
March 21, 2017 
Abstract: 
When a physical parameter in an oscillatory
system is modulated to vary in time, it may cause a dynamic instability associated
with the system. This phenomenon is
referred to as parametric resonance. The mathematical models amenable to such
phenomena are differential equations with periodic coefficients,
specifically, the Mathieu equation. In this talk, I will discuss some
parametrically excited systems and their characteristics in resonance. I will
derive some simple schemes of electrical circuits into the Mathieu equation
and discuss the relevant analysis towards this phenomenon. 
Talk: 
Circumference over
diameter; the different universes of pi (𝝅 Day Colloquium) 
Speaker: 
Dr. Nate Iverson, The University of Toledo 
Date: 
4:005:00PM, Tuesday,
March 14, 2017 
Abstract: 
𝝅 is the ratio of circumference to diameter in
a circle. We define a circle to be a set of points equidistant from a common
point. When the method of measuring distance is changed different ratios are
possible. This talk will discuss the ratio of circumference to diameter in
all pnorms including p=1, the taxicab norm, and p=∞, infinity the
supremum norm. Results dating to 1932 using the Minkowski
functional norms will also be discussed along with further generalizations. 
Talk: 
Predatorprey models
with Holling types of functional responses (II) 
Speaker: 
Professor Chunhua
Shan, The University of Toledo 
Date: 
4:005:00PM, Tuesday,
February 14, 2017 
Abstract: 
Predatorprey system has been extensively
studied by biologists and mathematicians. In this talk I will introduce the
classical predatorprey models of Holling types of
functional responses. Dynamics of predatorprey
system with Holling type II functional response
will be reviewed by qualitative analysis and bifurcation theory. 
Talk: 
Predatorprey models
with Holling types of functional responses (I) 
Speaker: 
Professor Chunhua
Shan, The University of Toledo 
Date: 
4:005:00PM, Tuesday,
February 7, 2017 
Abstract: 
Predatorprey system has been extensively
studied by biologists and mathematicians. In this talk I will introduce the
classical predatorprey models of Holling types of
functional responses. Dynamics of predatorprey
system with Holling type II functional response
will be reviewed by qualitative analysis and bifurcation theory. 
Talk: 
Floquet Theory and periodic
linear differential equations 
Speaker: 
Paduma Eranga,
The University of Toledo 
Date: 
4:005:00PM, Tuesday
January 31, 2017 
Abstract: 
In this talk I'll discuss a main theorem in
Floquet Theory, which appear in the study of
periodic linear differential equations, of the form $x' = A(t)x , A(t+T)= A(t), T>0 $ where
$A(t)$ is a matrix of complex continuous functions. That main theorem; Floquet theorem due to Gaston Floquet(1883)
gives a representation of a fundamental matrix solution $\Phi(t)$, as the
product of periodic nonsingular matrix $P(t)$ with the same period $T$ and a
constant matrix $R$ such that $\Phi(t) = P(t)e^{tR}$.
As a result we can transform the periodic system into a usual linear system
with constant coefficients. 
Talk: 
A proof of uniformly
boundedness principle 
Speaker: 
Professor Alessandro Arsie,
The University of Toledo 
Date: 
4:005:00PM, Tuesday, ,
January 24, 2017 
Abstract: 
In this talk I'll discuss a main theorem in
Floquet Theory, which appear in the study of
periodic linear differential equations, of the form $x' = A(t)x , A(t+T)= A(t), T>0 $ where $A(t)$ is a matrix of complex continuous functions. That main
theorem; Floquet theorem due to Gaston Floquet(1883) gives a representation of a fundamental matrix solution
$\Phi(t)$, as the product of periodic nonsingular matrix $P(t)$ with the same
period $T$ and a constant matrix $R$ such that $\Phi(t) = P(t)e^{tR}$. As a result we can transform the periodic system
into a usual linear system with constant coefficients. 