Department of Mathematics
Thursday, February 28, 11:00 – 11:50pm in MH 480
Martial Aufranc (Lycee Pothier and CSUF visitor): Polynomial isometries in Z_p with coefficients in Q_p
Abstract. We will continue the analysis of polynomial isometries of Z_p by generalizing to polynomial expressions with Coefficients in Q_p.
Thursday, March 7, 11:00 – 11:50pm in MH 480
Zair Ibragimov (CSUF): Open problems on Polynomial isometries of Z_p
Abstract. We will discuss some open problems on the polynomial isometries of Z_p proposed by Martial Aufranc.
Thursday, March 22, 3:00 – 3:50pm in MH 480
Hrant Hakobyan (KSU): Frequency of dimension distortion under quasisymmetric mappings
Abstract. We discuss the distortion of Hausdor dimension of families of Ahlfors regular sets under quasisymmetric maps between met-
ric spaces. We show that such maps cannot increase the dimension of “most” d-regular sets and we estimate the number of exceptional sets whose images have dimension greater or equal to D>d; the precise statements of both results involve modulus estimates for families of measures.
Thursday, March 28, 11:00 – 11:50pm in MH 480
Chris Lyons (CSUF): Zeta functions of curves over F_p
Abstract. The analytical properties of the Riemann zeta function have been studied intensively for centuries, due to their implications for number theory. Generalizations of the zeta function abound, and I'll talk about one that comes from counting the points on an algebraic curve defined over a finite field, such as F_p. This zeta function has numerous properties that are similar to the Riemann zeta function, and in fact we actually know the analogue of the Riemann hypothesis for them!
In this expository talk, I'll define these zeta functions and discuss some of the things we know about them, including how they're connected to certain rational functions. My goal is to get to a point where I can talk about some related research problems that are of interest. Students are welcome!
Thursday, April 25, 4:00 – 4:50pm in MH 480
Pietro Poggi-Corradini (KSU): Effective resistance on graphs and the Epidemic quasimetric
Abstract. We introduce the epidemic quasimetric on graphs and study its behavior with respect to clustering techniques. In particular we compare its behavior to known objects such as the graph distance, effective resistance, and modulus of path families.
Friday, May 10, 1:00 – 1:50pm in MH 476
Xiangdong Xie (BGSU): Quasiconformal maps on model Filiform groups
Abstract. I will explain how some simple algebra and simple analysis can be used to find all the quasiconformal maps on the higher model Filiform groups (including nonsmooth ones). I will first give an introduction to Carnot groups.
Friday, May 10, 2:00 – 2:50pm in MH 476 David Carfi (University of Messina and UCR): A Speculative and Hedging Interaction Model about Oil and U.S. Doller Markets Abstract. The aim of this talk is twofold: by using Game Theory, we suggest a new way to make business on certain oil and U.S. Dollar markets and we propose to the regulatory authority a method to make more stable oil and U.S. Dollar markets.
Our idea is to exploit the hedging actions to obtain profit, saving at the same time the oil and the U.S. Dollar from speculative attacks. This goal is reached by the introduction of a financial transactions tax by the normative authority. We focus on a certain game theory interaction of two economic operators: a real economic subject (AIR), and an investment bank (BANK). We develop a complete game theory analysis: perfect knowledge of the payoff space, in a dynamic fashion; exam of Nash equilibria and of conservative strategies; study of the cooperative scenario and of the maximum aggregate utility Pareto boundary. The solutions more collectively desirable are represented by agreements between the two subjects on the maximum aggregate utility Pareto boundary. So, we propose and analyze three different possible fair divisions of collective gain, using Kalai-Smorodinsky method.
Thursday, May 16, 11:00 – 11:50am in MH 480
Adam Glesser and Sean Yee (CSUF): A new constructive proof of the density of the rationals in the reals
Abstract. The pure mathematician finds the mathematics educator’s work irrational; the mathematics educator finds the pure mathematician’s work dense. Come see how collaboration between such colleagues developed a new, succinct proof of the density of rationals and irrationals using constructivist methods instead of contradictions. The proof revolves around “thinking deeply of simple things” with respect to the floor function. This seminar will be helpful and illuminating for students of undergraduate and graduate analysis and function theory courses.
Thursday, September 13, 12:00 – 12:50pm in MH 476
John Simanyi (UCR): Hyperbolic Construction of the Cantor set
Abstract: The standard construction of the ternary Cantor set involves removing middle-third intervals. Instead, the set can also be constructed by first hyperbolizing (in the sense of Gromov) the collection of removed intervals, then defining a visual metric on its boundary at infinity. The resulting metric space is isometric to the Cantor set. This is a joint work with Z. Ibragimov.
Friday, September 14, 1:00 – 1:50pm in MH 484
Zair Ibragimov (CSUF): p-adic numbers, I
Abstract: I will discuss p-adic numbers from algebraic and geometric points of view. The goal is to learn the basic knowledge of p-adic analysis and start reading recent research articles in p-adic Analysis, p-adic Dynamics and Fractal Geometry. Students who intend to do undergraduate research projects are especially encouraged to attend. During the talks I will supply many problems for such projects.
Friday, September 21, 1:00 – 1:50pm in MH 484
Zair Ibragimov (CSUF): p-adic numbers, II
Friday, October 5, 1:00 – 1:50pm in MH 484
Nicholas Salinas (CSUF undergraduate): Classification of polynomial isometries of p-adic numbers
Abstract: We discuss polynomial isometries of the p-adic integers following the recent work of Prof. Aufranc. We will discuss some general results as well as some specific results for p=3,5,7.
Friday, October 26, 1:00 – 1:50pm in MH 484
Asuman Aksoy (Claremont McKenna College): Norms That Are Not: Projections With Respect to Numerical Radii
Abstract: Let T ∈ B(X ) where B(X ) is a Banach algebra of all continuous linear operators on a
Banach space X . Operator norm:
||T|| = sup |(T x, y)|
(x, y) ∈ B(X )×B(X ∗)
while numerical radius:
ν(T ) = sup |(T x, y)|
(x, y) ∈ B(X )×B(X ∗)
<x, y> = 1
The interplay between ||T|| and ν(T ) has been subject of much research since Bauer’s definition of numerical range in 1960’s. After pointing out some major results in this area, I will discuss how extension of operators, in particular minimality of projections, can be measured with respect to numerical radius.
Tuesday, October 30, 4:00 – 4:50pm in MH 480
Dilmurat Azimov (University of Hawaii at Manoa): TBA
Abstract: The objective is to design optimal trajectory, guidance and targeting laws for a real-time implementation on-board of aerospace systems to autonomously perform thrusting maneuvers utilizing analytical synthesis of optimal control solutions. The proposed theory can be employed to design guidance and targeting schemes for an on-board implementation. It leads to a better understanding and description of maneuvers, and interpretation of flight vehicle parameters. Explicit analytical synthesis of extremal and optimal trajectories will enable quick and reliable surveys of behaviors of the design parameters. Design of extremal maneuvers can serve as nominal- reference solutions in the design of autonomous guidance laws. To this day, no explicit and accurate guidance or targeting laws for a real-time implementation have been reported. The presentation will also highlight the resent research results on low- and high- thrust trajectory design and optimization with applications to low Earth orbital transfers, Mars Sample return, de-orbit maneuvers, powered descent and landing maneuvers, and asteroid rendezvous missions. Future topics and external funding opportunities are also discussed. The talk will be accessible to graduate and advanced undergraduate students with knowledge in Analysis and ODE.
Friday, November 16, 1:00 – 1:50pm in MH 484
Nicholas Salinas (CSUF undergraduate): Polynomial isometries of p-adic integers, II
Abstract: We discuss polynomial isometries of the p-adic integers following the recent work of Prof. Aufranc. We will discuss some general results as well as some specific results for p=3,5,7.
Friday, December 7, 1:00 – 1:50pm in MH 480
Adrian Vajiac (Chapman University): Bicomplex Analysis
Abstract: In the last several years, the theory of bicomplex numbers has enjoyed a renewed interest, and the theory of functions which are bicomplex holomorphic has been developed along many interesting directions, including extensions to several (bicomplex) variables, extension to the case of multicomplex numbers, extension to pseudoanalytic functions theory, etc. In this talk I will discuss our latest results in the study of the holomorphy of bicomplex functions, emphasizing on the differences between the traditional Several Complex Variables theory (in two complex dimensions) and the Bicomplex Analysis.
Friday, December 7, 2:00 – 2:50pm in MH 480
Bogdan Suceava (CSUF): Geometries Induced by Logarithmic Oscillations and their Natural Extensions
Abstract: Introduced originally in 1934, Barbilian’s metrization procedure induced a distance on a planar domain by a metric formula given by the so-called logarithmic oscillation. In 1959, Barbilian generalized this process to domains of a more general form, withstanding not necessarily on planar sets, but in a more abstract setting. We will show that there exists more general classes of distances than the ones produced by logarithmic oscillation. As a consequence, we will present the most general form of Barbilian’s metrization procedure. Additionally, we will introducing a new distance on a subset of the n-dimensional real space. We will prove it generates an example of Gromov hyperbolic distance on the punctured open unit ball and then study its geometric properties and its relations with other remarkable metrics. We will also introduce other metrics and we'll study their properties.
Tuesday, January 24, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Hyperbolization of Metric Spaces, I
Abstract: This is the first talk of a series of two talks I plan to give on the hyperbolization of metric spaces. I will discuss my recent paper, titled “Hyperbolizing Metric Spaces” and published in the proceedings of the AMS.
Tuesday, January 31, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Hyperbolization of Metric Spaces, II
Tuesday, February 7, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to p-adic numbers, VI
Abstract: This is a continuation of talks started last fall. I will give five talks this semester devoted to p-adic numbers. I will discuss p-adic numbers from algebraic, analytic and geometric points of view. The goal is to learn the basic knowledge of p-adic analysis and start reading recent research articles in p-adic Analysis, p-adic Dynamics and Fractal Geometry. The talks will be accessible to students who have taken basic courses in Algebra (Math 302), Analysis (Math 350) and Topology (Math 414). Students who intend to do undergraduate research projects are especially encouraged to attend. During the talks I will supply many problems for such projects.
Tuesday, February 14, 12:00 – 12:50pm in MH 484
Tuesday, February 21, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to p-adic numbers, VII
Tuesday, February 28, 12:00 - 12:50pm in MH 166 (conference room)
David Carfi (UCR and University of Messina): Coopetitive Games and Applications
Abstract. In this paper (based on researches conducted for three years) we define and apply the model of coopetitive game (in the sense recently introduced by David Carfì) to Economic Policy, Green Economy and Financial issues and in particular to the crisis of the Euro Zone (as already done in some published articles). The Crisis within the Euro Area has become frequent during 2010 and 2011. First was the Greek economy to face a default problem of its sovereign debt, then it was Ireland who has been in a serious financial situation at the verge of collapse causing difficulties to the euro. In this contribution we focus on the Greek crisis and we suggest, through a coopetitive game model conceived at a macro level, feasible solutions in a cooperative perspective, taking account of the divergent interests that drive the economic policies in Germany and Greece. We conduct a deep study of the particular model proposed, namely, for the analysis we conduct a Complete Analysis of the coopetitive game - in the sense introduced and already applied by D. Carfì in several papers. The key points of our coopetitive exam are essentially the following ones:
1) the complete study of an initial game G(0), in the Carfì’s sense, from which we obtain also a precise knowledge of its payoff space;
2) the study of a curve g of games with starting point the game G(0), by methodologies of essentially geometric nature;
3) the determination of the path of Nash equilibria (of the games forming the curve g) (that we will use to the selection of coopetitive Pareto strategies, see point 4);
4) the determination of the Pareto maximal boundary of the coopetitive game (that is the maximal boundary of the union of the payoff spaces of the games forming the curve g);
5) the determination of compromise solutions for our strategic interaction.
From an applicative point of view, our aim is to improve the position of the whole Euro area, also making a contribution to expand the set of macroeconomic policy tools. By means of our general analytical framework of coopetitive game, we show the strategies that could bring to feasible solutions in a cooperative perspective for the different country of the Euro zone (Germany and Greece in particular), where these feasible solutions aim at offering win-win outcomes for all countries in the EMU, letting them to share the pie fairly within a growth path represented by a non-zero sum coopetitive game. A remarkable analytical result of our work consists in the determination of a natural win-win solution by a new coopetitive selection method on the transferable utility Pareto boundary of the coopetitive game. Moreover the paper proposes a coopetitive model for the Green Economy. It addresses the issue of the climate change policy and the creation and diffusion of low-carbon technologies. In the present paper the complex construct of coopetiton is applied at macroeconomic level. The model, based on Game Theory, enables us to offer a set of possible solutions in a coopetitive context, allowing us to find a Pareto solution in a win-win scenario. The model, which is based on the assumption that each country produces a level of output which is determined in a non-cooperative game of Cournot-type and that considers at the same time a coopetitive strategy regarding the low technologies will suggest a solution that show the convenience for each country to participate actively to a program of low carbon technologies within a coopetitive framework to address a policy of climate change, thus aiming at balancing the environmental imbalances.
Thursday, March 1, 11:00 – 12:30pm in MH 484 (note: different day and time)
Martial Aufranc (Lycee Pothier and CSUF visitor): Isometries in Z_p and Q_p
Abstract. We give some general properties of isometries in Zp and in Qp. Then we discuss a special case of
a polynomial isometry. It is very simple in Qp. In Zp, the study of such isometries are simplifed by reduction methods to the
study of two reduced forms. We prove that there are no polynomial isometries of p-degree 2, 4 (if p > 11) and p-1 in Zp , and we describe the isometries of p-degree 3.
Tuesday, March 6, 12:00 – 12:50pm in MH 484
No seminar; moved to March 1
Tuesday, March 13, 12:00 – 12:50pm in MH 484
Dana Clahane (Fullerton College): Continuity and essential norms of composition operators on (k,theta)-logarithmic Bloch spaces
Abstract. In this talk, I will introduce the idea of a composition operator between two vector spaces of functions and induced by a map from the common domain of the functions in the first space to the common domain of the second space of functions. I will then define weighted Bloch spaces of a domain in n complex variables, and then for an n-unit ball, define a pair of parameterized k-theta logarithmic Bloch spaces of the ball, which are an important concrete class of weighted Bloch spaces. I will discuss what is now known about characterizing the boundedness and compactness of a composition operator and computation of its essential norm as it acts between the k-theta log Bloch spaces and the general weighted Bloch spaces of the disk, noting, along the way, a norm equivalence result, which may be of interest, involving these spaces.
This talk describes joint work with Rene Castillo, Juan F. Farias-Lopez, and Julio C. Ramos-Fernandez.
Tuesday, March 20, 12:00 – 12:50pm in MH 484
Sabrina Kombrink (Universität Bremen and UCR): A notion of volume for fractal sets
Abstract. In this talk, we will discuss how the notion of volume can be extended to fractal sets such as the Sierpinski gasket or the von-Koch curve. For this, we look into different notions of fractal dimensions and focus on the Minkowski content, as the Minkowski content can be viewed as a substitute for the notion of volume for fractal sets.
Tuesday, April 3, 12:00 – 12:50pm in MH 484
Lenny Fukshansky (Claremont McKenna College): On minimal lattice spherical configurations in three dimensions
Abstract: The kissing number problem asks for the maximal number of non-overlapping unit balls in R^n that touch another unit ball. The answer is only known in dimensions 1,2,3,4,8,24. In fact, in dimension 3 this was the subject of a famous argument between Isaac Newton and David Gregory, which was only settled in 1953. The kissing number problem can be reformulated as follows: find the maximal configuration of points on the unit sphere in R^n such that the angular separation between any pair of these points is at least pi/3. Such configurations are usually expected to come from sets of minimal vectors of lattices, at least this is the case in all known dimensions. This consideration raises the following natural related question: given a spherical lattice triangle, what is the minimal possible spherical area (i.e. measure of the corresponding solid angle) it can have? In this talk, I will give at least a partial answer to this question. This is joint work with Sinai Robins.
Tuesday, April 10, 12:00 – 12:50pm in MH 484
John Rock (Cal Poly Pomona): Self-similarity, fractal strings, and complex dimensions
Abstract: Self-similarity is a property held by many fractal objects and it is a key to understanding fractal geometry in general. When self-similarity holds for a given set in a strict mathematical sense, the determination of the set's fractal (possibly noninteger) dimension becomes a relatively simple endeavor. Moreover, the complex dimensions are readily available. As will be touched upon in this talk, these complex dimensions allow for, among other things, beautiful connections to be made between the geometry and spectra of (ordinary) fractal strings and the Riemann hypothesis.
Tuesday, April 17, 12:00 – 12:50pm in MH 484
Tuesday, April 24, 12:00 – 12:50pm in MH 484
Hassan Yousefi: Completely Rank Non-Increasing Maps
Abstract: In this talk we discuss the linear maps defined on finite dimensional vector spaces or on Banach spaces that have special property, namely, they are completely rank non-increasing. We will discuss characterization of these maps. After that we will discuss generalization of these ideas for bilinear maps.
Tuesday, May 1, 12:00 – 12:60pm in MH 565 (note: different room)
Martial Aufranc (Lycee Pothier and CSUF visitor): Polynomial Isometries of p-adic integers
Abstract. We give some general properties of isometries in Zp. Then we discuss a special case of
polynomial isometries. The study of such isometries are simplifed by reduction methods to the
study of two reduced forms.
Tuesday, May 8, 12:00 – 12:50pm in MH 484
Thursday, September 1, 12:00 – 12:50pm in MH 484
Marina Borovikova (CSUF): Hyperbolic characterization of ultrametric spaces, I
Abstract: In a series of two talks I will discuss Ibragimov’s recent preprint on the hyperbolic characterization of ultrametric spaces. I will provide detailed proof of the main results of the paper. The talks will be appropriate to undergraduate students who have taken Math 350 and Math 414.
Thursday, September 8, 12:00 – 12:50pm in MH 484
Marina Borovikova (CSUF): Hyperbolic characterization of ultrametric spaces, II
Thursday, September 15, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to p-adic numbers, I
Abstract: During 2011/2012 I will be giving a series of 10 talks on p-adic numbers, 5 in the fall and 5 in the spring. I will discuss p-adic numbers from algebraic, analytic and geometric points of view. The goal is to learn the basic knowledge of p-adic analysis and start reading recent research articles in p-adic Analysis, p-adic Dynamics and Fractal Geometry. The talks will be accessible to students who have taken basic courses in Algebra (Math 302), Analysis (Math 350) and Topology (Math 414). Students who intend to do undergraduate research projects are especially encouraged to attend. During the talks I will supply many problems for such projects.
Thursday, September 22, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to p-adic numbers, II
Thursday, September 29, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to p-adic numbers, III
Thursday, October 6, 12:00 – 12:50pm in MH 484
Thursday, October 13, 12:00 – 12:50pm in MH 484
Nishu Lal (UC Riverside): The spectral zeta function of fractal operators
Abstract. We will discuss the factorization formula of the spectral zeta function of Laplacian-like operators on
self-similar sets, in particular, those operators for which the decimation method is well established. We
will consider the fractal Sturm-Liouville operator on the half real line and C. Sabot's work connecting
the spectrum of this operator with the iteration of a rational map of several complex variables. The
Sturm-Liouville operator on [0;1) is viewed as a limit of the sequence of operators with Dirichlet boundary condition
on I<n> which are the infinitesimal generators of the Dirichlet form (a<n>;m<n>). In particular, it is defined in terms of a
self-similar measure m and Dirichlet form a, relative to a suitable iterated function system on I = [0; 1].
In the case of the Sierpinski gasket, as was shown by A. Teplyaev, extending the known relation by M. Lapidus
for fractal strings, the spectral zeta function of the Laplacian has a product structure with respect to the iteration of a rational map
on C which arises from the decimation method. In the case of the above self-similar Sturm-Liouville
problem, we obtain an analogous product formula, but now expressed in terms of the (suitably defined)
zeta function associated with the dynamics of the corresponding `renormalization map', viewed as a
rational function on P2(C). This is joint work with Dr. Michel Lapidus.
Thursday, October 20, 12:00 – 12:50pm in MH 484
Thursday, October 27, 12:00 – 12:50pm in MH 484
Martial Aufranc (Lycee Pothier and CSUF visitor): Generalized Absolute Values on the Rational Field
Abstract. Following the footsteps of the Swiss mathematician Alain M. Robert, this presentation identifies all absolute
values on the field of rational numbers by first identifying all the generalized absolute values and adapting some of the calculations
traditionally used for ultrametric absolute values. Eventually we obtain either the trivial absolute value or the
(acceptable) positive powers of either the usual Archimedean absolute value or the p-adic absolute values.
Friday, October 28, 3:00 – 3:50pm in MH 380 (special date, time and room)
Denis Labutin (UC Santa Barbara): Partial regularity for Monge-Ampere equation
Abstract. The standard elliptic regularity fails for Monge-Ampere equation in higher dimensions.
One needs to assume strict convexity of the solution. We present an estimate for the
Hausdorff dimension of the non-strict convexity set of a solution.
Thursday, November 3, 12:00 – 12:50pm in MH 484
Kevin Negron (CSUF undergraduate): Isometries of p-adic integers
Thursday, November 10, 12:00 – 12:50pm in MH 484
Thursday, November 17, 12:00 – 12:50pm in MH 484
Dominique Lee (Sunny Hills High): Extremal configuration of four points
Thursday, December 1, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to p-adic numbers, IV
Thursday, December 8, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to p-adic numbers, V
Tuesday, March 1, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Hyperbolic fillings of Ultrametric Spaces, I
Abstract: This is the first talk of a series of two talks I plan to give in on ultrametric spaces and p-adic numbers. I will discuss my recent paper on the hyperbolic filling of ultrametric spaces. Well-known examples of ultrametric spaces are p-adic numbers. I will also discuss canonical hyperbolic fillings and trees associated with p-adic integers.
Tuesday, March 8, 12:00 – 12:50pm in MH 484
Kevin Negron (CSUF): A Brief Introduction to p-adic numbers
Abstract: The p-adic numbers, which are produced by completing the field of rational numbers using the p-adic norm, non-Archimedean, instead of the traditional Archimedean norm, play a fundamental role in modern number theory. This brief lecture will introduce the audience to p-adic numbers from a geometric perspective.
Tuesday, March 15, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Hyperbolic fillings of Ultrametric Spaces, II
Tuesday, April 5, 12:00 – 12:50pm in MH 484
Alain Bourget (CSUF): Jacobi Matrices with slowly varying coefficients
Abstract: I will present new conditions to obtain trace formulas for Jacobi matrices as their dimensions go to infinity. I will also derive some existing trace formula due to Van Assche and Kuiljaars
Tuesday, April 12, 12:00 - 12:50pm in MH 484
David Carfi (UCR and University of Messina): A critical view of Dirac Calculus in Quantum Mechanics
Abstract: In his famous treatise “Principles of Quantum Mechanics” of 1930, the great mathematician and physicist Paul Dirac introduced several “manipulation rules” for vectors and operators of a linear spaces, which together constitute the so-called “Dirac Calculus”. This Calculus is nothing more than a wide set of formal extensions of the basic properties of the finite-dimensional Linear Algebra to the case of infinite-dimensional vector spaces. The discourse is elegant and surprisingly efficient, but it is far from being a rigorous mathematical treatment. As mathematicians well know, the passage from the finite to the infinite dimensional case does not amount to a mere substitution of finite linear combinations with formal integrals!
The goal of the research introduced in this talk is to give a precise mathematical meaning and rigorous support to many analytic methods of Quantum Mechanics, starting from the fundamental Dirac Calculus, under as few general conditions as possible. This approach will give a rigorous justification for the use of these tools, leaving them substantially “as they are” in Quantum Mechanics practice. Moreover, by providing a correct interpretation of these methods in terms of new mathematical entities and concepts, we will be helped in reaching a deeper understanding of the physical structures studied in Quantum Mechanics.
The operation of continuous-superposition and that of the Dirac product allow us to build - in a mathematically rigorous way - the "extended Linear Algebra" of Dirac in the spaces of tempered distributions, via their natural topological- linear structures. More precisely, we shall see that the algebraic-topological structure of those spaces allows us to define naturally the linear combinations of a continuous family of vectors and operators and a scalar product (of a vector by such continuous families of vectors) which are absolutely necessary (and already formally introduced and used by Dirac himself) for the theoretical development of Quantum Mechanics.
Tuesday, April 19, 12:00 – 12:50pm in MH 484
Hassan Yousefi (CSUF): C-Orbit Reflexivity, II
Abstract: We introduce the notion of C-orbit reflexivity of linear maps on a Banach space and study its properties. We will show that a matrix on the field of complex numbers is C-orbit reflexive if and only if among all the Jordan blocks with eigenvalues having modulus equal to r(T)>0, the two largest blocks differ in size by at most 1.
Tuesday, April 26, 12:00 – 12:50pm in MH 404
Megan Goode (CSUF): Periodic Jacobi Matrices
Abstract: Periodic Jacobi matrices play an important role in the study of the Schrodinger equation with periodic potential. For this reason, they have received a lot of attention in the last two decades. In this talk, I will present the asymptotic distribution of the spectrum of periodic Jacobi matrices. We will also deduce the well-known fact that the spectrum is absolutely continuous and consists of the union of closed intervals. Moreover, we give new expressions for these intervals.
Tuesday, May 10, 12:00 – 12:50pm in MH 484
Hafedh Herichi (UCR): GENERALIZED FRACTAL STRINGS, THE SPECTRAL OPERATOR AND A REFORMULATION OF THE RIEMANN HYPOTHESIS
Abstract: The spectral operator was introduced for the first time by M. L. Lapidus and his collaborator M. van Frankenhuijsen in their theory of complex dimensions in fractal geometry. The corresponding inverse spectral problem was first considered by M. L. Lapidus and H. Maier in their work on a spectral reformulation of the Riemann hypothesis in connection with the question "Can One Hear The Shape of a Fractal String?" The spectral operator is defined on a suitable Hilbert space as the operator mapping the counting function of a generalized fractal string η to the counting function of its associated spectral measure v= η*h, where * is the operation convolution of measures and h is the generalized harmonic string. It relates the spectrum of a fractal string with its geometry. The spectral operator also has an Euler product representation, which provides a counterpart to the usual Euler product expansion for the Riemann zeta function, but is convergent in the critical strip of the complex plane. During this talk, we will be discussing some fundamental properties of this operator and present conditions ensuring its invertibility.
Tuesday, May 24, 12:00 - 12:50pm in MH 484
David Carfi (UCR and University of Messina): Fibered spaces and financial structures
We study the plane of financial events, introduced and applied to financial problems by the author himself, considered as a fibred space in two different ways. The first fibration, the natural one, reveals itself to be isomorphic to the tangent bundle of the real line, when the last one is considered as a differentiable manifold in the natural way; the second one is a fibration induced by the compound interest capitalization at a given rate of interest. Moreover, in the paper we define on the first fibration an affine connection, induced again by compound interest at a given rate of interest. We show that all the effects determined by the status of compound interest are nothing but the consequences of the fact that the space of financial events is a fibration endowed with a particular affine connection, so they are consequences of purely geometric properties, at last, depending upon the curvature determined by the connection upon the fibration. A natural preorder upon the set of fibers of the second fibration is considered. Some remarks about the applicability to economics and finance of the theories presented in the talk, and about their possible developments are made in the directions of financial dynamical system.
Tuesday, June 7, 12:00 - 12:50pm in MH 484
David Carfi (UCR and University of Messina): Complete study of a C^1 games and applications
We shall deal with the Complete Analysis of a Continuously Differentiable Game (recently introduced by the author) and apply it to determine possible suitable behaviors (actions) of individuals during strategic interactions with other individuals, from both a non-cooperative and a cooperative point of view. To associate with a real strategic interaction among players a differentiable game any player’s strategy-set must, for instance, be a part of a topological vector space, closure of an open subset of the space. The most frequent case is that in which the strategy-sets are compact intervals of the real line. On the other hand, very often, the actions at disposal of a player can form a finite set, and in this case a natural manner to construct a game representing the real strategic interaction is the von Neumann convexification (also known as canonical extension) that leads to a differentiable game with probabilistic scenarios, and thus even more suitable for the purpose of represent real interactions. For what concerns the Complete Analysis of a Differentiable Game, its first goal is the precise knowledge of the Pareto boundaries (maximal and minimal) of the payoff space, this knowledge will allow us to evaluate the quality of the different Nash equilibria (by the distances from the Nash equilibria themselves to Pareto boundaries, with respect to appropriate metrics), in order to determine some “focal” equilibrium points collectively more satisfactory than each other. Moreover, the complete knowledge of the payoff-space will allow to develop explicitly the cooperative phase of the game and the various bargaining problems rising from the strategic interaction (Nash bargaining problem, Kalai-Smorodinski bargaining problem and so on).
Friday, November 5, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to the geometry of p-adic numbers, I
Abstract: This is the first talk of a mini-course I plan to give in the next three weeks on p-adic numbers. The goal of this course is to introduce the audience to the p-adic numbers from combinatorial and hyperbolic points of view. The talks will be appropriate to undergraduate students who have taken or currently taking Math 302 and 350. Overall objective of the course is to provide interested students with background materials and some open problems for research projects.
Friday, November 12, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to the geometry of p-adic numbers, II
Friday, November 19, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Introduction to the geometry of p-adic numbers, III
Friday, December 10, 12:00 – 12:50pm in MH 484
Hassan Yousefi (CSUF): C-Orbit Reflexivity
We introduce the notion of C-orbit reflexivity of linear maps on a Banach space and study its properties. We will show that a matrix on the field of complex numbers is C-orbit reflexive if and only if among all the Jordan blocks with eigenvalues having modulus equal to r(T)>0, the two largest blocks differ in size by at most 1.
Tuesday, February 2, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Open problems in Geometric Function Theory, I
Tuesday, February 9, 12:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Open problems in Geometric Function Theory, II
Tuesday, February 23, 12:00 – 12:50pm in MH 484
Marina Borovikova (CSUF): Symmetric products of lines and circles
Thursday, October 29, 11:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Hyperbolic geometry of ultrametric spaces, I
Thursday, November 5, 11:00 – 12:50pm in MH 484
Zair Ibragimov (CSUF): Hyperbolic geometry of ultrametric spaces, II
Thursday, November 12, 4:15 – 5:15pm in MH 484
Tuan Le (Fairmont Prep. Academy): On the extremal
configuration of points in the plane
Thursday, December 3, 11:00 – 12:50pm in MH 484
Hassan Yousefi (CSUF): Hyperconvexity of R-trees
Thursday, December 10, 11:00 – 11:50pm in MH 476
Cantor sets and their applications
Thursday, December 17, 11:00 – 12:50pm in MH 484
Steven Paul (Citrus College): Sets of constant diameter
Tuesday, March 17, 12:00 – 1:50pm in MH 484
Tuesday, March 24, 12:00 – 1:50pm in MH 484
Friday, October 3, 12:00 – 1:50pm in MH 484
Friday, October 10, 12:00 – 1:50pm in MH 484
Friday, October 17, 12:00 – 1:50pm in MH 484
Friday, October 24, 12:00 – 1:50pm in MH 484
Friday, December 12, 12:00 – 1:50pm in MH 484
Friday, April 25, 2:00 – 3:50pm in MH 476
Friday, April 18, 2:00 – 3:50pm in MH 476
Friday, April 11, 2:00 – 3:50pm in MH 476
Friday, March 28, 2:00 – 3:50pm in MH 476
Friday, March 14, 1:10 – 2:30pm in MH 476
Friday, March 7, 2:00 – 2:50pm in MH 476
Antonio Vargas (CSUF): Interlacing of Zeros and Non-Orthogonality of a Family of Polynomials.
Friday, February 22, 2:00 – 2:50pm in MH 476
Neil Donaldson (UCI): Isothermic surfaces in conformal geometry
Friday, January 25, 2:00 – 2:50pm in MH 476
Friday, August 31, 2:10 – 3pm in MH 390
Friday, September 14, 2:10 – 3pm in MH 390
Friday, September 28, 2:10 – 3pm in MH 390
Wednesday, October 3, 2:15 – 3:05pm in MH 484
Oliver Dragicevic, University of
Friday, October 5, 2:10 – 3pm in MH 390
Ali Lashgari (CSUF): Groebner Basis and free resolution of modules
Friday, November 2, 2:10 – 3pm in MH 390
Radu Gologan, University of Illinois at Urbana-Champaign and Institute of Romanian Academy: Mathematical results inspired by elementary problems
Friday, November 16, 2:10 – 3pm in MH 390
Friday, December 7, 2:10 – 3pm in MH 390