# MathCS Seminar

This is the homepage of the Chapman University Mathematics and Computational Science seminar

*Seminar Organizers:* Cyril Rakovski and Mihaela Vajiac

## Fall 2013

The seminar talks are in Von Neumann Hall VN 116 (545 W Palm Ave corner of W Palm Ave and railroad, Orange, CA 92866)

See Maps and directions, Von Neumann Hall is Building 38 on the Campus map

## Upcoming Talks and Workshops

### Thursday, Nov 21, 2013 from 2 pm to 4 pm in VN 116

#### Fifth Cal State University Fullerton and Chapman University Joint Mathematics Colloquium

*Organizers:* **Bogdan Suceavă** (CSUF) and **Peter Jipsen** (Chapman University)

*Program*

2:00 - 2:20 **Fernando Quintino** (Cal State Fullerton)

**Interpolating Legendre Multiplier Sequences**

2:20 - 2:40 **Allie Smith and Louis Ehwerhemuepha** (Chapman University)

**A Novel Exact Test for Association for Small Sample Case-Control Studies**

2:40 - 3:00 **Nathan Robertson, Susan Deeb, Soeun Park, and Reina Galvez** (Cal State Fullerton)

**A Comparative Analysis of Three Clustering Techniques with an Application to K6-11 Mathematics Achievement Data**

3:00 - 3:20 **Kevin Gomez** (Cal State Fullerton)

**A Ladder of Curvatures for Hypersurfaces in the Euclidean Ambient Space**

3:20 - 3:40 **Melissa Riddle** (Cal State Fullerton)

**A Pinching Theorem for Three-Dimensional Hypersurfaces in Euclidean Ambient Space**

3:40 - 4:00 **Kyle Lee** (Chapman University)

**Investigating Quantum Gravity through Causal Dynamical Triangulations**

## Previous Talks and Workshops

### Wednesday, Nov 13, 2013 at 12 noon in VN 116

#### *Speaker:* **Daniele Struppa, Chapman University**

*Title:* **Propagation of superoscillations as solutions to the Cauchy problem for generalized Schrodinger equations**

*Abstract:* Superoscillatory sequences have been introduced by Yakir Aharonov (and discussed in a series of seminars last year) as a byproduct of his theory of weak measurement. In this talk I will show that if we consider the Schrodinger equation (and some natural generalizations of it) , with superoscillatory initial conditions, the solution of the equation maintains superoscillatory behavior. The fundamental instruments necessary to prove such a result are the Fourier transform, and some results in the theory of convolution operators on spaces of rapidly growing entire functions (Berenstein and Struppa, Publ. RIMS Kyoto, 1988). The results that I will describe are the subject of three recent papers (coauthored with Aharonov, Colombo, Sabadini, and Tollaksen), the first of which has appeared in Journ. Math. Pures et Appliques, 2013.

### Wednesday, Oct 23, 2013 at 12 noon in VN 116

#### *Speaker:* **Atanas Radenski**, **Chapman University**

*Title:* **MapReduce Streaming Algorithms for Laplace Relaxation on the Cloud**

*Abstract:* I will begin this presentation with a gentle introduction to MapReduce parallelism. No preliminary knowledge of MapReduce is expected (but this presentation will be an opportunity to gain some MapReduce understanding). Technically, I will describe relaxation algorithms for the Laplace equation in MR streaming, and evaluate empirically their performance on Elastic MR, the Amazon MR cloud. These results can be beneficial to others who would like to develop and optimize MR streaming algorithms for grid-based models, such as PDE and cellular automata.

### Wednesday, Sept 18, 2013 at 12 noon in VN 116

#### *Speaker:* **Tadeusz Litak**, **Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany**

*Title:* **Friends, Likes and Coalitions: Coalgebraic Predicate Logic in Action**

*Abstract:* The talk is about a joint work with Dirk Pattinson, Katsuhiko Sano and Lutz Schröder.
It is about a generalization of first-order logic: a natural and generic language for non-relational structures which can be recast as Set-coalgebras.
However, I will assume no familiarity with coalgebras and coalgebraic logic. It is enough to know that the framework
can cover such diverse structures as Kripke frames, neighbourhood frames, topological spaces, discrete Markov chains,
conditional frames, multigraphs or game frames for coaliton logic/alternating time logics. As a taster, we will develop
an apparatus to reason about activities and preferences in social networks. Then we will shortly discuss issues likes
completeness, model theory and proof theory.

## Spring 2013

### Friday, April 26, 2013 at 2 pm - 5 pm Cal State Fullerton

#### Fourth Cal State University Fullerton and Chapman University Joint Mathematics Colloquium

*Program*

**Casey Coleman and Adrian Vajiac** (Chapman University)

*Title:* **A New Perspective on Geometry: Polynomials and Curved Spaces** (Research Adviser: Dr. Adrian Vajiac)

**Robert Giza** (Cal Poly Pomona)

*Title:* **Series associated with multifractal analysis** (Research adviser: Dr. John Rock)

**Duy D Ngo, Reina R Galvez, and Antouneo Kassab** (Cal State Fullerton)

*Title:* **A Multivariate Statistical Inference for the Analysis of Neuronal Spiking Rates** (Research adviser: Dr. Sam Behseta)

**Nathan Lawless** (Chapman University)

*Title:* **Generating all modular lattices of a given size** (Research adviser: Dr. Peter Jipsen)

**Yusuf Jabri** (Cal Poly Pomona)

*Title:* **Genesis of the ubiquitous Fibonacci Word**

**Jenny Chang** (Cal State Fullerton)

*Title:* **Robust Statistical Modeling of Neuronal Intensity Rates** (Research adviser: Dr. Sam Behseta)

**Cody Gruebele** (Cal State Fullerton)

*Title:* **Comparison of Two Models For Fat/Water Separation in Magnetic Resonance Imaging (MRI)** (Research adviser: Dr. Angel Pineda)

### Wednesday, April 24, 2013 at 2:30 pm in VN 116

#### *Speaker:* **Cynthia Northrup**, **University of California, Irvine**

*Title:* **Using Forcing to Obtain a Model of the Continuum Hypothesis**

*Abstract:* Forcing is a method used to extend a transitive model M by adjoining a new set G in
order to obtain a larger transitive model M[G]. Our choice of partial order, or notion of
forcing, determines what is true in M[G]. We will consider the forcing introduced by Paul
Cohen in proving the independence of the Continuum Hypothesis. The Diamond Principle,
introduced by Jensen in 1972, can be thought of as a strengthening of the Continuum
Hypothesis. From a diamond sequence of length k we can read off all of the subsets of k.
We are interested in using an iteration involving Radin forcing in order to obtain a model
of the failure of Diamond.

### Tuesday, April 23, 2013 at 1:15 pm in VN 116

#### *Speaker:* **Papiya Bhattacharjee**, **Penn State Erie, The Behrend College**

*Title:* **Extensions in Algebraic Frames**

*Abstract:* A frame L is algebraic if every element of L is expressed as a supremum of compact elements. In case of algebraic frames L that also satisfy the Finite Intersection Property, we investigate the spaces of minimal prime elements of L, called Min(L), with respect to the Zariski topology and the Inverse topology. The first part of the talk will describe these spaces. Finally, given two algebraic frames L and M (L is a subframe of M), the speaker will describe various extensions such as Rigid extension, r-extension, etc. and their relationship with the spaces of Min(L). In particular, it turns out that if M is a rigid frame extension of L, then Min(L) is homeomorphic to Min(M) with respect to both the Zariski topology and the inverse topology.

### Wednesday, April 17, 2013 at 2:30 pm in VN 116

#### *Speaker:* **Andres Forero Cuervo**, **University of California, Irvine**

*Title:* **Sets With No Length, Alternative Axioms and Infinite Games**

*Abstract:* The length of a subset of the real line can be defined in mathematical terms. A set of real numbers is called "measurable" if a precise, definite length can be assigned to it, following certain desired natural properties. Surprisingly, from the axioms of Set Theory we can show the existence of sets that are not measurable, somewhat violating our physical intuition of the notion of length in space. A natural logical question
arises: can some axioms of Set Theory be replaced by different axioms that not only prohibit the existence of the pathological sets just mentioned, but guarantee that every set is measurable? In this talk we will explore this possibility, and in this process we will explain the connection between infinite-length games, sets of real numbers and infinite trees.
This talk is mostly self contained. Only some basic knowledge of Real Analysis will be assumed.

### Friday, April 12, 2013 at 2:30 pm in VN 116

#### *Speaker:* **Ryan Lowenstein**, **Chapman University**

*Title:* **TuringPoint LearningJoint: A Technology Info Session **

*Abstract:* Teaching undergraduates can often be a challenging process, especially if the course is not found to be very interesting by many students (as may be the case with some introductory mathematics courses). Hence, many of us would like to add something to the classroom that could help us improve the engagement of our students (and make math fun again). TurningPoint, a form of clicker technology, does exactly that. This presentation focuses on its effectiveness and will also show you how to get started on your new TurningPoint classroom improvement project.

### Wednesday, April 3, 2013 at 2:30 pm in VN 116

#### *Speaker:* **Mustafa Said**, **University of California, Irvine**

*Title:* **Almost Commuting Matrices**

*Abstract:* We investigate a variant of an old problem in linear algebra and operator theory
that was popularized by Paul Halmos: Must almost commuting matrices be nearly commuting?
To be more precise, we say that a pair of n-by-n complex valued matrices (A, B)
are “almost commuting” if AB − BA is small in some sense. In the same manner, we say
that a pair of n-by-n complex valued matrices (X, Y) are “nearly commuting” if X − A
and Y − B are small in some sense and AB = BA. Although we will be exploring deep
ideas in operator theory, only a basic understanding of undergraduate linear algebra and
real analysis will be assumed. We will briefly discuss history of the problem, discuss the
progress on the problem, and sketch the proof of a quantitative result which establishes that
“almost commuting” matrices are “nearly commuting” for different types of matrices.

### Wednesday, January 16 -- Wednesday, January 23 2013

#### 5th Annual CECAT Workshop in Pointfree Mathematics

**Hosted by the Center of Excellence in Computation, Algebra and Topology (CECAT)**

Held at Chapman University, Von Neumann Hall (545 W. Palm Ave, Orange, CA 92866)

**Program**

**Wednesday 16th**

noon-2pm: **Open session**

**Thursday 17th**

12.30pm-2pm: **Bernhard Banaschewski**

*Title:* "Regular rings and the PIT"

**Friday 18th**

noon-1.30pm: **Bernhard Banaschewski**

*Title:* "On the minimal spectrum of a compact normal frame"

**Monday 21st**

noon-1.30pm: **Bernhard Banaschewski**

*Title:* "An example of a pointless countably compact completely regular frame

2pm-3.30pm: **Peter Jipsen**

*Title:* "Implementing decision procedures for (generalized) Basic Logic"

**Tuesday 22nd**

11am-12.30pm: **Ales Pultr**

*Title:* "Techniques on taking quotients in frames, lattices, quantales etc "

1pm-2pm **Joanne Walters-Wayland**

*Title:* "Some comments on Coz and quotients"

**Wednesday 23rd**

noon-1.30pm: **Ales Pultr**

*Title:* "Techniques on taking quotients in frames, lattices, quantales etc "

**Thursday 24th**

11am-12.30pm: **Bernhard Banaschewski**

*Title:* "Aspects of Strong 0-dimensionality"

1pm-2.30pm: Drew Moshier

*Title:* "An overview of Co-algebras on Compact Regular Spaces"

**Friday 25th**

noon-1.30pm: **Bernhard Banaschewski**

*Title:* "Aspects of Strong 0-dimensionality"

**Saturday 26th**

7pm: **Cello Concert** in Von Neumann Hall

### Wednesday, January 16, 2013 at 4:30 pm in VN

*Speaker:* **Dr. Scott Linfoot of the IEEE and De Montfort University**

*Title:* **Metadata: Making Molehills out of Mountains**

*Abstract:* This presentation will examine the two prominent media sectors, professional
and consumer, and show that in the near future, the amount of content created
from the consumer space will exceed that created in the professional space.
As a result, there is a vast amount of uncollated and disorganized media moving
around the internet unchecked.

There is a huge drive at the moment to try to establish some order to what appears to be a chaotic system. The problem is that using current methods, this is an extremely time consuming and expensive process. As a result, automatic metadata generation methods are needed to improve the process while providing a business case for exploitation.

This presentation will explore the metadata problem, looking from the consumer and professional vantage points, and try to open discussion on how this escalating problem might be averted.

## Fall 2012

### Thursday, November 15, 2012 at 2 pm - 5 pm in VN

#### Third Chapman University and Cal State University Fullerton Joint Mathematics Colloquium

held at **Chapman University, Von Neumann Hall** (545 W. Palm Ave, Orange)
meet at 1:30 pm in Von Neumann Hall for a brief reception

**PROGRAM**

**2:00 pm Lucy Odom (CSU Fullerton)** - "Amalgamatic Curvature and Absolute Umbilical Hypersurfaces"

**2:25 pm David Tyler (Chapman University)** - "Map the Network"

**2:50 pm Charley Conley (CSU Fullerton)** - "A Rigidity Theorem for Hypersurfaces"

**3:15 pm Adrian Vajiac (Chapman University)** - "Bicomplex Numbers"

**3:40 pm Coffee Break**

**4:10 pm Nicholas Salinas (CSU Fullerton)** - "Polynomial Isometries of P-adic Integers"

**4:35 pm Peter Jipsen (Chapman University)** - "A Category of Algebraic Contexts equivalent to Idempotent Semirings"

### Monday, October 22 -- Friday, October 26 2012

#### Workshop on Function Theories for Bicomplex and Hyperbolic Numbers

Hosted by the **Center of Excellence in Complex and Hypercomplex Analysis (CECHA)**

**PROGRAM**

**Monday October 22nd 2012**

9:30am-10:30am **Adrian Vajiac, Chapman University**

Title: “Bicomplex Analysis: an introduction”

10:45am-11:45am **Michael Shapiro, Instituto Politecnico Nacional, Mexico**

Title: “Bicomplex Derivability, Differentiability, and Holomorphy”

2:00pm-3:00pm **John Ryan, University of Arkansas**

Title: “Complex Clifford Analysis”

3:15pm-4:15pm **Craig Nolder, Florida State University**

Title: “Conformal Mappings in R1,1 are Quasi-Conformal”

**Tuesday October 23rd 2012**

9:30am-10:30am **Elena Luna Elizarraras, Instituto Politecnico Nacional, Mexico**

Title: “On Fundamentals of Functional Analysis with Bicomplex Scalars”

10:45am-11:45am **Dominic Rochon, Université du Québec à Trois-Rivières, Canada**

Title: “Infinite Dimensional Bicomplex Hilbert Spaces“

2:00pm-3:00pm **Daniele Struppa, Chapman University**

Title: “Holomorphic functions of a bicomplex variable and Ehrenpreis’ Fundamental Principle”

3:15pm-4:15pm **Franciscus Sommen, Universiteit Gent, Belgium**

Title: “Spherical Monogenics on the Lie Sphere”

**Wednesday October 24th 2012**

9:30am-10:30am **Uwe Kahler, University of Aveiro, Portugal**

Title: “Discrete Function theories in the case of bicomplex and hyperbolic numbers“

10:45am-11:45am **Paula Cerejeiras, University of Aveiro, Portugal**

Title: “On the Gabor Transform: the Bicomplex Case”

**Thursday October 25th 2012**

9:30am-10:30am **Daniel Alpay, Ben-Gurion University of the Negev, Israel**

Title: “Schur Analysis and Theory of Linear Systems: The Bicomplex Case“

10:45am-11:45am **Sebastien Tremblay, Université du Québec à Trois-Rivières, Canada**

Title: “Hyperbolic Pseudonanalytic Functions in Mathematical Physics“

2:00pm-3:00pm **Irene Sabadini, Politecnico di Milano, Italy**

Title: “Algebraic Analysis Methods in the Bicomplex setting “

3:15pm-4:15pm **Fabrizio Colombo, Politecnico di Milano, Italy**

Title: “Bicomplex Holomorphic Functional Calculus “

**Friday October 26th 2012**

9:30am-10:30am **Matvei Libine, Indiana University**

Title: “Introduction to Split Quaternionic Analysis “

10:45am-11:35am **Mihaela Vajiac, Chapman University**

Title: “Hyperbolic Analysis: an introduction”

### Thursday, October 4, 2012 at 1:15 pm in VN 116

*Speaker:* **Prof. Andrew Moshier, Faculty of Computer Science and Mathematics, Chapman University**

*Title:* **Generalizing Modal Logic for Compact Hausdorff Semantics**

*Abstract:* Normal modal logic can be regarded as a specification language for non-deterministic
state transition systems, modeled as compact, zero-dimensional topological spaces equipped
with a closed binary relation. The zero-dimensionality requirement, however, severely limits
potential applications. After all, this rules out such state spaces as spheres, tori and other
garden variety compact Hausdorff spaces.

In this talk we consider how to generalize descriptive frames to allow for compact Hausdorff state spaces, and then ask how modal logic can be adapted to this generalization. In the result, we show that a Sahlqvist Theorem holds, characterizing a class of formulas that determine first-order definable properties of the state transition.

This is joint work with Nick Bezhanishvili.

### Tuesday, August 28, 2012 at 4 pm in VN 116

*Speaker:* **Dr. Petr Vojtechovsky, Department of Mathematics, University of Denver**

*Title:* **Computational aspects of loop theory**

*Abstract:* Loop theory is closely related to group theory, but the lack of associativity makes calculations with loops difficult. Since 2000, there has been notable progress in several areas of loop theory thanks to a variety of computational tools, including group-theoretical packages, symbolic computation systems, automated theorem provers and finite model builders. In this talk I will present four projects where these computational tools were essential, although one would probably not have guessed it from the results alone. I will not assume any prior knowledge of loop theory in the talk.