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# Mathematics Colloquium Schedule

**Spring 2017 **

**Date: 5-5-2017 (12-1pm, F03-200A), Dr. Eyob Demeke, Department of Mathematics, Cal State Los Angeles**

**Title:** Proof Comprehension at the Undergraduate Level: An Exploratory Study

**Abstract: **This talk mainly discusses a study I conducted on proof comprehension with eleven undergraduate students. The proofs were taken from an undergraduate abstract algebra course. My interpretation of what it means to understand a proof is based on a proof comprehension model developed by Mejia-Ramos, et al. (2012). The talk, in particular, examines undergraduate students attempting to summarize a proof using its higher-level ideas. Focus is given to students’ attention to key ideas in the proof and to the method used in the proof.

**Date: 4-14-2017 (12-1pm, F03-200A), Dr. Dana Clahane, Division of Mathematics & Computer Science, Fullerton College**

**Title:** Spectra of compact composition operators on bounded symmetric domains

**Abstract: **In 1975, former CSULB Professor Howard Schwartz, along with James Caughran, published a now well-known result that if a self-map induces a compact composition operator on the Hardy space of the open complex unit disk D, then two nice things happen. First, the self-map's iterates under composition converge uniformly on compact sets to a unique fixed point in D. Furthermore, these authors showed that in this case, the spectrum of the composition operator induced by this self-map consists of 0, 1, and all possible powers of the derivative of the self-map at this fixed point, which turns out to be the so-called Denjoy-Wolff point of the self-map. Since then, these results have been generalized in a variety of interesting directions, such as to the unit ball in several complex dimensions. I will define what a bounded symmetric domain is, discuss Cartan's famous classification of these domains, and state results about self-maps and spectra of their composition operators in more general situations, including the polydisk in more than one complex variable where the Denjoy-Wolff point may not exist in general. Time permitting, I'll discuss a possible application to the Lapidus/Nest construction of so-called "fractal membranes."

**Date: 3-17-2017 (12-1pm, F03-200A), Dr. Benjamin Dyhr, Department of Mathematics, Metropolitan State University**

**Title:** Using Visual Art, Crafts and Music to Demonstrate Mathematics

**Abstract: **Quantitative reasoning skills are an essential component of an associate's or bachelor’s degree, but many college students do not have a personally meaningful engagement with mathematics in these courses. In some cases, student disengagement with mathematics prevents them from completing their degree. I will describe collaborative projects with Anne Hallam, MFA, from MSU Denver using math students from MSU Denver's quantitative literacy course (Mathematical Modes of Thought) and art students from MSU Denver's 2-d and 3-d Design courses. These projects can engage students and develop student ability and appreciation for mathematical communication. We will also work in groups on craft projects demonstrating mathematical concepts I have used for in-class and community events. Finally, I will describe work in progress related to similar collaborative projects that involve music.

**Fall 2016 **

**Date: 12-2-2016 (1:30-2:30pm, F03-200A), Dr. Kohei Kishida, University of Oxford**

**Title:** Non-Locality, Contextuality, and Topology

**Abstract: **Non-locality and contextuality are among the most paradoxical properties of quantum physics contradicting the intuitions behind classical physics. In addition to their foundational significance, non-locality is fundamental to quantum information, and recent studies suggest contextuality is a key computational resource of quantum computation. This has motivated inquiries into higher-level, structural expressions of non-locality and contextuality that are independent of the concrete formalism of quantum mechanics. One approach uses the mathematical tool of sheaf theory, and has yielded the insight that non-locality and contextuality are topological in nature. In this talk, I first review several ideas as well as formal expressions of non-locality, and extract from them the topological formalism for quantum measurement scenarios and a characterization of non-locality in this formalism. In fact, as we show, the same characterization captures contextuality as well (so that non-locality amounts to a special case of contextuality). We will then illustrate the power of this higher-level, unifying formalism: On the one hand, it leads to several new methods of contextuality argument. On the other hand, it shows contextuality to be a ubiquitous phenomenon that can be found in various other disciplines.

**Date: 11-18-2016 (12-1pm, F03-200A), Dr. Catherine Pfaff, UCSB**

**Title:** Outer Space and the Outer Automorphism Group of the Free Group

**Abstract: **A common strategy for studying a group is to study some object that it acts on and how it acts on this object. My favorite group is the outer automorphism group of the free group. I will introduce this group and the object, Culler-Vogtmann Outer Space, that it acts on.

**Date: 11-10-2016 Thursday (12:30-1:30pm, F03-200A), Dr. Bob Stein, Professor Emeritus of Mathematics, Cal State San Benardino**

**Title:** The Remarkable History of Exponents and Logarithms

**Abstract:** Today we rarely compute with logarithms, and we take exponents largely for granted, but those topics were once at the center of mathematical interest. This talk will focus both on the development of these ideas, and on the astonishing people involved. No mathematics beyond first year calculus will be needed to understand this talk.

**Date: 10-28-2016 (12-1pm, F03-200A), Dr. Lee Peterson, Jet Propulsion Laboratory**

**Title:** Simulating Space: Role of Advanced Modeling and Uncertainty Quantification in JPL Missions

**Abstract:** Critical phases of spacecraft missions often cannot be completely tested on Earth, because of differences in the environments found in space and on other planetary bodies. When this happens, engineers resort to high fidelity models, informed by tests, are needed to verify readiness for flight. This talk will provide an overview of some recent applications of high fidelity models and simulations at JPL. It will include some discussion of the role of uncertainty quantification (UQ) as part of a Quantification of Margins and Uncertainties (QMU) engineering approach.

**Date: 10-21-2016 (1pm-2pm, F03-200A), Dr. Khue Duong, CSULB library**

**Title:** Data Science, Data Services, a Sabbatical Reflection

**Abstract:** Data comes in different sizes and formats: computer codes, spreadsheets, audio recording, images, fieldnotes, genome sequences, or geospatial coordinates. Data science, as an interdisciplinary study, incorporates many academic disciplines from mathematics and statistics to computer science, information science and geographic information system. Furthermore, research articles from scientific journals such as Science, Nature, or PLOS One increasingly require supplementary data or pointers to data repositories where one can access the dataset for further analysis or replication of the original research. My talk approaches data from a librarian’s perspectives and is a direct result of a four-month sabbatical to learn about how academic libraries support of data services—from providing reviews of mandated data management plans and finding discipline-specific datasets or data repositories to teaching data literacy workshops. I hope to highlight a few resources where one can learn more about data science.

**Date: 10-11-2016 (Tuesday! 12-1pm, F03-200A), Dr. Geng Chen, University of Kansas**

**Title:** Lipschitz metric for a nonlinear wave equation

**Abstract:** The nonlinear wave equation: u_{tt} - c(u)[c(u)u_x]_x = 0 is a natural generalization of the linear wave equation. In this talk, we will discuss a recent breakthrough addressing the Lipschitz continuous dependence of solutions on initial data for this quasi-linear wave equation. Our earlier results showed that this equation determines a unique flow of conservative solution within the natural energy space H^1(R). However, this flow is not Lipschitz continuous with respect to the H^1 distance, due to the formation of singularity. To prove the desired Lipschitz continuous property, we constructed a new Finsler type metric, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, we carefully estimated how the distance grows in time. To complete the construction, we proved that the family of piecewise smooth solutions is dense, following by an application of Thom's transversality theorem. This is a collaboration work with Alberto Bressan.

**Date: 9-23-2016 (12-1pm, F03-200A), Dr. Gabriel Udomkesmalee, Jet Propulsion Laboratory**

**Title:** JPL Robotics

**Abstract:** The Robotics Section of the Jet Propulsion Laboratory (JPL), California Institute of Technology, is engaged in a full spectrum of flight project and research activities. This talk will provide an overview of the efforts and discuss the recent accomplishments and future directions of them. Specific activities will be high-lighted based on their level of accomplishment, impact on the community, maturity, or novelty. Robotics activities on flight projects are a significant subset of the full effort for these large missions. Complementing flight activities is a diverse set of research efforts for NASA and other U.S. Government agencies. Future directions will be motivated by NASA and other sponsor objectives, as well as success experienced in these current endeavors.

**Date: 9-2-2016 (12-1pm, F03-200A), Dr. Minh N. Tran, Department of Mechanical and Aerospace Engineering, UC Davis**

**Title:** Nuclear Engineering for Everyone

**Abstract:** External loads are important, often well understood, and taken into account in the design of mechanical or structural components. However, there are other factors that can significantly affect the performance of materials, such as pre-existing defects and residual stresses. Those factors are usually difficulty to detect and quantify, and thus they are easy to overlook and ignore in the design phase. The work presented in this talk focuses on the residual stresses due to welding and was developed in the context of research with the nuclear power industry. Weld process models, based on nonlinear finite element computations, are frequently employed to estimate residual stresses in plant components, and those estimates are used to support plant management decisions. Therefore, we will begin with an introduction of a finite element model to predict residual stresses due to the manufacturing process of a pressurizer surge nozzle, used in the cooling system of pressurized water reactors. Modeling results are commonly evaluated at room temperature in order to validate against measurements, which are conducted at room temperature. However, in addition to weld residual stress produced in the course of manufacturing, plant components are subject to internal water pressure and elevated temperature during operation. Thus, we will next investigate the changes in weld residual stress state due to the presence of internal pressure and temperature at operating conditions. In the end, the purpose of computing residual stress is most often to determine its effect on component operability. For that reason, we will conclude the talk with a service life assessment of the pressurizer surge nozzle presented in this talk.