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Articles 1 - 19 of 19
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A Tale Of Two Workshops: Two Workshops, Three Papers, New Ideas, Gizem Karaali
A Tale Of Two Workshops: Two Workshops, Three Papers, New Ideas, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Book Review: Philosophy Of Science After Feminism By Janet Kourany, Gizem Karaali
Book Review: Philosophy Of Science After Feminism By Janet Kourany, Gizem Karaali
Pomona Faculty Publications and Research
Janet Kourany’s book is a strange one: published by Oxford University Press (as a part of its Studies in Feminist Philosophy series), it is an academically oriented book, but reading it, you sense that this is not yet another theoretical monograph. For Kourany has her ax to grind, and more importantly she has a program to promote. The program is for philosophers of science and is motivated and encouraged by the amazing work done in the past few decades by feminist scientists and feminist scholars of science, technology, and society. In the following I will try to explain why I …
On The Quantization Of Zero-Weight Super Dynamical R-Matrices, Gizem Karaali
On The Quantization Of Zero-Weight Super Dynamical R-Matrices, Gizem Karaali
Pomona Faculty Publications and Research
Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical r-matrices. A super dynamical r-matrix r satisfies the zero weight condition if
[h ⊗ 1 + 1 ⊗ h, r(λ)] = 0 for all h ∈ ɧ, λ ∈ ɧ ∗ .
In this paper we explicitly quantize zero-weight super dynamical r-matrices with zero coupling constant for the Lie superalgebra gl(m, n) . We also answer some questions about super dynamical R-matrices. In particular, we prove a classification theorem and offer some support for one particular …
What Does It Take To Teach Nonmajors Effectively?, Feryal Alayont, Gizem Karaali, Lerna Pehlivan
What Does It Take To Teach Nonmajors Effectively?, Feryal Alayont, Gizem Karaali, Lerna Pehlivan
Pomona Faculty Publications and Research
Most MAA members teach mathematics at the college level, and many often teach courses intended for nonmajors. Indeed this is one of the main responsibilities of a mathematics department: offering service courses for client departments and general education courses for nonmajors. The three of us have been thinking about the question of how to teach nonmajors successfully for a while now. Finally we decided on a time-tested method of figuring things out: if you don't know what to do, ask the experts. We organized a panel titled "Effective Strategies for Teaching Classes for Nonmajors" for MAA MathFest 2012 and invited …
Ramanujan Sums As Supercharacters, Christopher F. Fowler '12, Stephan Ramon Garcia, Gizem Karaali
Ramanujan Sums As Supercharacters, Christopher F. Fowler '12, Stephan Ramon Garcia, Gizem Karaali
Pomona Faculty Publications and Research
The theory of supercharacters, recently developed by Diaconis-Isaacs and Andre, can be used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel formulas. In addition to exhibiting a new application of supercharacter theory, this article also serves as a blueprint for future work since some of the abstract results we develop are applicable in much greater generality.
Humanistic Mathematics: An Oxymoron?, Gizem Karaali
Humanistic Mathematics: An Oxymoron?, Gizem Karaali
Pomona Faculty Publications and Research
Mathematics faculty are trained as mathematicians, first and foremost. If we did not experience the soul-expanding possibilities of liberal education during our own undergraduate years, we may hesitate to bridge disciplinary divides when pursuing our core human need to inquire and understand. Although most mathematicians I know are amazing teachers, communicators, and mentors, many still teach the same material that their professors and their professors’ professors taught. This time-tested approach can be powerful, fascinating, and even quite entertaining. But it can also seem far removed from the world we inhabit. Yes, we teach “real world applications” of mathematical concepts. Yet …
In Defense Of Frivolous Questions, Gizem Karaali
In Defense Of Frivolous Questions, Gizem Karaali
Pomona Faculty Publications and Research
Is there any reason for today's academic institutions to encourage the pursuit of answers to seemingly frivolous questions? The opinionated business leader who does not give a darn about your typical liberal arts classes "because they do not prepare today’s students for tomorrow's work force" might snicker knowingly here: Have you seen some of the ridiculous titles of the courses offered by the English / literature / history / (fill in the blank) studies department in the University of So-And-So? Why should any student take "Basketweaving in the Andes during the Peloponnesian Wars"? Just what would anyone gain from …
Two Remarks About Nilpotent Operators Of Order Two, Stephan Ramon Garcia, Bob Lutz '13, D. Timotin
Two Remarks About Nilpotent Operators Of Order Two, Stephan Ramon Garcia, Bob Lutz '13, D. Timotin
Pomona Faculty Publications and Research
We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a complex symmetric operator. In fact, we prove that this property characterizes nilpotents of order two among all nonzero bounded operators. Second, we establish that every nilpotent of order two is unitarily equivalent to a truncated Toeplitz operator.
Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, Stephan Ramon Garcia, Daniel E. Poore '11, William T. Ross
Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, Stephan Ramon Garcia, Daniel E. Poore '11, William T. Ross
Pomona Faculty Publications and Research
Unlike Toeplitz operators on H², truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this paper we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive, and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension ≤ 3 is unitarily equivalent to a direct sum of truncated Toeplitz operators.
Review: Embeddings Of Model Subspaces Of The Hardy Class: Compactness And Schatten–Von Neumann Ideals, Stephan Ramon Garcia
Review: Embeddings Of Model Subspaces Of The Hardy Class: Compactness And Schatten–Von Neumann Ideals, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Unitary Equivalence To A Complex Symmetric Matrix: Low Dimensions, Stephan Ramon Garcia, Daniel E. Poore '11, James E. Tener '08
Unitary Equivalence To A Complex Symmetric Matrix: Low Dimensions, Stephan Ramon Garcia, Daniel E. Poore '11, James E. Tener '08
Pomona Faculty Publications and Research
A matrix T∈Mn(C) is UECSM if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we completely characterize 4×4 nilpotent matrices which are UECSM and we settle an open problem which has lingered in the 3×3 case. We conclude with a discussion concerning a crucial difference which makes dimension three so different from dimensions four and above.
On The Closure Of The Complex Symmetric Operators: Compact Operators And Weighted Shifts, Stephan Ramon Garcia, Daniel E. Poore '11
On The Closure Of The Complex Symmetric Operators: Compact Operators And Weighted Shifts, Stephan Ramon Garcia, Daniel E. Poore '11
Pomona Faculty Publications and Research
We study the closure $\bar{CSO}$ of the set $CSO$ of all complex symmetric operators on a separable, infinite-dimensional, complex Hilbert space. Among other things, we prove that every compact operator in $\bar{CSO}$ is complex symmetric. Using a construction of Kakutani as motivation, we also describe many properties of weighted shifts in $\bar{CSO} \backslash CSO$. In particular, we show that weighted shifts which demonstrate a type of approximate self-similarity belong to $\bar{CSO}\backslash CSO$. As a byproduct of our treatment of weighted shifts, we explain several ways in which our result on compact operators is optimal.
Changes Across 25 Years Of Statistics In Medicine, Johanna S. Hardin
Changes Across 25 Years Of Statistics In Medicine, Johanna S. Hardin
Pomona Faculty Publications and Research
[This piece is a series of interviews with giants in the field of medicine on their views of how statistics is changing medicine. I interviewed the editor of the New England Journal of Medicine, a preeminent doctor/researcher of lung cancer, the director of the LA County Department of Public Health, and a Harvard statistician who sits on the editorial board of the New England Journal of Medicine.]
Review: Classification Of Four And Six Dimensional Drinfel'd Superdoubles, Gizem Karaali
Review: Classification Of Four And Six Dimensional Drinfel'd Superdoubles, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Lusztig Symmetries And Automorphisms Of Quantum Superalgebras, Gizem Karaali
Review: Lusztig Symmetries And Automorphisms Of Quantum Superalgebras, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: An Operator Approach To The Rational Solutions Of The Classical Yang-Baxter Equation, Gizem Karaali
Review: An Operator Approach To The Rational Solutions Of The Classical Yang-Baxter Equation, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Medicine, Statistics, And Education: The Inextricable Link, Katharine K. Brieger '11, Johanna S. Hardin
Medicine, Statistics, And Education: The Inextricable Link, Katharine K. Brieger '11, Johanna S. Hardin
Pomona Faculty Publications and Research
No abstract provided.
Review: The Dirichlet Space: A Survey, Stephan Ramon Garcia
Review: The Dirichlet Space: A Survey, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
On The Matrix Equation Xa + Ax_T = 0, Stephan Ramon Garcia, Amy L. Shoemaker '14
On The Matrix Equation Xa + Ax_T = 0, Stephan Ramon Garcia, Amy L. Shoemaker '14
Pomona Faculty Publications and Research
The matrix equation XA+AXT=0, which has relevance to the study of Lie algebras, was recently studied by De Terán and Dopico (Linear Algebra Appl. 434 (2011), 44–67). They reduced the study of this equation to several special cases and produced explicit solutions in most instances. In this note we obtain an explicit solution in one of the difficult cases, for which only the dimension of the solution space and an algorithm to find a basis of this space were known previously