Mathematics Colloquium Archive

Spring 2024

Dr. Maya Chhetri, UNC Greensboro

Abstract

In this presentation, we explore linear elliptic problems with nonlinear boundary condition. While problems involving linear diffusion and nonlinear reaction in the interior, satisfying either zero or linear boundary conditions, have garnered considerable attention for their practical applications, there's a natural curiosity surrounding nonlinear boundary conditions. Our focus will be on a class of boundary value problems distinguished by linear diffusion term in the interior coupled with a nonlinear boundary conditions, where the bifurcation parameter is on the boundary. This allows us to look at this problem through the lens of an eigenvalue problem.

Bio Sketch

Gunther Uhlmann is the Robert R. and Elaine F. Phelps Professor of Mathematics at the University of Washington. His research focuses on inverse problems and imaging, microlocal analysis, partial differential equations and invisibility.

Professor Uhlmann was an Invited Speaker at The International Congress of Mathematicians in Berlin in 1998 and a Plenary Speaker at the International Congress on Industrial and Applied Mathematics in Zurich in 2007. He was elected to the American Academy of Arts and Sciences in 2009 and a SIAM Fellow in 2010. In 2011 he was awarded the American Mathematical Society Bôcher Memorial Prize and the Society for Industrial and Applied Mathematics Kleinman Prize. Professor Uhlmann delivered the American Mathematical Society Einstein Lecture in 2012. In 2013, he was elected Foreign Member of the Finnish Academy of Science and Letters. He gave a Plenary Lecture at the International Congress on Mathematical Physics in 2015. In 2017 he was awarded the Solomon Lefschetz Medal by the Mathematical Council of the Americas. In 2021 he was awarded by AMS and SIAM the George David Birkhoff Prize. In 2023 he was elected as a member of the National Academy of Sciences.

Dr. Thomas Hagstrom, Southern Methodist University

Abstract

Although many mathematical models in wave theory lead to hyperbolic initial-boundary value problems which are inherently local due to the finite domain-of-dependence of the solution at any point on past values, there are also examples where nonlocal operators, in particular space-time integral operators, arise. A primary example is the radiation boundary condition needed to truncate an unbounded domain to a finite one to enable numerical solutions, as well as closely-related operators for unidirectional propagation. In this work we show how to leverage results from rational function approximation theory to construct spectrally-convergent local algorithms for evaluating such operators. For an important class of problems - systems equivalent to the scalar wave equation, such as acoustics or Maxwell’s equations in homogeneous, isotropic media, we will explain the construction, analysis, and implementation of our complete radiation boundary conditions, which are in a certain sense optimal. We will also discuss other applications of these approximation methods, as well as the fundamental barriers to extending the successful methods to other systems.

Daniel Lévesque, Polytechnique Montreal

Details unavailable.

Dr. Heyrim Cho, Arizona State University

Abstract

Recent advances in biotechnology and genome sequencing, resulting in a surge of data, are bringing in new opportunities in mathematical modeling of biological systems. However, the amount of data that can be practically collected in everyday patients in the clinic is limited due to various reasons including the cost and the patient’s burden. Especially the amount of data that can be collected in the time domain is limited. This motivates us to transfer the mathematical and computational models to meet the challenges in clinical setting, to guide patient therapy via prediction. In this talk, I will discuss modeling approaches on the two ends of the spectrum of data. In the first part, I will discuss a Bayesian information-theoretic approach to determine effective scanning protocols of cancer patients. We propose a modified mutual information function with a temporal penalty term to account for the loss of temporal data. The effectiveness of our framework is demonstrated in determining patient scanning scheduling for prostate cancer patients. In the second part, I will discuss modeling work using single-cell gene sequencing data. Due to the high cost of obtaining gene sequencing data, temporal data also lacks. We show that our cell state dynamics model can be used to incorporate genetic alteration with low cost, where we show an example of modeling hematopoiesis system and simulating abnormal differentiation that corresponds to acute myeloid leukemia.

Biosketch

Heyrim Cho received her Ph.D. degree in 2015 from the Applied Math department at Brown University, then was a Brin-Postdoc fellow in the Math department at University of Maryland, College Park, and an assistant professor in the Math department at University of California Riverside. She recently moved to Arizona State University as an assistant professor in the School of Mathematical and Statistical Sciences. Her research areas are: Mathematical and computational biology especially focusing on oncology and medical applications, Stochastic modeling and simulation, Uncertainty quantification, and Scientific Computing.

Fall 2023

Dr. Evan T. R. Rosenman, Claremont McKenna College

Abstract

Statistics and data science play a crucial role in modern presidential campaigns. Models are used to estimate the probability that each registered voter casts a ballot, and the probability that each voter supports a given candidate. Moreover, analysts' recommendations play a key role in the broader campaign strategy, including the decision to invest resources in particular states.

In this talk, I will discuss my experience leading the turnout modeling effort on the Biden for President 2020 campaign, including the unique challenges for campaign analytics in the midst of a global pandemic. I will also highlight some of the broader research questions that emerged out of the campaign, including questions about polling bias and forecasting error.

Bio Sketch

Evan T. R. Rosenman is an Assistant professor of Statistics at Claremont McKenna College. His research focuses primarily on problems in data science and causal inference, with applications to political science and public health. He is particularly intrigued by problems involving hybridizing observational and experimental data to better estimate causal effects, and by challenges in modern electioneering, such as ecological inference and prediction calibration. He earned his Ph.D. in Statistics from Stanford University, advised by Art Owen and Mike Baiocch. He also completed a postdoctoral fellowship at the Harvard Data Science Initiative, advised by Kosuke Imai and Luke Miratrix.

The original puzzle assumes that the light is described by rays (a so-called billiards problem) so that the light cannot "bend around corners." Here we model light by solving the Helmholtz equation with a point source in one of the regions of the room and study (among other things) how dark the other region of the room actually is as we change the frequency of the light-source.

To model the unilluminable room we introduce and discuss the WaveHoltz iteration for solving the Helmholtz equation. This method makes use of time domain methods for wave equations to design frequency domain Helmholtz solvers. We show that the WaveHoltz iteration results in a positive definite linear system whose solution gives the solution to the (indefinite) Helmholtz equation.

Bio Sketch

Before joining the CMDA program and the Department of Mathematics at Virginia Tech Daniel was a faculty at CMSE and the Department of Mathematics at MSU, the University of Colorado Boulder and at The University of New Mexico in Albuquerque. Before that Daniel was a postdoc in Mechanical Engineering at Caltech with Tim Colonius. Prior to Caltech Daniel worked at Lawrence Livermore National Laboratory in the Applied Math. group at the Center for Applied Scientific Computing. At LLNL he was a part of the Serpentine project where he and Anders Petersson, Bjorn Sjögreen developed massively parallel numerical methods for seismology. Together with Anders he also developed high order accurate embedded boundary methods for the wave equation. While at LLNL Daniel also worked with Bill Henshaw on simulations of converging shocks and on a parallel overset grid solver for solid mechanics.

Daniel was a Hans Werthen (the founder of Electrolux) Prize postdoc at the Department of Mathematics and Statistics at UNM where he worked with Tom Hagstrom on a general formulation of perfectly matched layer models for hyperbolic-parabolic systems and Hermite methods.

Daniel obtained a PhD in Numerical Analysis at NADA, KTH under the supervision of Gunilla Kreiss. His thesis considered different aspects of the perfectly matched layer method. It turned out that the well-posedness of general pml models could always be guaranteed by a parabolic complex frequency shift and that stability can be established for a certain class of hyperbolic systems.

Dr. Roummel Marcia, UC Merced

Abstract

In everyday life, we are constantly inundated with digital signals and, in particular, images, from web browsing and video meetings to movie streaming and video gaming. These signals can carry large volumes of data, but the information they contain are often redundant, meaning they have inherent structures that can be exploited to facilitate storage and transfer. In this talk, I will discuss some of the mathematics underlying image processing techniques (specifically linear algebra and optimization) and describe how they can be used in several important applications.

Spring 2023

Shiyun Wang, USC

Abstract

This talk presents my collaborative work that extends the current investigations on the (3+1)-free posets conjectures by Stanley-Stembridge and Shareshian-Wachs with the q-parameterized version. We expand the chromatic symmetric functions for Dyck paths of bounce number three in the elementary symmetric function basis using a combinatorial interpretation of the inverse of the Kostka matrix studied in Egecioglu-Remmel (1990). We construct sign-reversing involutions to prove that certain coefficients in this expansion are positive. We use a similar method to establish the e-positivity of chromatic symmetric functions for Dyck paths of bounce number three beyond the “hook-shape” case of Cho-Huh (2019). Our results provide more supportive evidence for the Stanley-Stembridge Conjecture by extending the e-positive class of the incomparability graph of natural unit interval orders.

Bio Sketch

Shiyun Wang's educational background includes a B.A. in management from Central South University in China, a Master of Public Administration from the University of Southern California (USC), and an M.S. in Mathematics from �� (��). She is a Ph.D. candidate in mathematics at USC and will join the University of Minnesota as a postdoc this fall. Shiyun has developed research interests in algebraic and enumerative combinatorics, tableaux combinatorics, symmetric functions, and quasi-symmetric functions in relation to representation theory. Her current work focuses on chromatic quasisymmetric functions and row-strict dual immaculate functions with connections to 0-Hecke algebra.

Dr. Cash Bortner, CSU Stanislaus

Abstract

Since Recovering parameter values from mathematical models is a primary interest of those that use them to model the physical and biological world. This recovery, or identification, of parameters within models is also an interesting mathematical problem that we call Identifiability. In this talk, we will explore the identifiability of a specific type of model called Linear Compartmental Models, which are often used to understand biological phenomena and have an underlying graphical structure. Starting with an introduction to graph theory, we will explore the relationship that this graphical structure has to Linear Compartmental Models and their defining differential equations. At the end of the talk, we classify identifiability criteria for an interesting subclass of Linear Compartmental Models called tree models.

Dr. Yat Sun Poon, UC Riverside

Abstract

Since the success of Nomizu in 1954 in showing that the DeRham cohomology on compact nilmanifolds are given by invariant differential forms, there have been many attempts to accomplish the same on various cohomology theories on compact complex manifolds. After a brief review of such accomplishments, we focus on the role of abelian complex structures in both the classical and modern perspectives. Our goal is to present a few issues for consideration within the realm of Hitchin's generalized geometry, a geometry that encompass both complex and symplectic structures.

Bio Sketch

Dr. Yat Sun Poon obtained his Ph.D. degree from Oxford University in 1985 under the direction of Dr. Nigel Hitchin. Dr. Poon's research program anchors in mathematical physics as developed by Atiyah, Hitchin, and Penrose, especially on quantum gravity, twistor theory, monopole, and string theory. In recent years, his research focus is on the deformation theory of generalized comple geometry. He is currently an editor for the journal Complex Manifolds.

Dr. Siqi Fu is a Professor and the Chair of the Department of Mathematical Sciences at Rutgers University, Camden. He received his Ph.D. degree in Mathematics from Washington University in St. Louis under the supervision of Steven George Krantz. Professor Fu was a recipient of an American Mathematical Society Centennial Research Fellowship in 2000.

Dr. Fu's research interest is spectral analysis of partial differential operators and geometric analysis in several complex variables. The basic theme is to study the interplay among geometric, analytic, and algebraic structures of a complex manifold.

Dr. Jessi Lajos, Colorado State University

Abstract

In this descriptive case study, we explored how an embodied cognition researcher integrated embodiment beyond gesture as she taught a first semester abstract algebra course. We found that this instructor intentionally used embodiment to motivate and ground formal definitions, theorems, and proofs. In addition to her use of gesture, she encouraged students to interact with physical materials and simulate the mathematics with their bodies. Simulations opened communication lines between the instructor and students, who were not fluent in formal language. Furthermore, the instructor's simultaneous use of various forms of embodiment highlighted and disambiguated referents of student's speech, positioned students' contributions as legitimate, and carried forth students' theories. Our results offer practical implications for teaching by illustrating examples of how embodiment can be incorporated into an abstract algebra classroom.

Bio Sketch

Dr. Jessi Lajos is a postdoctoral scholar at Colorado State University, specializing in undergraduate abstract algebra education.

Dr. Jim Stein, CSU Long Beach

11/8/2022 Presentation Slides (PDF)

Abstract

This talk will explore three related problems in probability in which a simple technique can be used to improve one's chances of making the correct guess in what initially appears to be a 50-50 situation. The talk can be understood by anyone familiar with the fact that for two independent events A and B, P(AnB) = P(A)P(B) -- and even if you're not familiar with that there's better than a 50-50 chance you will enjoy the talk.

Problem I - Blackwell's Bet

You have two envelopes with differing sums of money. You open one of them, look at the amount of money in it, and are offered the following choice - you can either keep the money in the opened envelope, or take the money in the unopened envelope. There's a really cute and simple technique, often ascribed to David Blackwell, of making your choice in such a way that you have better than a 50-50 chance of choosing the larger of the two amounts.

Dr. Neha Murad is an Applied Mathematician with a Ph.D. in Biomathematics and a minor in Statistics from North Carolina State University. She is a senior data scientist in the Translational Computing team at Calico Life Sciences, where she uses a combination of epidemiological, bioinformatics and QSP models and tools to understand the biology that controls aging and lifespan. Prior to Calico, Neha was a postdoc at GSK where she was part of the Pharmacokinetics (PK) team and used systems models in combination with machine learning approaches to build Physiologically Based Pharmacokinetic (PBPK) Models.

Priyanga Ganesan is a fifth year doctoral student at Texas A&M University working with Dr. Michael Brannan. Her research explores the interaction between operator algebras and quantum information theory through the study of quantum graphs and non-local games. Before starting her Ph.D., she completed an integrated Bachelors-Masters degree in Mathematics at the National Institute of Science Education and Research in India. She is actively involved with several diversity programs in mathematics, and has also served as the President of the TAMU Association for Women in Mathematics graduate student chapter, board member of the worldwide Operator Algebras Mentor Network, and co-founded an I DP program for Math graduate students at Texas A&M.

Dr. Xiaodong Yan is a math professor in the University of Connecticut. Her research area is nonlinear partial differential equations. She is mainly interested in regularity issues and pattern formations for nonlinear PDEs coming from continuum mechanics and materials science. Yan gets her Ph.D from University of Minnesota with the advising of Vladimir Sverak. Before joining UCONN, Yan worked as a postdoc in the Courant Institute of Mathematical Sciences and assistant professor in Michigan State University.

Dr. Adi Tcaciuc, Department of Mathematical and Statistical Sciences, MacEwan University.

Abstract

The Invariant Subspace Problem is one of the most famous problem in Operator Theory, and is concerned with the search of non-trivial, closed, invariant subspaces for bounded operators acting on a separable Banach space. Considerable success has been achieved over the years both for the existence of such subspaces for many classes of operators, as well as for non-existence of invariant subspaces for particular examples of operators. However, for the most important case of a separable Hilbert space, the problem is still open.

The social structure of a population can often influence movement and inform researchers on a species' behavioral tendencies. Social networks can be studied through movement data; however, modern sources of data can have complex patterns of missingness that are not straightforward to address using existing methods. For example, drone-gathered observations of trajectories, while highly precise, can introduce labeling issues when individuals in a study population move in and out of the camera's active field of view. When individuals cannot be uniquely identified visually, multiple labels may be assigned to a single individual. Since all available social movement models rely on unique identification of all individuals in the population, we extend an existing Bayesian hierarchical movement model that makes use of a latent social network to accommodate "multiply-labeled" movement data. We apply our model to drone-gathered observations of dolphins to study the effect of sonar exposure on the dolphins’ social structure. Our proposed framework can be applied to all unlabeled movement data for various social movement applications and has potential implications for the study of privacy-protected movement data.

Dr. Estrella Johnson, Department of Mathematics, Virginia Tech ()

Abstract

Inquiry-oriented instruction has shown promise in regards to many features of student success, including conceptual understanding, affective gains, and persistence in STEM degrees. However, instructional change is difficult (especially at scale) and the research literature has documented a number of challenges instructors face when shifting their instructional practice. During this talk I will provide a characterization of inquiry-oriented instruction; discuss an instructional support model that was developed to support inquiry-oriented instruction in undergraduate mathematics courses; and present preliminary evaluation findings, drawing on a national sample of content assessment data, collected from 513 students at 46 different institutions. Analysis of this assessment data revealed no difference in the performance of men and women in the comparison sample; however, under the inquiry-oriented treatment, a gender performance difference was present - with men outperforming women. In an effort to understand this finding, I present related research literature on gendered experiences in collaborative settings and some of our ongoing analysis into the experiences of our students in these inquiry-oriented courses.

Bio Sketch

Dr. Johnson is the Director for Inclusion and Diversity for the College of Science, and a Associate Professor of mathematics, at Virginia Tech. Her research focuses on the pedagogical practices of mathematicians, with the goal of better understanding and supporting high quality, ambitious teaching in undergraduate mathematics classrooms. She has worked extensively on investigating and supporting mathematicians as they work to implement inquiry-oriented instructional materials (NSF #143195). Additionally, Dr. Johnson has worked on large-scale national survey projects investigating instructional practice, and influences on practice, in undergraduate STEM education (e.g., NSF #1430540, NSF #0910240, NSF #1726281).

Dr. Xiaochuan Tian, Department of Mathematics, UC San Diego

Abstract

Nonlocal continuum models are in general integro-differential equations in place of the conventional partial differential equations. While nonlocal models show their effectiveness in modeling a number of anomalous and singular processes in physics and material sciences, for example, the peridynamics model of fracture mechanics, they also come with increased difficulty in computation with nonlocality involved. In this talk, we will give a review of the asymptotically compatible schemes for nonlocal models with a parameter dependence. Such numerical schemes are robust under the change of the nonlocal length parameter and are suitable for multiscale simulations where nonlocal and local models are coupled. We will discuss finite difference, finite element and collocation methods for nonlocal models as well as the related open questions for each type of the numerical methods.

Dr. Katherine Kinnaird, Smith College. ()

Abstract

Data science seems to be everywhere these days. This talk will discuss examples of data science being applied to music and TED talks, as well as introducing publicly available resources for exploring culturally motivated data. This talk will delve deeply into the multidisciplinary field of Music Information Retrieval (MIR) motivated by the comparisons that we, as humans, make about music and the various contexts of these comparisons. By defining tasks such as building better song recommendation systems or finding structural information in a given recording, MIR seeks to algorithmically make these musical comparisons in the same manner that a human being would, but on a much larger scale. In this talk, we will introduce the field of MIR, including popular tasks and cutting edge techniques, including aligned hierarchies, a structure-based representation that can be used for comparing songs, and new extensions of aligned hierarchies that leverage ideas from topological data analysis.

Dr. Michael Barany, History of Science, University of Edinburgh ()

Abstract

If mathematics is in principle universal, mathematicians certainly are not. The striking demographic differences between the world of mathematicians and the world at large are a product of the history of where and how mathematicians have been trained, supported, and celebrated. In the twentieth century, a particular image of mathematics as a "young man's game" came to dominate both popular images of mathematicians and many mathematicians' own ideas of who can do mathematics and how. I will identify specific historical circumstances and developments that made mathematics appear to be a "young man's game" in the context of the politics and institutions of an internationalizing discipline. These circumstances converge in the quadrennial International Congresses of Mathematics and the history of the Fields Medal, which has become an accidental symbol of the preeminence of young men in modern mathematics. Recognizing the history, contingency, and politics of this dominant mathematical identity and image can offer a means of understanding and confronting present and future challenges around identity and diversity that continue to matter for mathematics and mathematicians.

Dr. Ying-Fen Lin is a Senior Lecturer in the School of Mathematics and Physics at Queen's University Belfast. She obtained her PhD in 2005 from National Sun Yat-Sen University. Her research interests are in the areas of Operator Algebras, Abstract Harmonic Analysis, Linear Preservers and their interactions. More specifically, she is interested in operator algebras arising from locally compact groups, and in their concrete descriptions in terms of operator fields, as well as their rigidity properties.

Naneh Apkarian (Arizona State University)

Abstract

Undergraduate mathematics teaching and learning are cultural activities, situated within communities. Understanding aspects of these communities and their cultures can reveal much about how current practices work, and how we might change them for the better. This seminar will include: an overview of relevant theories; how to gather and interpret social network data related to education; and results from research studies.

Much of the talk will center on an investigation of instructional leadership at five university mathematics departments, in the context of lower-division mathematics courses. Guided by sociocultural theories, we use social network analysis to identify patterns of influence on instruction using the relations: seeking advice, sharing instructional materials, discussing instructional matters, and explicitly influencing teaching approach. Analysis of social network data gathered through surveys indicates that in these five communities, not all those with hierarchical authority have real influence over instructional practice, but those with the most influence over instruction do hold formally recognized positions.

Diversity and inclusion projects to support aspiring and current mathematicians from marginalized communities are often framed through some need for diversity and inclusion to advance the fields of mathematics. However, these conversations often fail to center the needs and goals of marginalized and underrepresented communities. In this talk, I discuss diversity and inclusion initiatives through a lens that is informed by frameworks that identify mathematics education as settler colonialism and my own experiences of inclusion/exclusion.

I call for a shift in the ways we can frame conversations of justice, equity, diversity, and inclusion in community college settings by asking: How do diversity and inclusion efforts in mathematics and mathematics education directly empower marginalized communities?

Nan Hu (Genentech Inc.)

Abstract

This talk will give you a sneak peak of how applied mathematics and statistics are used in the biotech industry. I will first introduce an important statistical model in late-phase clinical trials: random coefficient regression model (RCRM). Through an examination of the RCRM, this talk then illustrates how mathematics can influence key decisions in a biotech company. I will also discuss the skillset needed for an industry job and how you can get ready for it as a graduate student. Lastly, a brief description of Genentech will be presented.

About the Presenter

Nan Hu is currently a Principal Statistical Scientist at Genentech Inc. He obtained his Ph.D. in Applied Mathematical & Computational Sciences from the University of Iowa in 2016; he also holds a MS degree in Biostatistics from the University of Iowa.

Over the past ~5 years, Nan has served as the study statistician on multiple Phase I, II, and III Alzheimer’s clinical trials. Nan is currently the project lead statistician on crenezumab Alzheimer’s program, serving as a member of the Genentech global development team. In early 2019, Nan was a key member coming up with statistical strategies on crenezumab Phase III futility analysis. Nan is also a member of the cross-industry working group on endpoints in early Alzheimer’s disease.

In 2020, Nan also worked as the study statistician on a COVID-19 Phase III clinical trial at Genentech.

Full title: "I Do Think Race and Gender Play a Role… I Would Analyze That Statement and Think, ‘Oh, Should I Not Take STEM?'”: Problematizing Neutrality in Undergraduate Calculus Instruction Entrenched in Racialized-Gendered Logics and Mechanisms of Inequality

Dr. Luis Leyva (Vanderbilt University)

Abstract

In this presentation, I characterize seemingly neutral features of undergraduate calculus instruction that insidiously contribute to the well-documented function of calculus in higher education as a racialized-gendered gatekeeper of advanced mathematics coursework and STEM majors. Drawing on published analyses of student interviews based on journaling of instructional events in calculus classrooms, I present how underrepresented students perceived seemingly neutral instructional practices as being entrenched in exclusionary logics that collide with stereotypes and other sociohistorical forces to fuel racialized-gendered mechanisms of inequality in student outcomes. In particular, my analyses revealed two logics in calculus instruction — (i) Instructors hold more mathematical authority than students; and (ii) Calculus is used to weed out students ’not cut out’ for STEM success — that underrepresented students perceived as producing inequitable opportunities for classroom participation, support from instructors and same-race/same-gender peers, and persistence in the calculus sequence and STEM majors. Throughout the presentation, I illustrate how ideologies of colorblindness and gender neutrality rooted in white supremacy and patriarchy, respectively, justify seemingly neutral instructional practices that have academically and socially damaging impacts on underrepresented students. I conclude the presentation by highlighting implications for practice in mathematics departments to support faculty with engaging in critical reflection and inquiry of their instructional practices, especially in introductory courses, that disrupt mechanisms of inequality rooted in white, patriarchal logics.

Dr. Hsioa-Fan Liu (Tamkang University, Taiwan)

Abstract

The Sine-Gordon equation was discovered in the 19 century and S. S. Chern in 1981 gave a geometric interpretation of solutions to the Sine-Gordon equation, that is the pseudosphere. This relates partial differential equations and differential geometry. Such relation gives rise to the study of integrable systems and geometries. In this talk, we will recall the history of the Sine-Gordon equation and the pseudosphere at first. Then we will introduce some related and generalized questions with the known results. In the end, we will discuss our recent results on Heisenberg groups in this direction.

About the Presenter

Hsiao-Fan Liu is an Assistant Professor of Mathematics at Tamkang University, Taiwan. Her research interests lie at differential geometry, PDE and discrete mathematics, especially integrable geometric curvature flows and integrable systems. She earned a PhD in mathematics from UC Irvine in 2014 (with Chuu-Lian Tern). Before joining Tamkang University, she has worked in Institute of Mathematics, Academia Sinica, Taipei and National Tsing Hua University as posdoc.

Dr. Chris Marx, Oberlin College

Abstract

In this talk we will explore the dependence of the density of states for Schrödinger operators on the potential. The density of states characterizes the averaged spectral properties of a quantum system. Formally, it can be obtained as an infinite volume limit of the spectral density associated with finite-volume restrictions of a quantum system. Such limit is known to exist for certain quantum mechanical models, most importantly for Schrödinger operators with periodic and random potentials.

Following ideas by J. Bourgain and A. Klein, we will consider the density of states outer measure (DOSoM) which is well defined for all Schrödinger operators. We will explicitly quantify the parameter dependence of the DOSoM by proving a modulus of continuity with respect to the potential (in $L^\infinity$-norm and weak topology). This result is obtained for all discrete Schrödinger operators on infinite graphs and captures the geometry of the graph at infinity.

This talk is based on joint work with Peter Hislop (University of Kentucky).

About the Presenter

Chris Marx is an Associate Professor of Mathematics at Oberlin College. His research interests lie at the intersection of analysis and mathematical physics, more specifically in spectral theory of Schrödinger operators. He earned a masters degree in theoretical and physical chemistry at the University of Vienna, Austria in 2007, and a PhD in mathematics from UC Irvine in 2012 (with S. Jitomirskaya). From 2012 to 2014, he held a postdoctoral position at Caltech as Harry Batement Instructor with Barry Simon. Since 2014 he has taught at Oberlin College, with promotion to Associate Professor in June 2020. In his spare time, Chris is a passionate amateur musician (harpsichord and voice), with a keen interest in early music and historical performance technique.

Fall 2020

Dr. Carrie Diaz Eaton, Bates College

Abstract

We are in a new age of digital information. Information is a form of power, and our students consume and produce more unfiltered information than ever. They need agency as individuals and tools as members of a future workforce to ethically and responsibly process this information. What is the role of mathematics instruction in helping students in their role as a digital citizen? I talk about my journey to developing an information literacy course using Open Educational Resources, including Calling Bull, Figure of the Day, and RStudio. This course serves as a forum to think meaningfully about probability, data analysis, and data visualization, a gentle introduction to programming, and a context to examine the interplay of information, power, and social justice. It also asks students to use these tools to explore and develop their own agency as a digital citizen.

About the Presenter

Dr. Carrie Diaz Eaton's research in undergraduate interdisciplinary STEM education is grounded in community network theory and analysis. As an Associate professor of Digital and Computational Studies at Bates College in Maine, Dr. Diaz Eaton co-leads a number of digital community projects such as QUBES Director of Partnerships (Quantitative Undergraduate Biology Education and Synthesis) and Math Mamas. Carrie Diaz Eaton currently serves as the Chair for the Committee for Minority Participation in Mathematics for the Mathematical Association of America [MAA], is a MAA blogger for MathValues, and serves on the Editorial board of PRIMUS and CourseSource. She has also served as the past Program Chair and Electronic Communications Chair of BIO SIGMAA, as Education Subgroup Chair for the Society of Mathematical Biology, and for the editorial board for Letters in Biomathematics.

In 2012, Dr. Diaz Eaton was an MAA Project NExT Fellow, and in 2018 was selected as a Linton-Poodry SACNAS Leadership Institute Fellow. In 2020, Dr. Diaz Eaton was awarded the Society for Mathematical Biology John Jungck Excellence in Education Prize to recognize her for her work in interdisciplinary computational and mathematical biology education and mentorship. Dr. Diaz Eaton is also a proud 1st generation Latinx - her father is from Peru. She is also a mother. Dr. Diaz Eaton values the complex interplay at the intersection of her identities, professional activism in STEM education, and her research.

Kari Eifler, Texas A&M

We describe several aspects of an analytic/geometric framework for the three-dimensional Navier-Stokes regularity problem, which is directly inspired by the morphology of the regions of intense vorticity/velocity gradients observed in computational simulations of three-dimensional turbulence. Among these, we present our proof that the scaling gap in the 3D Navier-Stokes regularity problem can be reduced by an algebraic factor within an appropriate functional setting incorporating the intermittency of the spatial regions of high vorticity.

About the Presenter

Aseel Farhat finished her PhD work in the Department of Mathematics at University of California Irvine in 2012. She was a Zorn Postdoctoral Fellow in the Department of Mathematics at Indiana University Bloomington between 08/2012 and 08/2015, and later joined the Department of Mathematics at University of Virginia as a Whyburn Instructor (Postdoc) till 08/2018. She is currently an Assistant Professor in the Mathematics Department at the Florida State University.

Abstract

Insurance is a contractual promise to reimburse policyholders for future losses. Consumers often comment that they don't understand their insurance rates – it all seems very mysterious to them. But in reality, creating insurance rates is very logical when broken down into its component parts. The fundamentals of insurance ratemaking are very similar to the pricing of many other products, i.e., understanding cost and determining a target profit load. The major difference is that for many products, the cost is easily determined from the manufacturing process. However, for insurance, the cost involves significant uncertainty about the future. This presentation will introduce the audience to fundamental insurance principles and the mystery behind insurance ratemaking.

About the Presenter

Professor Janet Duncan has over 30 years of property/casualty financial analysis experience, including commercial and personal lines reserving and pricing, financial and capital modeling, planning, and management reporting. Janet's work experience includes six years as CNA's senior vice president and signing actuary, responsible for $17 billion of property/casualty reserves, including standard commercial lines, specialty lines, and discontinued operations. Prior to CNA, Janet worked at XL Capital, serving in roles of increasing responsibility including executive vice president and chief finance officer of XL Insurance Europe and Asia. She also worked with PricewaterhouseCoopers LLP (consulting and audit support), and served in various actuarial roles with Aetna Life & Casualty where she began her insurance career. Janet has a bachelor's degree in Math/Actuarial Science from the University of Connecticut. She has served on many actuarial committees including the CAS Committee on Professionalism Education, the CAS Committee on Reserves, the AAA IFRS Task Force, the AAA Opinion Seminar Committee, and the SOA Strategic Planning Task Force. She is now working as a lecturer at the Department of Applied Probability and Statistics at UC, Santa Barbara.

Dr. Gülden Karakök, University of Northern Colorado

Abstract

Numerous reports, policy and standards documents, and research studies emphasize the importance of creativity. For example, the recent report from the World Economic Forum noted that creativity at work is one of the top-three demanded skills, and that it "has jumped from 10th place to third place in just five years" (Schöning & Witcomb, 2017, para. 12). Within the domain of mathematics, similar emphases are made by mathematicians, mathematics education researchers and policy/standards makers. For example, the Mathematical Association of America's (MAA) CUPM Curriculum Guidelines (Schumacher & Siegel, 2015) for majors in the mathematical sciences states that "a successful major offers a program of courses to gradually and intentionally lead students from basic to advanced levels of critical and analytical thinking, while encouraging creativity and excitement about mathematics" (p. 9). In this talk, I will briefly summarize some of the research on mathematical creativity at the K-16 levels and introduce the work of the Creativity Research Group focusing on undergraduate mathematics courses. Our research group aims to explore ways in which undergraduate students' mathematical creativity can be fostered and explicitly valued in mathematics courses that include proof-construction and/or problem solving activities. I will introduce the Creativity-in-Progress Reflections (CPR) on Proving and Problem Solving tools that we designed. These formative assessment tools were created to enhance mathematical creativity (of users) while facilitating proof-construction and problem-solving heuristics as well as fostering metacognition. With two categories, Making Connections and Taking Risks, these formative assessment tools aim to develop mathematical discourse centered around aspects of creativity related to fluency, elaboration, flexibility, and originality. I will provide some examples of how one might implement these tools in various mathematics courses as well as discuss some illustrative empirical examples from our research studies.

Spring 2020

Note: Most of the Colloquia were cancelled due to COVID-19.

Spring 2020 Colloquia
Date	Title	Speaker and Affiliation
January 31, 2020	Radar Topics with Quantitative Examples	Tim Rambach, Retiree from Raytheon

Fall 2019

Fall 2019 Colloquia
Date	Title	Speaker and Affiliation
November 22, 2019	Region Coverage from a Satellite ... (Insight into Industrial Mathematics)	Dr. Gary Green, retired from Aerospace Corporation
November 19, 2019*	Learning turbulence from deep learning	Dr. Alessandro Corbetta, Eindhoven University of Technology
November 15, 2019	Bayesian Sparse Functional Principal Components Analysis Models Dynamic Temporal Changes in Longitudinal Microbiome Studies	Lingjing Jiang, UC San Diego
November 8, 2019	Applications of Mathematics in Telecommunications	Dr. Shabnam Sodagari, CSU Long Beach
November 1, 2019	Energy Stable Semi-Implicit Schemes for Allen-Cahn-Ohta-Kawasaki Model in Binary/Ternary System	Dr. Yanxiang Zhao, George Washington University
October 25, 2019	On the interplay of functional analysis and operator theory	Dr. Yunied Puig de Dios, UC Riverside
October 11, 2019	Property/Casualty Insurance Loss Reserving Methods	Janet Duncan, UC Santa Barbara
October 4, 2019	Impacts of Cellular Heterogeneity on Hair Follicle Growth Dynamics	Dr. Qixuan Wang, UC Riverside
September 27, 2019	Modeling Colony Pattern Formation under Differential Adhesion and Cell Proliferation	Dr. Jiajia Dong, Bucknell University

Summer 2019

Summer 2019 Colloquia
Date	Title	Speaker and Affiliation
June 3, 2019	Pseudocompact spaces -- Various Characterizations	Dr. Sudip Kumar Acharyya, University of Calcutta, India

Spring 2019

Spring 2019 Colloquia
Date	Title	Speaker and Affiliation
May 3, 2019	The Teichmüller TQFT	Dr. Jørgen Ellegaard Anderson, Aarhus University, Denmark
April 19, 2019	Chemical Reactions and Diffusions	Dr. Peyam Tabrizian, UC Irvine
April 12, 2019	Free-boundary Minimal Surfaces in the 3-ball with Connected Boundary	Dr. David Wiygul, CSU Long Beach
March 8, 2019	Expanding Competence: Uncovering the Possibilities of Children’s Mathematical Thinking	Dr. Nick Johnson, UCLA

Fall 2018

Fall 2018 Colloquia
Date	Title	Speaker and Affiliation
October 19, 2018	Mathematical Models of Human Immunodeficiency Virus Reservoirs	Dr. Naveen Vaidya, CSU San Diego
October 12, 2018	Fibonacci and Lucas Analogues of Binomial Coefficients and What They Count	Dr. Curtis Bennett, CSU Long Beach

Summer 2018

Summer 2018 Colloquia
Date	Title	Speaker and Affiliation
June 14, 2018	Characterizing pseudocompact spaces in terms of C-type intermediate rings	Sudip Kumar Acharyya, University of Calcutta, India
June 8, 2018	Abundance of nonisomorphic intermediate rings of continuous functions	Sudip Kumar Acharyya, University of Calcutta, India

Spring 2018

Spring 2018 Colloquia
Date	Title	Speaker and Affiliation
April 27, 2018	Study Gene Regulatory Networks Using Boolean Models	Dr. Yi-Ming Zou, University of Wisconsin-Milwaukee
April 20, 2018	New Ranking Measures and Algorithms for Expanding Robust Group Decision-Making Frameworks	Dr. Adolfo Escobedo, Arizona State University
April 18, 2018	Geometric Recursion	Dr. Jørgen Ellegaard Andersen, Aarhus University, Denmark
April 13, 2018	CNSM Munch N' Learn. Students Speak: What Professors Should Know	Students, CSU Long Beach
April 6, 2018	Finitely Additive Invariant Set Functions and Paradoxical Decompositions, or: How I Learned to Stop Worrying and Love the Axiom of Choice	Dr. Adam D. Richardson, CSU Long Beach
March 16, 2018	How to Predict the Fate of Schrodinger's Cat	Dr. Jim Stein, CSU Long Beach
February 23, 2018	Expansion Dynamics of Bacterial Populations	Dr. Jonas Cremer, UC San Diego
February 16, 2018	RNA secondary structures enumeration and prediction and their relation to moduli spaces	Dr. Jørgen Ellegaard Andersen, Aarhus University, Denmark
February 9, 2018	Interpolation of Manifold-Valued Functions	Dr. Evan Gawlik, UC San Diego
February 2, 2018	Discrete Means: generalizing a theorem of Kolmogorov and social choice	Dr. Curtis Bennet, CSU Long Beach

Fall 2017

Fall 2017 Colloquia
Date	Title	Speaker and Affiliation
December 1, 2017	Minimization of inhomogeneous biharmonic eigenvalue problems	Dr. Chiu-yen Kao, Claremont McKenna College
November 3, 2017	Distribution of Descents in Matchings	Dr. Gene Kim, USC
October 27, 2017	From Arrow's Social Choice Theorem to the compelling "dark matter" mystery	Dr. Donald Saari, UC Irvine
October 20, 2017	Shooting from singularity to singularity and a semilinear Laplace-Beltrami equation	Dr. Alfonso Castro, Harvey Mudd College
October 6, 2017	Mathematical Structures: Up Close and Afar	Dr. Stacy Musgrave, Cal Poly Pomona
September 22, 2017	From Macro to Micro and Back: Complexity, Simplicity and Optimality of Bacterial Cells	Dr. Matteo Mori, UC San Diego

Spring 2017

Spring 2017 Colloquia
Date	Title	Speaker and Affiliation
June 8, 2017	Relation between z-ideal and z^0-ideals in intermediate ring of continuous functions	Dr. Sudip Acharyya, University of Calcutta, India
June 6, 2017	Some new results on real valued continuous functions on a space X whose support lie on ideals of closed sets in X	Dr. Sudip Acharyya, University of Calcutta, India
May 5, 2017	Proof Comprehension at the Undergraduate Level: An Exploratory Study	Dr. Eyob Demeke, CSU Los Angeles
April 14, 2017	Spectra of compact composition operators on bounded symmetric domains	Dr. Dana Clahane, Fullerton College
March 17, 2017	Using Visual Art, Crafts and Music to Demonstrate Mathematics	Dr. Benjamin Dyhr, Metropolitan State University

Fall 2016

Fall 2016 Colloquia
Date	Title	Speaker and Affiliation
December 2, 2016	Non-Locality, Contextuality, and Topology	Dr. Kohei Kishida, University of Oxford
November 18, 2016	Outer Space and the Outer Automorphism Group of the Free Group	Dr. Catherine Pfaff, UC Santa Barbara
November 10, 2016	The Remarkable History of Exponents and Logarithms	Dr. Bob Stein, CSU San Benardino
October 28, 2016	Simulating Space: Role of Advanced Modeling and Uncertainty Quantification in JPL Missions	Dr. Lee Peterson, Jet Propulsion Laboratory
October 21, 2016	Data Science, Data Services, a Sabbatical Reflection	Dr. Khue Duong, CSU Long Beach
October 11, 2016	Lipschitz metric for a nonlinear wave equation	Dr. Geng Chen, University of Kansas
September 23, 2016	JPL Robotics	Dr. Gabriel Udomkesmalee, Jet Propulsion Laboratory
September 2, 2016	Nuclear Engineering for Everyone	Dr. Minh N. Tran, UC Davis

Spring 2016

Spring 2016 Colloquia
Date	Title	Speaker and Affiliation
May 6, 2016	Clots or not? Mathematics making the invisible visible	Dr. Ami Radunskaya, Pomona College
April 29, 2016	Generalized Wronskians and linear dependence of formal power series	Dr. Wai Yan Pong, CSU Dominguez Hills
April 22, 2016	A Relational Category of Formal Contexts	Dr. M. Andrew Moshier, Chapman University
April 8, 2016	Hearing the Shapes of Surfaces of Revolution	Dr. Thomas Murphy, CSU Fullerton
March 4, 2016	Liberal Arts Math	Dr. Jim Stein, CSU Long Beach
February 19, 2016	Geometry in the Dark Ages: Games of Shadows and Lights	Dr. Bogdan Suceava, CSU Fullerton

Fall 2015

Fall 2015 Colloquia
Date	Title	Speaker and Affiliation
November 13, 2015	Part I: Collaborative Filtering and the Yelp Dataset Part II: Python Introduction	Students, CSU Long Beach
October 30, 2015	Two Applications of the Arithmetic of Elliptic Curves	Dr. Jasbir Chahal, Brigham Young University
October 23, 2015	Compact manifolds with integral bounds on the negative part of Ricci curvature and the Kato class	Dr. Christian Rose, Technische Universität Chemnitz
October 16, 2015	From Residuated Lattices to Boolean Algebras with Operators	Dr. Peter Jipsen, Chapman University
October 9, 2015	Energy driven pattern formation in thin fluid layers: The good, the bad and the beautiful	Dr. Andrew J. Bernoff, Harvey Mudd College
September 11, 2015	Numerical Simulation of Solvent Stokes Flow and Solute-Solvent Interface Dynamics	Dr. Hui Sun, UC San Diego

Spring 2015

Spring 2015 Colloquia
Date	Title	Speaker and Affiliation
May 15, 2015	Old and New Approximations for Bessel Functions	Dr. Mark Dunster, CSU San Diego
April 24, 2015	Alternating Volume, a Hyperbolic Invariant of Knots	Heidi Furlong and Leslie Rodriguez, CSU Long Beach
April 17, 2015	Analysis of 2+1 Diffusive-Dispersive PDE Arising in River Braiding	Dr. Charis Tsikkou, West Virginia University
March 27, 2015	Graph Representatives of Positroid Strata	Dr. Michaela (Puck) Rombach, UCLA
March 13, 2015	Can one hear the shape of a drum?---An Introduction to spectral theory in math physics	Dr. Shiwen Zhang, UC Irvine
March 6, 2015	Crimes with Undergraduates	Dr. Scott McCalla, Montana State University
February 27, 2015	Mathematica 10 & Wolfram Alpha Pro	Paul Fish, Wolfram Technologies in Education and Research
February 20, 2015	The Differential Geometry of the Maxwell Equations	Dr. Casey Kelleher, UC Irvine

Fall 2014

Fall 2014 Colloquia
Date	Title	Speaker and Affiliation
December 5, 2014	A Nonlinear Model for Tumor Growth: Global in time weak solutions	Dr. Konstantina Trivisa, University of Maryland
November 14, 2014	Dynamics of a soccer ball	Dr. Scott Crass, CSU Long Beach
November 7, 2014	Secure Computation and its Applications	Dr. Mehrdad Aliasgari, CSU Long Beach
October 17, 2014	How Wide is a 3-Manifold?	Dr. Diane Hoffoss, University of San Diego
October 10, 2014	Variational image segmentation with dynamic artifact detection and bias correction	Dr. Dominique Zosso, UCLA
October 3, 2014	Topic Point Processes	Dr. Blake Hunter, Claremont McKenna College
September 26, 2014	Knots, Fiber Surfaces, and the Building Blocks of Life	Dr. Matt Rathbun, CSU Fresno
September 19, 2014	Geotagging One Hundred Million Twitter Accounts with Total Variation Minimization	Dr. Ryan Compton, HRL Laboratories
September 12, 2014	An invitation to Floer homology	Dr. Ko Honda, UCLA

Spring 2014

Spring 2014 Colloquia
Date	Title	Speaker and Affiliation
May 9, 2014	Topological symmetry groups	Dr. Erica Flapan, Pomona College
May 2, 2014	Recent results on axially symmetric Navier-Stokes equations	Dr. Qi Zhang, UC Riverside
April 17, 2014	Geometric Methods for Graph Partitioning	Dr. Braxton Osting, UCLA
February 28, 2014	The Sound of Symmetry	Dr. Zhiqin Lu, UC Irvine

Fall 2013

Fall 2013 Colloquia
Date	Title	Speaker and Affiliation
December 6, 2013	Augmented Birack Homology	Dr. Sam Nelson, Claremont McKenna College
November 15, 2013	A Generalized Left-to-Right (GLR) parser for Tree-Adjoining Grammars (TAG) using Matrices	Nen Huynh, CSU Long Beach
November 8, 2013	Involutory Quandles of Knots	Dr. Jim Hoste, Pitzer College
October 25, 2013	Categorification and the Alexander polynomial	Dr. Kristen Hendricks, UCLA
October 11, 2013	From Soap Films to the Shape of Space	Dr. David Bachman, Pitzer College
October 4, 2013	An Illustrated Approach to Special Relativity and Its Paradoxes	Dr. John dePillis, UC Riverside
September 27, 2013	Adventures in Noether-Lefschetz Theory II: Base Loci, Singularities, and Class Groups both Geometric and Algebraic (Joint work with Scott Nollet at TCU)	Dr. John Brevik, CSU Long Beach
September 20, 2013	Kauffman Brackets on Surfaces	Dr. Francis Bonahon, USC
September 6, 2013	Adventures in Noether-Lefschetz Theory I: Curves, Surfaces, and Curves on Surfaces	Dr. John Brevik, CSU Long Beach

Spring 2013

Spring 2013 Colloquia
Date	Title	Speaker and Affiliation
May 3, 2013	A Brief Overview of Financial Mathematics	Dr. Triet Pham, USC
April 19, 2013	Using Forcing to Obtain a Model of the Continuum Hypothesis	Dr. Cynthia Northrup, UC Irvine
April 12, 2013	Cardiovascular Event Risk Dynamics Over Time in Older Patients on Dialysis: A Generalized Multiple-Index Varying Coefficient Model Approach?	Dr. Damla Senturk, UCLA
March 22, 2013	Mathematical Modeling of Language	Dr. Jacquelyn Rische, UC Irvine
February 15, 2013	Incidence Algebras	Dr. Muge Kanuni, Bogazici University, Istanbul, Turkey
February 1, 2013	Digital Microfluidics via Electrowetting	Dr. Ali Nadim, Claremont Graduate University
January 25, 2013	Exploring Ground States and Excited States of Spin-1 Bose-Einstein Condensates	Dr. I-Liang Chern, National Taiwan University

Fall 2012

Fall 2012 Colloquia
Date	Title	Speaker and Affiliation
December 7, 2012	Numerical Modeling of Transport Processes in the Subsurface	Dr. Antonella Sciortino, CSU Long Beach
November 30, 2012	Biomedical signal processing for the improvement of health care of patients with brain-related disorders	Dr. Shadnaz Asgari, CSU Long Beach
November 16, 2012	Machine learning, Balance cut and Total variation	Dr. Thomas Laurent, UC Riverside
November 9, 2012	Statistical Challenges in Molecular Diagnostics	Dr. Ming Ji, CSU San Diego
October 19, 2012	Fluids and Boundaries	Dr. James Kelliher, UC Riverside
September 28, 2012	A Little Big Problem in Graph Theory	Dr. Robert Mena, CSU Long Beach
September 21, 2012	Motion of Fluids in the Presence of a Boundary	Dr. Gung-Min Gie, UC Riverside

Spring 2012

Spring 2012 Colloquia
Date	Title	Speaker and Affiliation
May 4, 2012	Mathematics and Astronomy, Kepler's Laws of Planetary Motion	Dr. Arlo Caine, Cal Poly Pomona
April 20, 2012	Shape optimization problem involving principal eigenvalue in population dynamics	Dr. Chiu-Yen Kao, Claremont McKenna College
April 13, 2012	Helping Ford’s Fleet Customers Reach Their Sustainability Goals Through Optimization	Dr. Daniel Reich, Ford Motor Co. Research and Advanced Engineering
February 24, 2012	How to Distinguish a Football from a Basketball Mathematically	Dr. Jeremy Jankans, UC Irvine
February 17, 2012	Does a Statement of Whether Order Matters in Counting Problems Affect Students' Strategies?	Dr. Todd CadwalladerOlsker, CSU Fullerton
January 27, 2012	Stability theory of polytropic gaseous stars	Dr. Juhi Jang, UC Riverside

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37th Annual ������ Student Research Competition