Student Research
Abra Brisbin
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Research Areas: Mathematical Biology, Probability and Stochastic Processes Advisor(s): Carlos Bustamante Research Description: Tracking the Elusive Gene: I am interested in how to identify genes that are responsible for diseases and other traits. There are good techniques available to do this when the trait is binary--either you have the disease or you don't--but what if there are more possibilities? I'm working on ways to analyze the genotypes of individuals in a family affected by a disease with ordered categories--such as mild, moderate, or severe--to find the genes for that disease. This work draws on techniques from probability, statistics, and computer science. |
Adam Chacon
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Research Areas: Numerical Analysis Advisor(s): Alexander Vladimirsky Research Description: I am studying pdes that describe optimization problems, such as Hamilton-Jacobi equations, and designing numerical methods that combine classical approaches with domain decomposition ideas. |
Christian Kuehn
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Research Areas: Dynamical Systems Advisor(s): John Guckenheimer Research Description: Please refer to my website for a research description and recent publications. |
Christopher Scheper
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Research Areas: Dynamical Systems Advisor(s): John Guckenheimer Research Description: I am working in multiple time scale dynamics, whose systems are also known as fast/slow systems. These particular dynamical systems exhibit many novel types of behaviors including canards, mixed-mode oscillations, and relaxation oscillations. My research involves fast/slow dynamics in chemical oscillators. |
Daniel Romero
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Research Areas: Mathematical Biology, Dynamical Systems, Computer Science Advisor(s): Jon Kleinberg Research Description: I am interested in utilizing tools from machine learning, data mining, graph theory, and sociology to study online social and information networks both empirically and theoretically. |
Diarmuid Cahalane
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Research Areas: Mathematical Biology, Dynamical Systems Advisor(s): Veit Elser Research Description: Traditionally, science has taken an "atomizing" approach to figuring out how things work: the hope being that if we understand how the smallest parts work, then we can understand the system as a whole. In many systems, however, putting the small pieces back together has proven to be more difficult than might have been imagined. The collective behavior of the constituent parts is not always obvious from their individual properties. Broadly speaking, I like investigating complex systems and emergent behavior. The notion of populations of (essentially dumb) agents cooperating to achieve collective dynamics more robust or complex than they could achieve in isolation is, to me, intriguing. Whether it’s the population of heterogeneous cells that somehow agrees on the rhythm your heart will beat at, the dynamics governing the emergence of social norms or the mechanisms that allow the bundle of neurons that comprises the human brain to form a cognitive moment, such systems are clearly important and ubiquitous. Needless to say, our current understanding of systems like these leaves much to be desired. When one talks about the emergence of order in large systems (phase transitions et cetera) it sounds like Physics, statistical mechanics. Dynamical systems, it could be argued, are the turf of applied mathematicians. Meanwhile many of the systems to which I have alluded come from biology, sociology, technology and so on. A healthy disrespect for the boundaries of traditional scientific disciplines will be needed if we are to make progress. This interdisciplinary bent has been referred to succinctly as being part of an “era of integrationist science”. Such an era will see significant challenges. While numerical simulation has driven progress in the past, often leading theoretical understanding, many of the systems one would ultimately wish to model are simply too complex or have too many constituents to yield to "brute force" numerical simulation (the human brain is a prime example). New ways to approach the modeling of such systems will need to be devised. |
Duc Tilo Nguyen
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Research Areas: Finance and Economics, Probability and Stochastic Processes Advisor(s): Research Description: Math finance |
Igor Gorodezky
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Research Areas: Computer Science, Discrete Math Advisor(s): David Williamson Research Description: I enjoy studying combinatorics, algorithms, computational complexity, and other topics at the interface between mathematics and theoretical computer science. |
Ilias Bilionis
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Research Areas: Probability and Stochastic Processes Advisor(s): Steve Koutsourelakis Research Description: Multiscale Modeling, Coarce Graining, Machine Learning and applications in material science. Currently developing a statistical scheme to "learn" the strain energy density from atomistic calculations using the Temperature-Related Cauchy-Born rule for different deformation gradients. This would eventually predict the constitutive relation of a given solid and therefore enable us to treat it using finite elements. Applications to crystalline solids (carbon nanotubes, plates, beams etc.). |
Josef Broder
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Research Areas: Mathematical Biology, Dynamical Systems, Algorithms, Computer Science Advisor(s): Paat Rusmevichientong Research Description: Learning theory and online decision problems |
June Andrews
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Research Areas: Mathematical Biology, Algorithms, Numerical Analysis, Optimization Advisor(s): Alexander Vladimirsky Research Description: My research exploits properties of partial differential equations(PDEs) to quickly compute numerical solutions to optimization problems. In particular, the PDEs I look at are first order Hamilton Jacobi equations derived from optimality conditions equivalent to 'shortest path' in physical settings and minimizing expectation in stochastic processes settings. Applications have been the continuous Traveling Salesman Problem, emergency service planning, and factory planning as an example of the Uncertain Horizon Problem. |
Kimberly Weston
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Research Areas: Finance and Economics Advisor(s): Philip Protter Research Description: Math finance |
Lauren Childs
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Research Areas: Mathematical Biology Advisor(s): Steven Strogatz Research Description: Mathematical biology, specifically complex cellular systems. |
Matthew Holden
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Research Areas: Mathematical Biology Advisor(s): Stephen Ellner Research Description: My research entails the population dynamics of invasive species, agricultural pests and their biological control agents. Invasive species can be a leading cause of extinctions and source of economic losses exceeding $120 billion dollars per year. These species often succeed because they lack natural enemies in their new range. Therefore, by introducing an antagonist from the native range, biological control may limit the growth and spread of invaders. However, biological control often is unsuccessful, for reasons that generally are not well understood. Hence, I am interested in studying dynamic models of biological control to help better understand the successes and failures of pest management strategies. |
Michael Cortez
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Research Areas: Mathematical Biology, Dynamical Systems Advisor(s): Stephen Ellner Research Description: I am interested in modeling how rapid evolution affects population dynamics in biological communities. |
Michael McCourt
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Research Areas: Mathematical Biology, Dynamical Systems, Numerical Analysis, Optimization, Computer Science Advisor(s): Charles Van Loan Research Description: Some applications generate systems which are too large to be handled (or even stored) with conventional methods so new approximation techniques need to be designed. My main research right now is the design of a software library similar to BLAS and LAPACK except that it would allow people to handle high dimensional objects. In addition to this, I'm also involved in using radial basis functions for approximation and collocation, and specifically in determining the appropriate scaling parameter for the kernels. |
Nathaniel Karst
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Research Areas: Signal and Image Processing Advisor(s): Research Description: I work at the intersection of electrical engineering and mathematics. Most recently, I've been applying ideas from orthogonal design theory to problems in wireless communications. Using complex orthogonal designs to transmit cellular signals over multiple antennas has been shown to significantly increase performance in channels with multipath fading (e.g., dense urban environments). While these designs were first discovered in the early 20th century, their generalizations and optimizations for use in wireless communications are still an active topic of research. |
Paul Hurtado
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Research Areas: Mathematical Biology, Dynamical Systems Advisor(s): Stephen Ellner Research Description: My research involves using mechanistic models of population-level processes to understand problems in disease ecology in non-human disease systems. Currently, I am working on two projects. One involves using
a model of a pathogen population in a host where it causes an inflammatory disease (based on the House Finch conjunctivitis system)
My interests are broad and encompass various topics in ecology and population biology, however my primary research interests fall into the theoretical population dynamics and infectious disease in "natural" populations. I'm particularly interested in understanding when and how variation among individuals gives rise to population level phenomenon, and how seasonally varying changes in underlying biological processes affect population level dynamics. |
Stefan Ragnarsson
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Research Areas: Numerical Analysis Advisor(s): Charles Van Loan Research Description: My research is on tensor networks and numerical mulitilinear algebra. |
Stephen Moseley
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Research Areas: Mathematical Biology, Probability and Stochastic Processes Advisor(s): Rick Durrett Research Description: I am modeling cancerous cell populations at different mutation levels using branching processes. |
Thanh Nguyen
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Research Areas: Mathematical Biology, Dynamical Systems, Algorithms, Computer Science Advisor(s): Eva Tardos Research Description: I am working on Algorithms and Game Theory. I am especially interested in Algorithm Design for Combinatorial Problems and Mechanisms Design for large systems involving selfish users. |
Timothy Novikoff
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Research Areas: Dynamical Systems Advisor(s): Steven Strogatz Research Description: I'm interested in network theory and dynamical systems. In particular I do research in coupled oscillator theory and dynamics on graphs, and I work on the mathematical modeling of human learning and automated pedagogy. I'm also interested in the communication of mathematics, and in particular using ideas, techniques and technologies from far-flung fields and industries such as user-interface design and show business to enhance the ability of mathematicians and scientists to communicate their ideas. |
Zoryanna Slater
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Research Areas: Finance and Economics, Probability and Stochastic Processes Advisor(s): Robert Jarrow Research Description: Super-replication under constraints (e.g. margin requirements, restrictions on short-selling and borrowing, stochastic volatility) |