Graduate Student Research

Research opportunities for graduate students abound. In addition to working directly with a Physics Department faculty member, graduate students also conduct research with faculty in Astronomy & Astrophysics, Chemistry, Geophysical Sciences, Biological Sciences, Molecular Engineering, as well as at Fermilab, Argonne, CERN, and many other facilities.

In many cases, graduate students can get involved in research immediately upon, and sometime before, beginning their first quarter in the program. The best way for graduate students to get involved in the research of his or her choice is to communicate with the faculty members working in their area(s) of interest to find out how to best proceed based on their specific situations. A great way to explore an experimental research group early-on is to satisfy the experimental physics requirement by doing a year-long project with that group.

Below, you will find a sampling of some of the fore-front-level research being done by our graduate students. You may also view the graduate research archive for previous profiles. Enjoy…


Shanthanu Bhardwaj

Degrees: M.Sc., Indian Institute of Technology-Kanpur, 2007 (Physics)
Graduate Student (2007-pres), Dept. of Physics, James Franck Inst.
ResearchCondensed Matter Theory
Awards: Michelson Fellow, Wentzel Research Prize (Dept. of Physics)
Research Advisor: Ilya Gruzberg, Paul Wiegmann

My research interests lie broadly in theoretical condensed matter physics.  The idea that systems composed of well understood constituents can still behave in ways which are difficult to predict was perhaps most famously expressed in Phil Anderson's "More is Different" mantra.  The variety of electrical behaviour from metals, insulators, and semi-conductors to more  interesting phases like superconductors, and topological insulators in systems made up of electrons and nucleons with all their physics governed by electromagnetism, proves that more is indeed different.

One of the most interesting systems is the critical state of the Integer Quantum Hall Effect.  Although the initial prediction of the quantization of transverse conductivity in the presence of a magnetic field is nearly forty years old, the exact nature of the quantum hall state and the associated critical exponents is still unknown.  My research has largely been in trying to work on understanding this and hopefully connecting it to a conformal field theory that can predict the nature of these critical exponents.  There are several different approaches to this problem, and the one I have been working on is to attempt to describe the behaviour of these systems by using 'network models'.  These simple discrete models - based on Chalker and Coddington's network model to describe the Quantum Hall transition at strong magnetic field - capture the essential physics of the system.  We then attempt to construct such a discrete model that captures all the relevant behaviour of the system we wish to understand and use this to guide us to the appropriate conformal field theory (CFT) describing the transition at the critical point.

Several of the mathematical techniques involved in studying the Quantum Hall Effect are also applicable to other systems of interest in 2-dimensions, and that is one of the future avenues of interest for me.

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Samuel Meehan

- B.S., University of New Hampshire, 2009 (Physics)
- M.S., University of Chicago, 2010 (Physics)
Graduate Student (2009-pres), Dept. of Physics, Enrico Fermi Inst.
Research: Experimental High-energy Physics
Awards: Elsevier Best Poster Award (EPS2013), Nathan Sugarman Graduate Research Award (EFI), Robert Millikan Fellowship (Dept. of Physics), Arts-Sciences Graduate Collaboration Award, Robert G. Sachs Fellowship (Dept. of Physics)
Research Advisor: Mark Oreglia

My research interests lie broadly in the field of experimental high energy particle physics and during my time at the university, I have been involved in the ATLAS collaboration and so have focused on the physics of the Large Hadron Collider (LHC) based in Geneva, Switzerland. The LHC has been used to produce proton-proton collisions at energies four times greater than those at the Tevatron and at a rate that, during one year, delivered twice the amount of data accumulated during the lifetime of the Tevatron. At such high energies, the collisions that occur are between the underlying quarks and gluons within the proton and with such a large dataset, we can study in great detail fundamental physics of the Standard Model that we think we understand and search for physics beyond the Standard Model that may or may not exist.

My work focuses on the latter and I have been involved in two main projects during my time at the university. The first was an analysis of the data collected in 2011 when the collider ran at a 7 TeV center of mass energy. We used the dataset to search for a heavy fourth generation up and down vector-like quark that couple to the standard model through the W and Z bosons. This type of new particle appears in many new physics scenarios including extra dimensions and in the absence of super-symmetry, such heavy quarks can help to stabilize the Higgs mass against perturbative corrections. The second project in which I am involved is searching for massive resonances that couple to pairs of massive bosons, whether those pairs involve W's or Z's.   This is well motivated from beyond the Standard Model physics scenarios involving Randall-Sundrum gravitons produced in warped extra dimensions and grand unified theories that posit the existence of heavy partners of the W boson, but the approach we take is agnostic in that it focuses on the distinct experimental signature left by the decays of such particles. Namely, for very massive (~1 TeV) new particles, the intermediate bosons produced will be so energetic that if it decays to a quark anti-quark pair, then the resulting energy deposition (called a "jet") will be, to first order, indistinguishable from a single quark or gluon entering the detector. However, by exploiting the underlying distribution of energy within the jet, one can identify such energetic decays and become more sensitive to such massive particles. Thus, during the course of this project, I have contributed to understanding these techniques and in doing so, exploited their ability to search for new physics above mass scales of 1 TeV.

In addition to performing data analysis to search for new physics, I have been involved in the operation and calibration of the hadronic tile calorimeter in ATLAS. This is a detector used to measure the energy of strongly interacting particles and thus reconstruct the observable jets that serve as proxies for quarks and gluons when interpreting our measurements in terms of physics. During my time at Cern, I was involved in the day to day operation of the detector during the 2012 data taking period that lead to the discovery of the Higgs boson and also contributed to the maintenance of the calibration of front-end readout electronics designed by the Chicago group.

Beyond my research within high energy physics, during my time at Chicago, I have also taken an interest in science teaching and outreach. I am currently the instructor for a yearlong program through the KICP called Space Explorers. This program recruits students from under-represented groups in Chicago to mentor them in a number of academic disciplines including physics. Throughout the course of the academic year, we work through a number of lab-based activities culminating in a week-long summer institute based at the Yerkes observatory in Wisconsin. In addition to being a great supplement to learning and practicing teaching pedagogy in a very hands-on way, working with students is simply tons of fun.


  • Search for heavy vector-like quarks coupling to light quarks in proton-proton collisions at √s = 7 TeV with the ATLAS detector, Phys Lett B 712, 22 (2012).
  • Search for Resonant ZZ Production in the ZZ → ℓℓqq Channel with the ATLAS Detector Using 7.2 fb-1 of √s = 8 TeV pp Collision Data, ATLAS-CONF-2012-150, Nov. 2012.

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satomi Satomi Shiraishi

- B.A., University of Chicago, 2007 (Physics with Honors)
- B.S., University of Chicago 2007 (Mathematics)
Graduate Student (2007-pres) Dept. of Physics, Enrico Fermi Institute
Research: Accelerator Physics
Awards: Robert R. McCormick Fellow, Robert G. Sachs Fellow, Gaurang & Kanwal Yodh Prize (Dept. of Physics)
Research Advisors: Young-Kee Kim and Wim Leemans

State of the art particle accelerators are used in many scientific disciplines including biology, materials science and particle physics. Improved understanding of plasma physics and advances in laser technology opened up a new field of R&D for the next generation of accelerators. Under the faculty advisory of Professor Young-Kee Kim and research supervision of Dr. Wim Leemans, I study laser-plasma accelerators (LPAs) at the LOASIS Program at Lawrence Berkeley National Laboratory.

Experimental investigation of LPAs is a topic pushing the limits of physics and technology. In 1979, Tajima and Dawson proposed an idea to use the 4th state of matter, plasma, as a medium to exchange electromagnetic energy into the kinetic energy of charged particles. In principle, this novel concept offered a potential to reduce the size of accelerators by a factor of a thousand: plasma can sustain thousands times larger electric fields than a conventional radio-frequency cavity. Experimental investigation of LPAs advanced rapidly since the 1990’s following the invention of the chirped-pulse amplification (CPA) technique to produce ultra-high intensity laser pulses. Employing a hydrogen-filled capillary waveguide, high-quality electron beams (e-beams) of energy in the GeV’s have been produced within a few centimeters. Today, improved understanding of plasma physics and rapidly advancing laser technologies are producing higher and higher intensity laser pulses and continue to expand the realm of LPA experiments

Currently, I participate in experiments using 100 TW-class, 40 fs laser pulses to understand and diagnose laser propagation in plasma with application to future high-energy accelerators. My thesis topic, referred to as staging of LPAs involves adding a second, independently driven laser acceleration stage to boost the electron energy from the primary stage. So far, LPA experiments have been done using only a single driving laser pulse. Staging is necessary because, by exciting plasma wakes, a driving laser pulse transfers energy in plasma such that it eventually becomes too weak to excite wakefields. The staging experiment involves precise control of two high intensity short laser pulses and plasma modules, coupled in a very compact manner using a disposable plasma mirror. This experiment represents a milestone in the development of LPAs and makes LPAs even stronger candidates for the next generation accelerator technology.

An understanding of laser-plasma interaction using the laser profile and its spectra is another of my research topics. Plasma is a dynamic accelerating structure that changes with time as well as with the shape and the strength of the driving laser pulse. This dynamic nature of the plasma structure represents a freedom and also a challenge in controlling the particle acceleration, and a single-shot diagnostic of the plasma wave is critical. By comparing how the driving laser pulse changes in shape and color before and after the interaction with plasma, we intend to deduce the properties of the excited wakefield structure. In particular, we learn about the energy transfer from laser to plasma and obtain a measure of electric field amplitude. Along with simulation studies, the shape of accelerating structures can be inferred. Understanding the laser-plasma interaction and the development of a single-shot diagnostic using laser spectra are complex topics but critical for the successful development of LPAs.


  • S. Shiraishi, C. Benedetti, A. J. Gonsalves, K. Nakamura, B. H. Shaw, T. Sokollik, J. van Tilborg, C. G. R. Geddes, C. B. Schroeder, Cs. Toth, E. Esarey, and W. P. Leemans, "Laser red shifting based characterization of wake_eld excitation in a laser-plasma accelerator," Phys. Plasmas 20, 063103 (2013)
  • G. R. Plateau, C. G. R. Geddes, D. B. Thorn, M. Chen, C. Benedetti, E. Esarey, A. J. Gonsalves, N. H. Matlis, K. Nakamura, C. B. Schroeder, S. Shiraishi, T. Sokollik, J. van Tilborg, Cs. Toth, S. Trotsenko, T. S. Kim, M. Battaglia, Th. Stoehlker, and W. P. Leemans, "Low-Emittance Electron Bunches from a Laser-Plasma Accelerator Measured using Single-Shot X-Ray Spectroscopy," Phys. Rev. Lett. 109, 064802 (2012)
  • C. Lin, J. van Tilborg, K. Nakamura, A. J. Gonsalves, N. H. Matlis, T. Sokollik, S. Shiraishi, J. Osterho, C. Benedetti, C. B. Schroeder, Cs. Toth, E. Esarey, and W. P. Leemans, "Long-Range Persistence of Femtosecond Modulations on Laser-Plasma-Accelerated Electron Beams," Phys. Rev. Lett. 108, 094801 (2012).
  • A. J. Gonsalves, K. Nakamura, C. Lin, D. Panasenko, S. Shiraishi, T. Sokollik, C. Benedetti, C. B. Schroeder, C. G. R. Geddes, J. van Tilborg, J. Osterhoff, E. Esarey, C. Toth, W. P. Leemans, "Tunable Laser Plasma Accelerator based on Longitudinal Density Tailoring," Nature Physics 7, 862 (2011).
  • A. J. Gonsalves, K. Nakamura, C. Lin, J. Osterhoff, S. Shiraishi, C. B. Schroeder, C. G. R. Geddes, Cs. Toth, E. Esarey, W. P. Leemans, "Plasma Channel Diagnostic Based on Laser Centroid Oscillations," Phys. Plasmas 17, 056706 (2010).
  • G. R. Plateau, N. H. Matlis, C. G. R. Geddes, A. J. Gonsalves, S. Shiraishi, C. Lin, R. A. van Mourik, and W. P. Leemans, "Wavefront-sensor-based electron density measurements for laser-plasma accelerators," Rev. Sci. Instrum. 81 (3), 033108 (2010).

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mikhail Mikhail Solon

- B.S., Univ. of the Philippines, 2009 (Physics, Summa cum laude)
- M.S., University of Chicago, 2010 (Physics)
Graduate Student (2009-pres) Dept. of Physics, Enrico Fermi Institute
Research: Theoretical High-energy Physics
Awards: Bloomenthal Fellowship, Robert R. McCormick Fellowship, Sachs Fellowship (Dept. of Physics), Oblation Scholar, Gawad Chancellor Outstanding Student, BPI-DOST Best Project of the Year (U-Philippines)
Research Advisor: Richard Hill

My research concerns particle physics that involves rich quantum field theory structures such as symmetries and the interplay of multiple scales through effective field theory. This includes the development of tools for controlled theoretical calculations, and their application for making robust predictions within and beyond the Standard Model. These activities are aimed at complementing the wealth of data from experimental frontiers, but often require new understanding of basic ideas in quantum field theory.

Effective field theory is the description of physics in terms of its underlying symmetries, its relevant degrees of freedom, and a power counting expansion based on the scales of the system. These simple ingredients lead to a framework for efficient and precise calculations, that is particularly useful in identifying universal features of a physical process, i.e., factorizing a system into physics at different scales.

One framework I have helped develop is the effective field theory for heavy or nonrelativistic particles. The scale separation between heavy and light degrees of freedom underlies the universality of heavy-particle interactions, as echoed in the predictions of heavy-quark systems, nonrelativistic atomic spectra, and the scattering of heavy dark matter off a nucleon. An important question is how to construct such field theories without matching to a microscopic theory. This is relevant to applications where the microscopic theory is unknown as in the case of dark matter, or may not even exist as in the case of a bound state arising from strong dynamics. The key is in understanding how the symmetries of spacetime are implemented. In work with Prof. Richard Hill and collaborators, I showed that the usual finite dimensional representations of the Lorentz group are not applicable to the case of heavy particles, and one must instead use induced representations. Employing the time-like class of such representations, I developed the formalism for constructing heavy particle effective Lagrangians with constraints enforcing Lorentz invariance. This opened up new questions such as the relation of induced representations to nonlinearly realized subgroups, and the possibility of applying the light-like class of induced representations towards a rigorous analysis of soft-collinear effective theory.

At a practical level, these formal developments have lead to new applications of heavy-particle methods for studying properties of nucleons and the interaction of dark matter with the Standard Model. With Prof. Richard Hill and collaborators, I developed high-order nonrelativistic QED. This provides the rigorous framework for a range of phenomenological analyses such as computing radiative corrections to low-energy lepton-nucleon scattering, analyzing generalized electromagnetic moments of a nucleon, and understanding a sharp discrepancy in proton charge radius measurements through scrutinizing proton structure effects in atomic bound states. In a series of papers with Prof. Richard Hill, I identified universal behavior in the scattering of heavy, weakly interacting dark matter on nuclear targets. The universality emerges when the dark matter is much heavier than the electroweak scale particles, and is motivated in part by the hitherto absence of new states at the LHC. The recent determination of the Higgs boson mass and improvements in lattice studies of nucleon matrix elements allow for definite predictions in the heavy dark matter limit, but demand a robust analysis of dark matter-nucleon interactions. The complete treatment of this phenomenon requires effective field theory to link physics at different scales and to provide a systematically improvable method of computation. The resulting cross section targets have minimal model dependence and may be probed in underground search experiments such as Xenon and LUX.

Selected Publications:

  • R. J. Hill and M. P. Solon, "WIMP-nucleon scattering with heavy WIMP effective theory" arXiv:1309.4092 [hep-th].
  • R. J. Hill, G. Lee, G. Paz, and M. P. Solon, "The NRQED lagrangian at order 1/M4" Phys. Rev. D. 87, 053017 (2013).
  • J. Heinonen, R. J. Hill, and M. P. Solon, "Lorentz invariance in heavy particle effective theories" Phys. Rev. D. 86, 094020 (2012).

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cacey Cacey Stevens

- B.S., Southern University-Baton Rouge, 2008 (Physics with Honors)
- M.S., University of Chicago, 2010 (Physics)
Graduate Student (2008-pres) Dept. of Physics, James Franck Inst.
Research: Experimental Soft Condensed Matter
Awards: Robert Millikan Fellowship (Dept. of Physics), NSF Graduate Research Fellowship, Chancellor's Award (Southern U), Willie H. Moore Scholarship (NSBP), Minority Scholarship (APS)
Research Advisor: Sidney Nagel

I am a Ph.D. candidate in experimental soft condensed matter physics working with Prof. Sidney Nagel. The Nagel group studies far-from-equilibrium phenomena on a macroscopic scale such as how liquids break apart or coalesce, how drops behave on a really hot surface, how sand flows and how things become jammed.

My research investigates the following question: How does a liquid drop behave when it impacts a dry solid surface? If it hits at a sufficiently high velocity, we expect the drop to splash, breaking apart into many smaller droplets. The splash, of course, depends on surface roughness and liquid properties such as surface tension or viscosity. For many years, researchers only considered these control parameters when studying drop impact. However, there is another surprisingly essential parameter for creating a splash: the ambient gas pressure. Our group has recently shown that one can prevent a drop from splashing by decreasing the ambient pressure below a threshold value that depends on liquid and surface properties. Using high-speed imaging, we have investigated how the surrounding air influences the splash dynamics.

For one of my projects, we developed a criterion for when a low-viscosity liquid drop will splash on smooth, dry glass. Even for this seemingly simple occurrence, it is difficult to define the onset of splashing in terms of all parameters. We determined the splash threshold pressure as a function of impact speed, liquid viscosity, and drop size. We found that by rescaling the axes in terms of dimensionless variables, we could collapse all our data onto a single master curve.

If the drop viscosity is increased to over three times that of water, the splash evolves more slowly than that of very low viscosity liquids.   In this regime we can see more clearly the splash evolution. As the drop spreads, a thin sheet of liquid is ejected and then breaks into droplets. We have shown that decreasing the air pressure acts to delay sheet ejection until, below a critical value, splashing stops entirely.

If the surface is rough, with an average roughness of a few microns, the impacting drop no longer ejects a thin sheet, as it does on a smooth surface, but promptly ejects droplets at contact. This allows a range of intermediate surface roughness for which no splash occurs. However, splashes on rough surfaces are still influenced by air pressure; as the pressure is lowered, droplet ejection is suppressed for prompt splashing. Thus, air pressure effects are robust for drop impact on dry surfaces. My research projects represent only a few directions that our group has taken to understand splashing phenomena.

While in graduate school, I have also been involved in several education and outreach activities. As a student coordinator of University of Chicago MRSEC Science club, an after-school program at a public elementary school near the University, I teach science concepts to young students through simple experiments and demonstrations. The students meet a diverse group of scientists and are encouraged to pursue careers in science. I have also gained experience engaging children in science as a guest lecturer for the Junior Science Cafes of the Museum of Science and Industry. Because of my interest in education, I am also involved in a research project that, using analysis methods from fluid mechanics, allows one to visualize patterns in educational data. In this work, I represent school performance scores on Illinois math and science exams as flow vectors and extract information about educational progress from the flow patterns. These flow charts could ultimately be used to show the most effective math and science educational programs in public schools.


  • C. S. Stevens and S. R. Nagel, "Scaling of the Low Viscosity Splash Threshold" (in preparation) (2013).
  • A. Latka, A. Strandburg-Peshkin, M. M. Driscoll, C. S. Stevens, and S. R. Nagel, "Creation of Prompt and Thin-Sheet Splashing by Varying Surface Roughness or Increasing Air Pressure" Phys. Rev. Lett. 109, 054501 (2012).
  • M. M. Driscoll, C. S. Stevens, and S. R. Nagel, "Thin Film Formation During Splashing of Viscous Liquids" Phys. Rev. E 82, 036302 (2010).

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kyle Kyle Story

- B.A., Cornell University, 2007 (Physics)
- B.A., Cornell University, 2007 (Mathematics)
- M.S., University of Chicago, 2009 (Physics)
Graduate Student (2008-pres) Dept. of Physics, Kavli Institute
Research: Experimental Cosmology
Awards: Grainger Graduate Fellowship, Robert R. McCormick Fellowship (Dept. of Physics), William Rainey Harper Dissertation Fellowship (Physical Sciences Division), NSF Graduate Fellowship Honorable Mention
Research Advisor: John Carlstrom

As physicists, we live in a remarkable time in which we can quantitatively study our entire observable universe. Over the past few decades, physicists have made striking progress towards a robust standard model of cosmology; we know we live in a universe that continues to expand from a hot, dense origin, and we have a conceptual framework that successfully describes phenomena from the scale of single atoms (such as the formation of the light elements) up to the largest scales in the observable universe. Yet much remains mysterious. This standard model posits that only ~5% of the total energy density of the universe is comprised of ordinary matter, while poorly understood dark matter and dark energy contribute the remaining ~25% and ~70%, respectively. According to this model, the very early universe underwent a period of super-luminal expansion known as "inflation." We know that neutrinos have mass but have not measured the absolute mass, and there are tantalizing hints that neutrino physics could be more complicated than the standard 3-flavor picture.

Advances in the field of cosmology are driven by measurements and observations. One of the richest sources of information is the Cosmic Microwave Background (CMB). Serendipitously discovered in 1964, the CMB is thermal radiation left over from the hot, dense early universe. The universe cooled as it expanded from its hot, dense origin, and after ~380,000 years the ambient temperature dropped below the ionization energy of hydrogen. At this transition, the universe rapidly became neutral as most of the free electrons and protons paired off to form hydrogen, and the universe quickly became transparent to light. The photons that last scattered at this time have been streaming through the universe ever since, and comprise the CMB. Thus, observations of the CMB can give physicists an incredibly informative snap-shot picture of the infant universe.

In my research, I observe and study the CMB to understand the basic physics of how the universe works. Our group built and continues to operate the South Pole Telescope (SPT), a millimeter-wave telescope located at - can you guess it? - the south pole in Antarctica. In the austral summer of 2011-2012, I helped deploy a new polarization-sensitive camera for the SPT, called SPTpol. As a part of this research I have traveled to the south pole four times, with my fifth trip scheduled for this January.

In my graduate career, I have used data collected with the SPT to study several different science topics. As CMB photons travel through the universe, some will traverse through clusters of galaxies and will scatter off of intra-cluster gas, thus distorting the primary CMB spectrum in a process known as the Sunyaev-Zel'dovich effect (SZE). We use these distortions in SPT data to find and study these clusters of galaxies. Clusters of galaxies are informative since they trace large-scale dark matter structures and are sensitive to the composition and expansion history of the universe. In 2011 the Planck satellite published its first catalog of SZE-selected clusters; I led observations and an analysis which used the SPT to confirm the five previously unconfirmed clusters in the southern hemisphere from that catalog.

In 2012, I led an analysis in which we used data from the full 2500 square-degree SPT-SZ survey to measure the power spectrum of the CMB. The power spectrum is a powerful way to quantify the statistical properties of the anisotropy in the CMB. This anisotropy arises from - and therefore probes - a wealth of interesting physics including the energy composition and expansion history of the universe, particle interactions at early times, and potential gravitational waves from inflation. Additionally, effects closer to today imprint signals in the CMB, including the SZE and gravitational lensing by large-scale dark matter structures. In a pair of papers resulting from the analysis I led, we published the most precise measurement of the CMB power spectrum over angular scales between ~0.06 and 0.25 degrees, and discussed the resulting constraints on models of cosmology.

For my thesis work, I am now focusing on the signal of gravitational lensing in the measurements taken with SPTpol. Gravitational lensing bends the paths of CMB photons as they travel from the surface of last scattering to Earth, thus distorting the anisotropy pattern of the CMB. The strength of this gravitational lensing signal is sensitive to the structure of ordinary and dark matter, cosmic acceleration (dark energy), neutrino physics, and the nature of gravity itself. Finally, gravitational lensing distorts the polarization patterns in the CMB, creating odd-parity swirl-patterns. Similar swirl-patterns could have been created by gravity waves from inflation in the very early universe; thus understanding and removing the lensing signal will be important in the search for these signals of inflation. The information we will gain by studying gravitational lensing in the CMB with SPTpol will shed light on all of these topics.

Selected Publications:

  • Hou,, "Constraints on Cosmology from the Cosmic Microwave Background Power Spectrum of the 2500-square degree SPT-SZ Survey" arXiv:1212.6267 (2012).
  • Story,, "A Measurement of the Cosmic Microwave Background Damping Tail from the 2500-square degree SPT-SZ Survey" arXiv:1210.7231 (2012).
  • Story,, "South Pole Telescope software systems: control, monitoring, and data acquisition" Proceedings of SPIE 8451 (2012); arXiv:1210.4966 (2012).
  • Story,, "South Pole Telescope Detections of the Previously Unconfirmed Planck Early Sunyaev-Zel'dovich Clusters in the Southern Hemisphere" Astrophys Journal Lett 735 L36 (2011).

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