Professor Eduardo Fradkin received his Licenciado (master's) degree in physics from Universidad de Buenos Aires (Argentina) and his PhD in physics from Stanford University in 1979. He came to the University of Illinois in 1979 as a postdoctoral research associate, and became an assistant professor of physics at Illinois in 1981. He was promoted to associate professor in 1984, and became a full professor in 1989. Professor Fradkin is an internationally recognized leader in theoretical physics, who has contributed to many problems at the interface between quantum field theory (QFT) and condensed matter physics (CMP).

In his early work, he pioneered the use of concepts from CMP and statistical physics, such as order parameters and phase diagrams, to problems of QFT and high energy physics, in particular to the non-perturbative behavior of gauge theories. Perhaps his most important result in this area was the proof that when matter fields carry the fundamental unit of charge, the Higgs and confinement phases of gauge theories are smoothly connected to each other and are as different as a liquid is from a gas. This result remains one of the cornerstones of our understanding of the phases of gauge theories and represents a lasting contribution to elementary particle physics.

Professor Fradkin's unique perspective has allowed him to invoke and apply results from QFT to CMP. He was one of the first theorists to use gauge theory concepts in the theory of spin glasses and to use concepts of chaos and non-linear systems in equilibrium statistical mechanics of frustrated systems. Professor Fradkin has pioneered the application of QFT methods to the physics of correlated disordered electronic systems and the quantum stability of the spontaneously dimerized state of polyacetylene.

Professor Fradkin also pioneered the use of Dirac fermions for CMP problems, particularly in two space dimensions. A prime example is his work on Dirac fermions on random fields (which he began with former graduate student Dr. Matthew Fisher), which is now regarded as the universality class of the transition between quantum Hall plateaus in the integer Hall effect. This work is also important for the description of quasiparticles in disordered d-wave superconductors. He also applied, quite early on, these ideas to the physics of what nowadays are known as topological insulators, showing that in the presence of lattice topological defects, these systems exhibit a non-trivial electronic spectrum with a parity anomaly.

A major achievement of Professor Fradkin's recent research has been the development, in collaboration with former graduate student Dr. Ana Lopez, of the fermion Chern-Simons field theory of the fractional quantum Hall effect. This theory has played a central role in the current research effort in this exciting problem in CMP. Professor Fradkin and his collaborators have extended this theory to the more challenging problem of the non-Abelian quantum hall states and developed a theory of a non-Abelian interferometer to study the unusual properties of the vortices of these quantum fluids.

More recently Professor Fradkin and his collaborators introduced the notion of electronic liquid crystal states, which are phases of quantum fermionic strongly correlated systems exhibiting properties akin to those of classical complex fluids. These ideas play a crucial role in the current understanding of the pesudogap regime of high temperature superconductors.

Professor Fradkin is an internationally recognized leader in theoretical physics, who has contributed to many problems at the interface between quantum field theory (QFT) and condensed matter physics (CMP). He pioneered the use of concepts from CMP and statistical physics, such as order parameters and phase diagrams, to problems of QFT and high energy physics. Perhaps his most important result in this area was the proof that when matter fields carry the fundamental unit of charge, the Higgs and confinement phases of gauge theories are smoothly connected to each other and are as different as a liquid is from a gas. This result remains one of the cornerstones of our understanding of the phases of gauge theories and represents a lasting contribution to elementary particle physics. Professor Fradkin's unique perspective has allowed him to invoke and apply results from QFT to CMP. He was one of the first theorists to use gauge theory concepts in the theory of spin glasses and to use concepts of chaos and non-linear systems in equilibrium statistical mechanics of frustrated systems.

Professor Fradkin has pioneered the application of QFT methods to the physics of correlated disordered electronic systems and the quantum stability of the spontaneously dimerized state of polyacetylene. Professor Fradkin also pioneered the use of Dirac fermions for CMP problems, particularly in two space dimensions. A prime example is his work on Dirac fermions on random fields, which is now regarded as the universality class of the transition between quantum Hall plateaus in the integer Hall effect. This work is also important for the description of quasiparticles in disordered d-wave superconductors. A major achievement of Professor Fradkin's recent research has been the development of the fermion Chern-Simons field theory of the fractional quantum Hall effect. This theory has played a central role in the current research effort in this exciting problem in CMP. He has recently developed a theory of electronic liquid crystal phases in strongly correlated systems and formulated a mechanism of high temperature superconductivity based on this new concept. This theory plays a central role in the interpretation of experiments in these systems of foremost importance. He is also a leader in the theory of topological phases in condensed matter and on the role of quantum entanglement at quantum critical points.

- Associate of the Center for Advanced Study (UIUC)
- Donald Biggar Willett Professor of Physics, department of Physics, University of Illinois at Urbana-Champaign (since Spring 2014)
- Cesar Milstein Fellowship, Ministry of Science, Technology and Productive Innovation, Argentina, July 2007, June 2011
- Arnold O. Beckmann Award of the research Board of the University of Illinois
- Fellow of the American Academy of Arts and Sciences (2009)
- Member, National Academy of Sciences, April 30, 2013
- Simon Guggenheim Memorial Foundation Fellowship Award (1998)
- Fellow of the American Physical Society (1998)
- Incomplete List of Teachers Ranked as Excellent by Their Students; Spring Semester 1996.

**Fall 2000:**PHYS 498 (*outstanding*)

- E. H. Fradkin. Field Theories of Condensed Physics, Second Edition. Cambridge University Press. (2013).
- E. H. Fradkin. Field Theories of Condensed Matter Systems. (Addison-Wesley Advanced Book Program: Redwood City). Frontiers in Physics Series (1991).
- N. Samkharadze, K. A. Schreiber, G. C. Gardner, M. J. Manfra, E. Fradkin and G. A. Csáthy. Observation of a transition from a topologically ordered to a spontaneously broken symmetry phase. Nature Physics, advanced online publication, 26 October, 2015.
- Kai Sun, Krishna Kumar, and Eduardo Fradkin. A discretized Chern-Simons gauge theory on arbitrary graphs. Physical Review B 92, 115148 (2015). (Editor's suggestion)
- X. M. Chen, A. J. Miller, C. Nugroho, G. A. de la Peña, Y. I. Joe, A. Kogar, J. D. Brock, J. Geck, G. J. MacDougall, S. L. Cooper, E. Fradkin, D. J. Van Harlingen, P. Abbamonte. Influence of Ti doping on the incommensurate charge density wave in 1T-TaS2. Physical Review B 91, 245113 (2015).
- Jeffrey C. Y. Teo, Taylor L. Hughes, and Eduardo Fradkin. Theory of Twist Liquids: Gauging and Anyonic Symmetry. Annals of Physics 360, 349 (2015).
- Eduardo Fradkin, Steven A. Kivelson, and John M. Tranquada. Colloquium: Theory of intertwined orders in high temperature superconductors. Reviews of Modern Physics 87, 457 (2015)
- Rodrigo Soto-Garrido, Gil Young Cho, and Eduardo Fradkin. Quasi-one-dimensional pair density wave superconducting state. Physical Review B 91, 195102 (2015).
- Xiao Chen, Gil Young Cho, Thomas Faulkner, and Eduardo Fradkin. Scaling of entanglement in 2+1-dimensional scale-invariant field theories. Journal of Statistical Mechanics, 2015, P02010 (2015).
- Andrey Gromov, Gil Young Cho, Yizhi You, Alexander G. Abanov, and Eduardo Fradkin. Erratum: Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect [Phys. Rev. Lett. 114, 016805 (2015)]. Physical Review Letters 114, 149902 (2015).
- Andrey Gromov, Gil Young Cho, Yizhi You, Alexander G. Abanov, and Eduardo Fradkin. Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect. Physical Review Letters 114, 016805(2015). (Editor's Suggestion)
- Yizhi You, Gil Young Cho and Eduardo Fradkin. Theory of the Nematic Fractional Quantum Hall State. Physical Review X 4, 041050 (2014).
- Gil Young Cho, Rodrigo Soto-Garrido and Eduardo Fradkin. Topological Pair-Density-Wave Superconducting States. Physical Review Letters 113, 256405 (2014).
- Krishna Kumar, Kai Sun, and Eduardo Fradkin. Chern-Simons theory for magnetization plateaus of the spin-1/2 XXZ quantum Heisenberg model on the kagome lattice. Physical Review B 90, 174409 (2014).
- Gil Young Cho, Yizhi You and Eduardo Fradkin. Geometry of fractional quantum Hall Fluids. Physical Review B 90, 115139 (2014).
- Rodrigo Soto Garrido and Eduardo Fradkin. Pair-Density-Wave Superconducting States and Electronic Liquid Crystal Phases. Physical Review B 89, 165126 (2014).
- Stefanos Papanikolaou, Daniel Charrier, and Eduardo Fradkin. Ising nematic fluid phase of hard-core dimers on the square lattice. Physical Review B 89, 035128 (2014).
- Yizhi You and Eduardo Fradkin. Field theory of nematicity in the spontaneous quantum anomalous Hall effect. Physical Review B 88, 235124 (2013). (Editor's Suggestion)
- Xiao Chen and Eduardo Fradkin. Quantum entanglement and thermal reduced density matrices in fermion and spin systems on ladders. J. Stat. Mech. (2013) P08013
- AtMa Chan, Taylor L. Hughes, Shinsei Ryu, and Eduardo Fradkin. Effective field theories for topological insulators by functional bosonization. Phys. Rev. B 87, 085132 (2013).
- Eduardo Fradkin and Steven A. Kivelson. High-temperature superconductivity: Ineluctable complexity. Nature Physics 8, 864 (2012).
- Xiao Chen, Benjamin Hsu, Taylor Hughes and Eduardo Fradkin, The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition. Phys. Rev. B 86, 134201 (2012).
- A. Jaefari and E. Fradkin. Pair-density-wave superconducting order in two-leg ladders. Phys. Rev. B 85, 035104 (2012).
- L. Arrachea and E. Fradkin. Chiral heat transport in driven quantum Hall and quantum spin Hall edge states. Phys. Rev. B 84, 235436 (2011).
- D. G. Barci and E. Fradkin. Role of nematic fluctuations in the thermal melting of pair-density-wave phases in two-dimensional superconductors. Phys. Rev. B 83, 100509(R) (2011).
- A. Jaefari, S. Lal, and E. Fradkin. Charge-density wave and superconductor competition in stripe phases of high-temperature superconductors. Phys. Rev. B 82, 144531 (2010).
- E. Berg, E. Fradkin, and S. A. Kivelson. Pair-density-wave correlations in the Kondo-Heisenberg model. Phys. Rev. Lett. 105, 146403 (2010).
- T. L. Hughes, R. G. Leigh, and E. Fradkin. Torsional response and dissipationless viscosity in topological insulators. Phys. Rev. Lett. 107, 075502 (2011).
- E. Fradkin, S. A. Kivelson, M. J. Lawler, J. P. Eisenstein, and A. P. Mackenzie. Nematic Fermi fluids in Condensed Matter Physics. Annual Reviews of Cond. Matter Phys. 1, 153 (2010).
- M. Kim, H. Barath, X. Chen, Y. -I Joe, E. Fradkin, P. Abbamonte, and S. L. Cooper. Magnetic field and pressure controlled phases in complex materials. Adv. Mat. 22, 1148 (2010).
- M. Kim, X. Chen, Y.-I. Joe, E. Fradkin, P. Abbamonte and S. L. Cooper. Mapping the magneto-structural quantum phases of Mn
_{3}O_{4}. Phys. Rev. Lett. 104, 136402 (2010). - B. Hsu, E. Grosfeld, and E. Fradkin. Quantum noise and entanglement generated by a local quantum quench. Phys. Rev. B 80, 235412 (2009). (Editor's Suggestion)
- B. M. Fregoso and E. Fradkin. Ferro-nematic ground state of the dilute dipolar Fermi gas. Phys. Rev. Lett. 103, 205301 (2009).
- E. Fradkin. Scaling of entanglement entropy at 2D quantum Lifshitz fixed points and topological fluids. J. of Phys. A 42, 504011 (2009). (Special issue on Entanglement Entropy: P. Calabrese, J. Cardy, and B. Doyon, editors)
- E. Berg, E. Fradkin, and S. A. Kivelson. Charge 4e superconductivity from pair density wave order in certain high temperature superconductors. Nature Physics 5, 830-833 (2009).
- E. Berg, E. Fradkin, S. A. Kivelson and J. M. Tranquada. Striped superconducting order: How the cuprtaes intertwine spin, charge, and superconducting orders. New J. of Phys. 11, 115004 (2009).
- B. M. Fregoso, K. Sun, E. Fradkin, and B. L. Lev. Biaxial nematic phases in ultracold dipolar Fermi gases. New J. of Phys. 11, 103003 (2009).
- K. Sun, H. Yao, E. Fradkin, and S. A. Kivelson. Topological insulators and nematic phases from spontaneous symmetry breaking in 2D Fermi systems with a quadratic band vrossing. Phys. Rev. Lett. 103, 046811 (2009).
- B. Hsu, M.l Mulligan, E. Fradkin, and E.-A. Kim. Universal entanglement entropy in two-dimensional conformal quantum critical points. Phys. Rev. B 79, 115421 (2009).
- E. Berg, E. Fradkin, and S. A. Kivelson. Theory of the striped superconductor. Phys. Rev. B 79, 064515 (2009). (Editor's Suggestion)
- K. Sun and E. Fradkin. Time reversal symmetry breaking and spontaneous anomalous Hall effect in Fermi fluids. Phys. Rev. B 78, 245122 (2008).
- K. Sun, B. M. Fregoso and E. Fradkin. Fluctuating stripes in strongly correlated electron systems and the nematic-smectic quantum phase transition. Phys. Rev. B. 78, 085124 (2008).
- E.-A. Kim, M. J. Lawler, P. Oreto, S. Sachdev, E. Fradkin, and S. A. Kivelson. Theory of the nodal nematic quantum phase transition in superconductors. Phys. Rev. B 77, 184514 (2008).
- S. Dong, E. Fradkin, R. G. Leigh, and S. Nowling, Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids. J. of High Energy Phys. 2008 (5),016 (2008).
- S. Papanikolaou, K. S. Raman, and E. Fradkin. Topological phases and topological entropy of two-dimensional systems with finite correlation length. Phys. Rev. B 76, 224421(2007).
- E. Berg, E. Fradkin, E.-A. Kim, S. Kivelson, V. Oganesyan, J. M. Tranquada, and S. Zhang. Dynamical layer decoupling in a stripe-ordered high T
_{c}superconductor. Phys. Rev. Lett. 99, 127003 (2007). - S. Papanikolaou, E. Luijten, and E. Fradkin. Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models}. Phys. Rev. B 76, 134514 (2007).
- C. Wu, K. Sun, E. Fradkin, and S. Zhang. Fermi liquid instabilities in the spin channel. Phys. Rev. B 75, 115103 (2007).
- M. Lawler and E. Fradkin. Local quantum criticality in the nematic quantum phase transition of a Fermi fluid. Phys. Rev. B 75, 033304 (2007).
- E. Fradkin and J. E. Moore. Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum. Phys. Rev. Lett. 97, 050404-1-4 (2006).
- E.-A. Kim, M. Lawler, S. Vishveshwara, and Eduardo Fradkin. Measuring fractional charge and statistics in fractional quantum Hall fluids through noise experiments. Phys. Rev. B 74, 155324-1-23 (2006).
- M. Lawler, D. Barci, V. Fernandez, E. H. Fradkin, and L. Oxman. Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid. Phys. Rev. B 73, 085101(2006).
- P. Fendley and E. H. Fradkin. Realizing non-Abelian statistics in time-reversal-invariant systems. Phys. Rev. B 72, 024412-1-8 (2005).
- M. J. Lawler and E. H. Fradkin. Quantum Hall smectics, sliding symmetry, and the renormalization group. Phys. Rev. B 70, 165310-1-7 (2004).
- E. H. Fradkin, D. A. Huse, R. Moessner, V. Oganesyan, and S. L. Sondhi. Bipartite Rokhsar-Kivelson points and cantor deconfinement. Phys. Rev. B 69, 224415-1-8 (2004).
- E. Ardonne, P. Fendley, and E. H. Fradkin. Topological order and conformal quantum critical points. Ann. of Phys. 310, 493-551 (2004).
- S. A. Kivelson, I. P. Bindloss, E. Fradkin, V. Oganesyan, J. Tranquada, A. Kapitulnik, and C. Howald. How to detect fluctuating stripes in the high-temperature superconductors. Rev. Mod. Phys. 75, 1201-1241 (2003).
- S. A. Kivelson, D. H. Lee, E. H. Fradkin, and V. Oganesyan. Competing order in the mixed state of high-temperature superconductors. Phys. Rev. B 66, 144516-1-8 (2002).
- D. G. Barci and E. H. Fradkin. Theory of the quantum Hall smectic phase. II. Microscopic theory. Phys. Rev. B 65, 245320-1-19 (2002).
- R. Moessner, S. L. Sondhi, and E. H. Fradkin. Short-ranged resonating valence bond physics, quantum dimer models, and Ising gauge theories. Phys. Rev. B 65, 024504-1-16 (2001).
- E. H. Fradkin, V. Jejjala, and R. G. Leigh. Non-commutative Chern-Simons for the quantum Hall system and duality. Nucl. Phys. B 642, 483-500 (2002).
- V. Oganesyan, S. A. Kivelson, and E. H. Fradkin. Quantum theory of a nematic Fermi fluid. Phys. Rev. B 64, 195109-1-6 (2001).
- E. H. Fradkin, S. A. Kivelson, E. Manousakis, and K. Nho. Nematic phase of the two-dimensional electron gas in a magnetic field. Phys. Rev. Lett. 84, 1982-1985 (2000).
- E. H. Fradkin and S. A. Kivelson. Liquid-crystal phases of quantum Hall systems. Phys. Rev. B 59, 8065-8072 (1999).
- A. Lopez and E. H. Fradkin. Universal structure of the edge states of the fractional quantum Hall states. Phys. Rev. B 59, 15323-15331 (1999).
- E. H. Fradkin, C. Nayak, and K. Schoutens. Landau-Ginzburg theories for non-Abelian quantum Hall states. Nucl. Phys. B 546, 711-730 (1999).
- N. P. Sandler, C. C. C. Chamon, and E. H. Fradkin. Andreev reflection in the fractional quantum Hall effect. Phys. Rev. B 57, 12324-12332 (1998).
- E. H. Fradkin, C. Nayak, A. Tsvelik, and F. Wilczek. A Chern-Simons effective field theory for the Pfaffian quantum Hall State. Nucl. Phys. B 516, 704-718 (1998).
- S. A. Kivelson, E. H. Fradkin, and V. J. Emery. Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550-553 (1998).
- H. E. Castillo, C. Chamon, E. H. Fradkin, P. M. Goldbart, and C. Mudry. Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field. Phys. Rev. B 56, 10668-10677 (1997).
- E. H. Fradkin and S. Kivelson. Modular invariance, self-duality and the phase transition between quantum Hall plateaus. Nucl. Phys. B 474, 543-574 (1996).
- A. H. Castro Neto and E. H. Fradkin. Bosonization of the low energy excitations of Fermi liquids. Phys. Rev. Lett. 72, 1393-1397 (1994).
- A. H. Castro Neto and E. H. Fradkin. Bosonization of Fermi liquids. Phys. Rev. B 49, 10877-10892 (1994).
- E. H. Fradkin and F. A. Schaposnik. The fermion-boson mapping in three-dimensional quantum field theory. Phys. Lett. B 338, 253-258 (1994).
- A. Lopez and E. H. Fradkin. Response functions and spectrum of collective excitations of fractional-quantum-Hall effect systems. Phys. Rev. B 47, 7080-7094 (1993).
- A. H. Castro Neto and E. H. Fradkin. The thermodynamics of quantum systems and generalizations of Zamolodchikov's C-theorem. Nucl. Phys. B 400, 525-546 (1993).
- E. H. Fradkin, E. F. Moreno, and F. A. Schaposnik. Ground-state wave functionals for (1 + 1)-dimensional fermion field theories. Nucl. Phys. B 392, 667-699 (1993).
- A. Lopez and E. H. Fradkin. Universal properties of the wave functions of fractional quantum Hall systems. Phys. Rev. Lett. 69, 2126-2129 (1992).
- E. H. Fradkin and F. A. Schaposnik. Chern-Simons gauge theories, confinement and the chiral spin liquid. Phys. Rev. Lett. 66, 276-279 (1991).
- A. Lopez and E. Fradkin. The fractional quantum Hall effect and Chern-Simons gauge theories. Phys. Rev. B 44, 5246 (1991).
- D. Withoff and E. H. Fradkin. Phase transitions in gapless Fermi systems with magnetic impurities. Phys. Rev. Lett. 64, 1835-1838 (1990).
- E. H. Fradkin and S. Kivelson. Short range resonating valence bond theories and superconductivity. Mod. Phys. Lett B [Rapid Commun. in High T
_{c}Superconductivity] 4, 225-232 (1990). - E. H. Fradkin. Jordan-Wigner transformation for quantum-spin systems in two dimensions and fractional statistics. Phys. Rev. Lett. 63, 322-325 (1989).
- E. Dagotto, E. H. Fradkin, and A. Moreo. SU(2) gauge invariance and order parameters in strongly coupled electronic systems. Phys. Rev B [Rapid Comm.] 38, 2926-2929 (1988).
- E. H. Fradkin and M. Stone. Topological terms in one and two-dimensional quantum Heisenberg antiferromagnets. Phys. Rev. B 38, 7215-7218 (1988).
- E. H. Fradkin, C. M. Naón, and F. A. Schaposnik. The complete bosonization of two-dimensional QCD in the path-integral framework. Phys. Rev. D 36, 3809-3812 (1987).
- F. Nori, Q. Niu, E. H. Fradkin, and S.-J. Chang. Superconducting-normal phase boundary of quasicrystalline arrays in a magnetic field. Phys. Rev. B 36, 8338-8342 (1987).
- E. H. Fradkin, E. Dagotto, and D. Boyanovsky. Physical realization of the parity anomaly in condensed matter physics. Phys. Rev. Lett. 57, 2967-2970 (1986).
- E. H. Fradkin. Critical behavior of disordered degenerate semiconductors. II: Spectrum and transport properties in mean field theory. Phys. Rev. B 33, 3263-3268 (1986).
- E. H. Fradkin. Critical behavior of disordered degenerate semiconductors. I: Models, symmetries and formalism. Phys. Rev. B 33, 3257-3262 (1986).
- M. P. A. Fisher and E. H. Fradkin. Localization in a magnetic field: Tight binding model with one-half of a flux quantum per plaquette. Nucl. Phys. B 251, 457-471 (1985).
- E. H. Fradkin. The roughening transition in quantum interfaces. Phys. Rev. B 28, 5338-5341 (1983).
- E. H. Fradkin and J. E. Hirsch. Phase diagram of one-dimensional electron-phonon systems I: The Su-Schrieffer-Heeger model. Phys. Rev. B 27, 1680-1697 (1983).
- J. E. Hirsch and E. H. Fradkin. Effects of quantum fluctuations on the Peierls instability: A Monte Carlo study. Phys. Rev. Lett. 49, 402-405 (1982).
- E. H. Fradkin and L. P. Kadanoff. Disorder variables and para-fermions in two-dimensional statistical mechanics. Nucl. Phys. B 170, 1-15 (1980).
- E. H. Fradkin and S. Shenker. Phase diagram of Lattice gauge theories with Higgs fields. Lattice Gauge Theories, 1979 (The Physical Society of Japan)) Phys. Rev. D 19, 3682-3697 (1980).
- E. H. Fradkin and L. Susskind. Order and disorder in gauge systems and magnets. Phys. Rev. D 17, 2637-2658 (1978).
- E. H. Fradkin, B. A. Huberman, and S. H. Shenker. Gauge symmetries in random magnetic systems. Phys. Rev. B 18, 4789-4812 (1978).
- Eduardo Fradkin, "Electronic Liquid Crystal Phases in Strongly Correlated Systems", in Proceedings of the Les Houches Summer School on "Modern theories of correlated electron systems", Les Houches, Haute Savoie, France (May 2009), Daniel C. Cabra, Andreas Honecker, and Pierre Pujol, editors, Lecture Notes in Physics 843, Springer-Verlag Berlin Heidelberg (2012).

**Office**

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**Phone**

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**Fax**

217.244.7704

**Email**

efradkin@illinois.edu

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