Reka Z. Albert, assistant professor of physics

Reka Albert

Reka Albert is studying the underlying network structure of complex systems such as the World-Wide Web and the cell. “The topology of this network structure can give us important insights into the organization of the system,” she explains. “Network modeling is based on a synthesis of experimental information available about the processes taking place in a system. These models lead to predictions that motivate new experiments.”

Her research accomplishments have been recognized with a Soros Mobility Grant in 1996, the Shaheen Graduate School Award from the University of Notre Dame in 2001, and a Sloan Research Fellowship in 2004. She has published more than 20 scientific papers and has contributed chapters to three books. She also has presented invited talks at several institutions across the United States and Canada, and has made presentations at professional conferences in the United States and The Netherlands.

Albert is a member of the American Association for the Advancement of Science, the American Physical Society, and the Society for Mathematical Biology. She serves as a reviewer for more than 20 journals and several foundations, such as the National Science Foundation and the National Institutes of Health.

Prior to joining Penn State in June of 2003, Albert was a postdoctoral associate at the University of Minnesota from 2001 to 2003, and a research assistant and teaching assistant at the University of Notre Dame from 1996 to 2001. She also was a teaching assistant at the Babes-Bolyai University in Romania from 1995 to 1996.

Albert received her bachelor’s degree and master’s degree in physics from the Babes-Bolyai University in Romania in 1995 and 1996, respectively. She received a doctoral degree in physics from the University of Notre Dame in 2001.

Alberto Bressan, professor of mathematics

	Alberto Bressan

Alberto Bressan’s research interests fall within the broad area of nonlinear analysis, which includes such topics as nonlinear partial differential equations and the mathematical theory of control. He is particularly interested in the controllability and optimal control of nonlinear systems, and in the geometric structure of optimal feedbacks. He also studies the blow-up behavior of solutions to reaction-diffusion equations, which model explosion phenomena in solids or gases.

Bressan has made breakthroughs in the field of hyperbolic conservation laws, where he established fundamental properties of solutions and the convergence of vanishing viscosity approximations. “Conservation laws are basic equations of mathematical physics,” he explains. “They describe, in particular, the evolution of a gas in terms of the conservation of mass, momentum, and energy. The theory of shock waves in nozzle flow is a specific example.” For his work on conservation laws, Bressan was invited to deliver a plenary lecture at the International Congress of Mathematicians in Beijing, China, in 2002.

He has published one book, titled Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem (Oxford University Press, 2000), and more than 100 scientific papers. He also serves on editorial boards for the journal Analysis and Applications, Archive for Rational Mechanics and Analysis, Discrete and Continuous Dynamical Systems, Nonlinear Differential Equations and Applications, Rendiconti del Seminario Matematico of the University of Padova in Italy, Set Valued Analysis, and SIAM Journal of Mathematical Analaysis.

Prior to joining Penn State in November of 2003, Bressan was a professor at the International School for Advanced Studies (SISSA) in Trieste, Italy, from 1991 to 2003 and an associate professor at the University of Colorado in Boulder from 1986 to 1990. He received his bachelor’s degree in mathematics from the University of Padova in Italy in 1978, and his doctoral degree in mathematics from the University of Colorado in Boulder in 1982. In his free time, he enjoys listening to classical music and playing the flute and piano.

John Clemens

John Clemens’s primary research areas are Mathematical Logic and Descriptive Set Theory. He explains, “Descriptive Set Theory is the study of issues of definability and complexity of sets of real numbers and related objects, and it has close connections to computability theory, analysis of functions, and topology.”

Clemens is particularly interested in the theory of definable equivalence relations, which he describes as “the study of the complexity and embeddability of quotient spaces obtained from metric spaces by using definable equivalence relations to combine similar points into one class.” This method can be used to gauge the complexity of various classification problems arising in many areas of mathematics, and has strong ties to the field of ergodic theory.

Clemens is a member of the Association for Symbolic Logic. He serves as a referee for the Journal of Mathematical Logic, Fundamenta Mathematicae, the Journal of Symbolic Logic, and Transactions of the AMS—a publication of the American Mathematical Society. He has published two scientific papers, and has presented invited talks at several institutions across the United States.

Prior to joining Penn State in August of 2003, Clemens was a Bateman Research Instructor in mathematics at the California Institute of Technology from 2001 to 2003. He received his bachelor’s degree in mathematics from Princeton University in 1994 and his doctoral degree in mathematics from the University of California at Berkeley in 2001.

Arthur Lesk, professor of biochemistry and molecular biology

	Arthur Lesk

Arthur Lesk has made significant contributions to the study of protein evolution. He and Cyrus Chothia, working at the MRC Laboratory of Molecular Biology in Cambridge, United Kingdom, discovered the relationship between changes in amino-acid sequence and changes in protein structure by analyzing the mechanism of evolution in protein families. This discovery has provided the quantitative basis for the most successful and widely used method of structure prediction, know as homology modelling.

Lesk and Chothia also studied the conformations of antigen-binding sites of immunoglobulins. They discovered the “canonical-structure model” for the conformation of the complementarity-determining regions of antibodies, and they applied this model to the analysis of antibody-germ-line genes, including the prediction of the structure of the corresponding proteins. This work has supported the “humanization” of antibodies for therapy in the treatment of cancer. “This approach to cancer therapy is based on the observation of H. Waldmann that rats can raise antibodies against human cancers, but that the rat antibodies lead to immune responses, similar to allergies, in human patients,” Lesk explains. “Humanization of these antibodies is the formation of hybrid molecules that are more human than rat, but that retain the therapeutic activity while reducing the patient’s immune response.”

Lesk’s work also involves the detailed comparison of proteins in different structural states as a means for understanding the mechanisms that enable the proteins to change conformation, both as part of their normal activity and in disease. The discovery and analysis of these mechanisms was the key to understanding conformation changes in serine protease inhibitors, also known as serpins, mutations of which are an important cause of several diseases, including emphysema and certain types of inherited mental illness.

Lesk used a systematic analysis of protein-folding patterns to develop a mathematical representation that aids in the recognition and classification of these patterns. He also wrote the first computer program to generate schematic diagrams of proteins using molecular graphics, and he developed many algorithms now used by other researchers to analyze the structures of proteins.

Lesk was formerly chair of the Task Group on Biological Macromolecules for the Committee on Data for Science and Technology (CODATA), which aimed to foster worldwide coordination of databases in molecular biology to enhance their quality and utility. He has given invited lectures and presentations related to his research at universities and professional conferences worldwide.

Lesk is a member of the American Physical Society. He has published 189 scientific articles and 8 books related to his research.

Prior to joining Penn State during the fall semester of 2003, Lesk was on the faculty of the clinical school at the University of Cambridge from 1990 to 2003. He was a group leader in the biocomputing program at the European Molecular Biology Laboratory in Heidelberg, Germany, from 1987 to 1990; a visiting scientist at MRC Laboratory of Molecular Biology in Cambridge, United Kingdom, between 1977 and 1990; and a professor of chemistry at Fairleigh Dickinson University in New Jersey from 1971 to 1987. He has held visiting fellowships at the University of Otago in New Zealand and Monash University in Australia. He also is a Life Member of Clare Hall at the University of Cambridge in the United Kingdom.

Lesk received a bachelor’s degree, magna cum laude, from Harvard University in 1961. He received his doctoral degree from Princeton University in 1966. He also received a master’s degree from the University of Cambridge in the United Kingdom in 1999.

Anna Mazzucato, assistant professor of mathematics

Anna Mazzucato

Anna Mazzucato conducts research in the analysis of non-linear partial differential equations, and is particularly interested in fluid mechanics. She studies viscous, incompressible fluids to learn how energy and vorticity transport—or are transferred—in turbulent flows. The study of turbulence is relevant to many fields, such as aerodynamics.

Mazzucato also studies elastodynamics; in particular, the problem of recovering material parameters, such as the density and Lamé constants, from measurements made at the surface of an elastic body. She explains, “In the case of anisotropic media, for which the elastic behavior depends on the direction of the material fibers, there is first a question of uniqueness; that is, determining when and if different parameters give the same elastic response. Then, we are interested in reconstructing, or approximating, the material parameters from surface measurements in the form of ‘traction-to-displacement’ measurements. This is done by applying force, or traction, to the surface and by measuring the resulting displacement due to the elastic deformation.” This research may have applications in fields such as medical imaging, seismology, and the detection of cracks.

Mazzucato is a member of the American Mathematical Society and the Society for Industrial and Applied Mathematics. She also is a member of the Association for Women in Mathematics, where she serves as a mentor for the Mentor Network. She serves as a referee for the Journal of Mathematical Analysis and Applications, Communications in Partial Differential Equations, and the Archive for Rational Mechanics and Analysis. She has given invited talks and presentations related to her research in the United States, France, Brazil, and Italy.

Prior to joining Penn State during the fall semester of 2003, Mazzucato was a Gibbs Instructor at Yale University from 2000 to 2003. She had been a Postdoctoral Fellow at the University of Minnesota Institute for Mathematics and its Applications in 2002 and at the Mathematical Sciences Research Institute in California in 2001.

Mazzucato received a laurea degree in physics—equivalent to a combined bachelor’s degree and master’s degree—with highest honors from the University of Milan in Italy in 1994. She received her doctoral degree in mathematics from the University of North Carolina in 2000.

Katsuhiko Murakami, assistant professor of biochemistry and molecular biology

	Katsuhiko Murakami

The long-term goal of Katsuhiko Murakami’s research is to understand the mechanism of transcription and its regulation. “Transcription is the major control process for gene regulation, and RNA polymerase (RNAP) is the central enzyme of transcription,” Murakami explains. “Determining the three-dimensional structures of RNAP and transcription complexes is essential to understanding their role in gene regulation.”

Murakami is particularly interested in using X-ray crystallography to determine the structure of RNAPs from different kinds of organisms such as bacteriophages, which are single-subunit RNAPs; bacteria and archaea, which are multi-subunit cellular RNAPs; and the influenza virus, which is an RNA-dependent RNAP.

He also hopes to solve the three-dimensional structures of RNAP complexes that have DNA or RNA, or that may have both. The ultimate goal of this structural-analysis effort is to reveal all the structures at different stages of the transcription process: promoter recognition, transcription initiation, elongation, and termination. Based on these structures, Murakami uses biochemical and biophysical methods to study the mechanisms of transcription and its regulation.

Murakami is a member of the American Crystallographic Association and the American Association for the Advancement of Science (AAAS). He has published more than thirty scientific papers related to his research.

Prior to joining Penn State during the fall semester of 2003, Murakami was a postdoctoral research fellow and research associate at The Rockefeller University from 1998 to 2003. He also was a postdoctoral researcher at the National Institute of Genetics in Japan from 1997 to 1998.

Murakami earned a bachelor’s degree in chemistry in 1992 and a master’s degree in chemistry in 1994 at the Yamaguchi University in Japan. He earned his doctoral degree in genetics at The Graduate University for Advanced Studies in Japan in 1997.

Alexander Nabutovsky, professor of mathematics

Alexander Nabutovsky

Alexander Nabutovsky conducts research in Differential Geometry. He is particularly interested in the best, or optimal, shapes of various geometric objects. He explains, “While it is intuitively clear that the ‘best’ shape of a closed curve in the plane is a round circle, the situation becomes less clear for more complicated objects of a higher dimension.” He introduces methods based on non-computability theory that can be used to solve such questions. “Unexpectedly,” he says, “it turned out that non-computable functions play an important role in the geometry of the set that includes all possible shapes of various high-dimension geometric objects.”

Besides differential geometry, his research interests include such areas of mathematics as algorithmically unsolvable problems in the topology of manifolds, geometric group theory, global analysis, and real algebraic geometry. He has published more than twenty scientific publications related to his research.

Nabutovsky has given presentations at conferences across the United States, as well as in Italy, Greece, Switzerland, France, Israel, Canada, Denmark, and Germany. He also was one of the organizers of a workshop in 1997 on “Singularity Theory and Geometry” in the Fields Institute in Toronto, Canada, and of the Seventeenth Annual Geometry Festival in 2002 at the Courant Institute of Mathematical Sciences in New York.

Prior to joining Penn State in August of 2003, Nabutovsky was an assistant professor and associate professor at the University of Toronto in Canada from 1993 to 2003. He also conducted postdoctoral research as a Courant Instructor at the Courant Institute of Mathematical Sciences from 1993 to 1995, and has held visiting positions at Stanford University, the University of Toronto in Canada, the Institute of Advanced Scientific Studies (IHES) in France, the Max-Planck Institute of Mathematics in Germany, and the Federal Institute of Technology (ETH) in Switzerland.

Nabutovsky received a master’s degree in applied mathematics from Novosibirsk Technical University in Russia in 1982 and a doctoral degree in mathematics from the Weizmann Institute of Science in Israel in 1993.

Alexei Novikov, assistant professor of mathematics

	Alexei Novikov

Alexei Novikov’s research involves the development of effective and reliable methods of predicting the overall physical properties of solids and fluids. He says, “I am particularly interested in the mathematical analysis of transport by advection-dominated fluid flows and the conductivity of high-contrast composite materials.”

The problem of transport by advection-dominated flows has applications in predicting flame propagation in combustion, tracking of pollutants in the atmosphere, and evaluating mixing rates in chemical reactions. Novikov’s research focuses on the two-dimensional model in which such flows have cell-like geometric patterns. He develops mathematical tools for investigating diffusion and eddy viscosity of fluid flows with very strong advection.

Novikov also studies high-contrast, highly packed composite materials in which inclusions are randomly distributed. He develops a discrete-network approximation of the conductivity of such composites, and uses variational techniques to provide rigorous mathematical justification for it. He has published seven scientific papers related to his research, and has given invited talks and presentations in Canada, Poland, Norway, and across the United States.

Prior to joining Penn State in the fall of 2003, Novikov was a Von Karman Instructor in Applied Mathematics at the California Institute of Technology from 2001 to 2003. He had been a postdoctoral associate at the University of California at Berkeley in 2000 and at the University of Minnesota in 1999.

Novikov received a master’s degree from Moscow State University in Russia in 1993 and a doctoral degree from Stanford University in 1999.

Regina Rotman, assistant professor of mathematics

Regina Rotman

Regina Rotman is interested in Riemannian Geometry; particularly, closed geodesics on Riemannian manifolds, closed geodesic nets, and minimal surfaces. “The notion of ‘geodesic’ is the generalization of the notion of ‘a straight line’ to Riemannian manifolds, and as such, it is one of the fundamental concepts of Riemannian Geometry,” she explains. “The merideans on the Earth’s surface are examples of geodesics because they minimize the distance between two points on a sphere that are close to each other—they are the shortest curves between the two points. Big circles, such as the Earth’s equator, are examples of closed geodesics on a sphere.” She also studies minimal surfaces, which can be viewed as mathematical models of soap bubbles. She applies both geometric and topological methods to study the properties of such objects.

Rotman received several undergraduate awards from New York University, including a Founders-Day Award, a Perley Lenwood Thorne Award in Mathematics, a Samuel F.B. Morse Medal in Physics, and a George Granger Brown Scholars Award in Physics. She has published six scientific papers related to her research.

Rotman has given invited talks and presentations in Germany, Canada, Israel, and across the United States. She also has participated in scientific conferences in Canada, Denmark, France, Switzerland, and the United States.

Prior to joining Penn State for the fall semester of 2003, Rotman was an assistant professor at the University of Toronto in Canada from 1999 to 2003. She was a postdoctoral fellow at the Courant Institute of Mathematical Sciences in New York between 1998 and 2002. She also has held visiting positions at the Max-Planck Institute in Germany, the Institute of Advanced Scientific Studies (IHES) in France, and the Federal Institute of Technology (ETH) in Switzerland.

Rotman received a bachelor’s degree, magna cum laude, in mathematics and physics from New York University in 1991. She received her doctoral degree in mathematics from the State University of New York at Stony Brook in 1998.

Omri Sarig, assistant professor of mathematics

	Omri Sarig

Omri Sarig’s research is focused on such mathematical topics as probability theory, ergodic theory, and dynamical systems. He is interested particularly in mechanisms that make deterministic processes seem “random” or “unpredictable.”

His research achievements have been recognized with a Wolf Foundation Gilboa award in 2000, with the Haim Nessyaho prize for the best Israeli Ph.D. dissertation in mathematics for the year 2001, and with a three-year long National Science Foundation award starting in 2004. He also has been recognized with Letters of Commendation for Excellence in Teaching from Tel-Aviv University in Israel in 2000 and from Warwick University in the United Kingdom in 2003.

He served in administrative positions as a member of the organizing committee of a year-long symposium on Probability and Dynamical Systems and as the Second-Year Coordinator, both at the University of Warwick in the United Kingdom.

He has published a dozen scientific papers related to his research and has given invited talks and presentations in Japan, Switzerland, the United Kingdom, France, Poland, Germany, and Israel.

Prior to joining Penn State during the fall semester of 2003, Sarig was a lecturer at the University of Warwick in the United Kingdom from 2000 to 2003 and a teaching assistant at Tel Aviv University in Israel from 1999 to 2000. He also has held visiting positions at the Max-Planck Institute for Mathematics in Germany and the Institute of the Advanced Scientific Studies (IHES) in France.

Sarig completed his education at Tel Aviv University in Israel, earning a bachelor’s degree summa cum laude in 1994, a master’s degree summa cum laude in 1997, and a doctoral degree with distinction in 2001. He also received a post-doctoral certification in Post-Compulsory Education from the University of Warwick Center for Academic Practice in the United Kingdom.

Wen Shen, assistant professor of mathematics

Wen Shen

Wen Shen’s research interests lie mainly in numerical analysis and partial differential equations. In particular, she has studied equations of hyperbolic conservation laws with relaxation, which are used in applications such as gas dynamics, traffic flow, viscoelasticity, and chromatography. As a further application of hyperbolic systems, she has studied non-cooperative differential games, establishing results related to the existence and stability of Nash equilibrium solutions. She also has worked on numerical methods for partial differential equations, including finite-element methods and large-scale programming for oil-reservoir simulations.

Shen has published more than a dozen scientific papers related to her research and has presented invited talks and presentations in Germany, Switzerland, and Hong Kong.

Prior to joining the Penn State faculty during the fall semester of 2003, Shen was a research associate at the International School for Advanced Studies (SISSA) in Italy from 2002 to 2003, and was an associate professor at the Norwegian University of Science and Technology from 2000 to 2001. She also had been a teaching assistant at the University of Oslo in Norway from 1993 to 1994.

Shen received a bachelor’s degree in electrical engineering in 1990 from Shanghai Jiao Tong University in China, and a second bachelor’s degree in informatics in 1993 from the University of Oslo in Norway. She received a master’s degree in informatics in 1994 and a doctoral degree in applied mathematics and informatics in 1998 from the Univesity of Oslo in Norway.

Ae Ja Yee, assistant professor of mathematics

	Ae Ja Yee

Ae Ja Yee focuses on such mathematical topics as partition theory, q-series, enumerative combinatorics, and special functions. These topics have found widespread uses in recent years in areas stretching from computer science to statistical mechanics. She has made major contributions to the elucidation of additional areas of interest in mathematics research, including Ramanujan’s Lost Notebook and the Alder Conjecture. She has published almost two dozen scientific papers related to her research.

Her research accomplishments were recognized with a Sloan Research Fellowship in 2004. She is a member of the American Mathematical Society.

Prior to joining Penn State in the fall of 2003, Yee held teaching positions at the University of Illinois from 2000 to 2003 and was a postdoctoral fellow at the Korea Science and Engineering Foundation in 2000. Yee received her bachelor’s degree from Ewha Womans University in Korea in 1993. She received her master’s degree in 1995 and her doctoral degree in 2000 from the Advanced Institute of Science and Technology in Korea.