Edmund R. Michalik has a long history with the University of Pittsburgh and the Department of Mathematics. He received his BA in education from Pitt in 1937 and went on to receive his MS in mathematics in 1940. After he graduated, Michalik joined the Navy to serve during WWII. The day after he was discharged in 1946, he met his future wife, Martha. He came back to teach at Pitt until 1951. Over the next few years Michalik worked for a variety of organizations, including the Army, Atlantic Research Corporation and the Department of Mathematics at the Mellon Institute, where he was the head of applied mathematics. In 1957 he worked for PPG as the head of the applied mathematics, and later as the senior engineer and head of computer research, when he retired in 1980. Throughout this time Michalik volunteered his time and taught as an adjunct professor in the Department of Mathematics. He was dedicated to the study of mathematics.
Speaker: Enrique Zuazua, Alexander von Humbolt Professor of Applied Mathematics
Title: Reaction-Diffusion Models: Dynamics, Control, and Numerics
Abstract: Reaction-diffusion equations are ubiquitous in a variety of fields including combustion and population dynamics. There is an extensive mathematical literature addressing the analysis of steady state solutions, traveling waves, and their stability, among other properties. Control problems arise in many applications involving these models. Often times, control and/or state constraints emerge as intrinsic requirements of the processes under consideration. There is also a broad literature on the control of those systems, addressing, in particular, issues such as the possibility of driving the system to a given final configuration in finite time. But, the necessity of preserving the natural constraints of the process are rarely taken into account. In this lecture we shall present the recent work of our team on the Fisher-KPP and Allen-Canh or bistable model, showing results of two different types depending of the initial and final states under consideration. First, the fact that, in some cases, constrained controllability for large enough time can be achieved, but that there is a minimal waiting time for the property to hold. And, second, negative results showing the existence of threshold effects, so that some targets can never be achieved. We shall also present some numerical experiments which indicated that optimal trajectories are often quite complex, and hard to deduce form purely analytical arguments.
Thanks to the generosity of the Michalik family and in honor of Edmund R. Michalik, the Department of Mathematics this semester brought Professor Martin Nowak to Pitt for two exciting events that provided a mathematical connection with Pitt's "Year of the Healthy U" theme. Nowak is a Professor of Mathematics and Biology and the Director of the Program for Evolutionary Dynamics at Harvard University. He is a world expert on evolutionary game theory (e.g, including the evolution of cooperation and other altruistic-seeming behaviors), population structures, cancer dynamics and treatment, and a range of other topics. He has written several hundred articles and has published books on virology, evolutionary dynamics, and cooperation.
On Wednesday, March 21st, Dr. Nowak was joined by Dr. Gilles Clermont (Pitt Critical Care Medicine and long-time collaborator of several current Pitt Mathematics faculty), Dr. David Galloway (Pitt Public Health Dynamics Lab), and Dr. Wilbert Van Panhuis (Pitt Epidemiology/Biomedical Informatics) for a panel on "Computational Methods for Fostering a Healthy Community". This event was organized by the Department of Mathematics and was moderated by Dean Donald Burke from Pitt's Graduate School of Public Health. The panelists discussed mathematical modeling of the complex interacting feedback loops associated with the immune response, the use of the FRED (A Framework for Reconstructing Epidemiological Dynamics) agent-based modeling system to predict geographic spread of disease outbreaks, the Project Tycho open-access global database of disease-related information, and how mathematical analysis of cancer as an evolving system can be used optimize cancer treatments. They also took questions from an audience eager to understand how mathematics and data can combine to revolutionize how we study and improve community health.
On Thursday, May 22nd, Dr. Nowak gave the Edmund R. Michalik Distinguished Lecture on "Evolutionary Dynamics". Nowak outlined principles of evolution, listing familiar ones such as mutation and selection but also proposing that cooperation belongs on the list as well. He discussed how mathematical frameworks, such as Moran or birth-death processes, graph theory, and evolutionary game theory (related to the methods applied in economics by famed mathematician John Nash), can be used to study the selection process. In particular, his mathematical analysis illustrated how certain patterns of interactions among individuals can allow a population to gain maximal advantage from cooperation. The lecture was well attended, with faculty and students both well represented in the audience, and led to interesting discussions about language, artificial intelligence, and, of course, the role of mathematics in understanding the living world.
John D. MacArthur Professor of Mathematics, University of Wisconsin at Madison
February 28, 2017
Ballroom, O'Hara Student Center
New York Times bestselling author Jordan Ellenberg has been writing for a general audience about math for more than fifteen years and his work has appeared in the New York Times, the Wall Street Journal, the Washington Post, Wired, The Believer, and the Boston Globe. He is author of How Not to Be Wrong: The Power of Mathematical Thinking (Penguin Press, 2014).
Prof. J. Tinsley Oden
Foundations of Predictive Computational Science:Selection and Validation of Models of Complex Systems in the Presence of Uncertainty
September 23, 2016
Ballroom, O'Hara Student Center
J. Tinsley Oden is Associate Vice President for Research, Cockrell Family Regents' Chair in Engineering No. 2, Peter O'Donnell Jr. Centennial Chair in Computing Systems, and the founding Director of the Institute for Computational Engineering and Sciences at The University of Texas at Austin. His research is on the mathematical theory and implementation of numerical methods applied to problems in linear and nonlinear solid and fluid mechanics. Dr. Oden has authored over 600 scientific publications and has authored or edited 56 books. He is a recipient of numerous awards, including a member of the U.S. National Academy of Engineering, a Fellow of the American Academy of Arts and Sciences, an Honorary Member of the American Society of Mechanical Engineers, the Theodore von Karman Medal, the John von Neumann medal, and the Newton/Gauss Congress Medal.
Prof. Martin Hairer, University of Warwick
December 2, 2015
Ballroom, O'Hara Student Center
Martin Hairer is an Austrian mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Regius Professor of Mathematics at the University of Warwick, having previously held a position at the Courant Institute of New York University. He was awarded the Fields Medal in 2014.
Prof. John Ball, Oxford University
Defects in Materials and their Mathematical Description
March 17, 2014 at 4 p.m.
Ballroom A, University Club at the University of Pittsburgh
John Ball is Sedleian Professor of Natural Philosophy at the University of Oxford and a Fellow of the Queen's College. He was President of the International Mathematical Union from 2003-06. His research interests include elasticity, the mathematics of solid and liquid crystals, the calculus of variations, and infinite-dimensional dynamical systems. He is a foreign member of the French Academy of Sciences and the Norwegian Academy of Science and Letters, and is a fellow of the Royal Societies of London and Edinburgh, and of the American Mathematical Society, among many other honors and prizes.
Prof. Frank Morgan
Soap Bubbles, Tilings, and Other Partitioning Problems
March 22, 2013 at 4 p.m.
Ballroom B, University Club at the University of Pittsburgh
Abstract: The Ancient Greeks proved that the circle is the least-perimeter way to enclose given area.Similarly the round soap bubble provides the least-perimeter way to enclose a given volume of air, although that was not proved until 1884 by Schwarz. Similarly the double bubble that forms when two soap bubbles come together is the least-perimeter way to enclose and separate two given volumes of air, although that wasn't proved until 2000 by Hutchings, Morgan, Ritoré, and Ros.
Lord Kelvin sought the least-perimeter way to divide all of space into unit volumes, and his conjecture stood for 100 years, until Weaire and Phelan found a better way in 1994. Whether their new candidate is best remains open today. Even the least-perimeter way to divide the plane into unit areas, using the bees' hexagonal honeycomb tiling, though conjectured by the Ancient Greeks, was not proven until 1999 by Hales. The most efficient tiling by pentagons remains open.
In many simple nonEuclidean possible universes, even the ideal shape for a single soap bubble remains open.
Prof. Shing-Tung Yau
Geometry: from Riemann to Einstein and on to String Theory"
October 5, 2012
Shing-Tung Yau has made fundamental contributions to differential geometry which have influenced a widerange of scientific disciplines, including astronomy and theoretical physics. Yau’s first major contribution to differential geometry was his proof of the Calabi conjecture, which concerns how volume and distance can be measured not in four, but in five or more dimensions. In 1979 Yau and Richard Schoen proved Einstein’s positive mass conjecture by applying methods devised by Yau. The proof was based on their work with minimal surfaces. In 1982 Yau was awarded the Fields Medal, the highest award in mathematics, and in 1994 he shared with Simon Donaldson of Oxford University the Crafoord Prize of the Royal Swedish Society, in recognition of his “development of nonlinear techniques in differential geometry leading to the solution of several outstanding problems.” In 2010 Yau published the book The Shape of Inner Space.
Sir Roger Penrose
"Can We See Through the Big Bang into Another World?"
January 24, 2011
Prof. Sir Roger Penrose has made many contributions to the fields of Mathematics and Physics. He proved that singularities (such as black holes) could be formed from the gravitational collapse of immense, dying stars and invented spin networks which later came to form the geometry of spacetime in loop quantum gravity. Prof. Penrose is also well known for his 1974 discovery of Penrose tilings, which are formed from two tiles that can only tile the plane non-periodically, and are the first tilings to exhibit fivefold rotational symmetry. He is the recipient of many awards and honors, including a Royal Medal from the Royal Society and a Wolf Prize, which he shares with Stephen Hawking. Prof. Penrose’s book "The Road to Reality" gives a comprehensive guide to the laws of physics. His latest book is "Cycles of Time."
Prof. Luis A. Caffarelli
"Non linear, geometric homogenization"
March 26, 2010
Professor Luis A. Caffarelli holds the Sid Richardson Chair in Mathematics at the University of Texas at Austin.The focus of his research has been elliptic nonlinear partial differential equations and their applications. Some of his most significant contributions are the regularity of free boundary problems and solutions to nonlinear
elliptic equations, optimal transportation theory and, more recently, results in the theory of homogenization.
Professor Caffarelli is a member of the National Academy of Sciences. He has been awarded Doctor Honoris Causa from l'Ecole Normale Superieure in Paris, Universidad Autónoma de Madrid, and Universidad de la Plata in Argentina. He received the Bôcher Prize in 1984 and the prestigious Rolf Schock Prize in Mathematics of the Royal Swedish Academy of Sciences in 2005. He was recently awarded the Leroy P. Steele Prize for Lifetime Achievement in Mathematics.
Tony F. Chan
"Images, PDEs and Wavelets"
March 20, 2009
Dr. Chan's research interests include mathematical image processing and computer vision, VLSI physical design and computational brain mapping. He is a Fellow of the American Association for the Advancement of Science. Dr. Chan has published over 200 refereed papers and has mentored over 25 PhD students and 15 postdoctoral fellows. He is a co-founder of the Institute for Pure and Applied Mathematics at UCLA, established to promote collaborations between the mathematical sciences and the general scientific and engineering disciplines. Dr. Chan currently serves as Assistant Director of the Directorate for Mathematical and Physical Sciences at the National Science Foundation. The MPS is the largest Directorate at NSF with an annual budget of just over $1B.
Neil J. A. Sloane
"The Online Encyclopedia of Integer Sequences: Solved and Unsolved Problems"
April 4, 2008
Neil Sloane is a Fellow at AT&T Shannon Labs in Florham Park, NJ. He
is a member of the National Academy of Engineering, an IEEE Fellow, and recipient of the IEEE Hamming Medal and the MAA Chauvenet Prize. He is the author or co-author of numerous books, including “The Theory of Error-Correcting Codes” (with F. J. MacWilliams) and “Sphere Packing, Lattices and Groups” (with J. H. Conway).
Dr. Cathleen Morawetz
"Collisionless Shocks in Space"
April 6, 2007
Professor Cathleen Morawetz is a Fellow of the American Association for the Advancement of Science, the American Academy of Arts and Sciences, and National Academy of Sciences. She was Director of the Courant Institute of Mathematical Sciences, and the President of the American Mathematical Society. She receieved the National Medal of Science in 1998, and the Lifetime Acheivement award from the Americam Mathematical Society in 2004.
Robert F. Engle, Ph.D., Nobel Laureate
"Global Volatility: its Measurement, Interpretation and Causes"
April 7, 2006
Dr. Engle was awarded the 2003 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for "methods of analyzing economic time series with time-varying volatility (ARCH)."
Dr. Engle received his PhD in economics from Cornell University in 1966. His work is distinguished by exceptional creativity in the empirical modeling of dynamic economic and financial phenomena. He is a renowned expert in Financial Economics, Time Series Analysis, Volitility and Risk Management and Empirical Market Microstructure.