Events
Michalik Distiguished Lecture Series
The 2019 Michalik Distinguished Lecture was delivered on October 10, 2019 by Professor Enrique Zuazua. Dr. Zuazua is the Alexander von Humboldt Professor of Applied Mathematics at Friedrich Alexander University in Erlangen-Nürnberg. He has received numerous prizes and distinctions including two ERC Advanced Grants (NUMERIWAVES 2010-2014 and DYCON 2016-2021), Doctor Honoris Causa from the Université de Lorraine (France), and the 2007 Rey Pastor Prize (the national prize in Mathematics and Computer Science in Spain). Professor Zuazua is a world leader in the field of Applied Mathematics with a particular interest in partial differential equations, control theory and numerical analysis.
To better understand Professor Zuazua's work, try to think about the world is as an accumulation of “shapes in motion”. Professor Zuazua has developed new mathematics to better understand this sophisticated dynamics of nature, to improve simulations of these processes, and, as far as possible, to design, control and guide their behavior. New mathematical methods are needed to, on one hand, anticipate and predict and, on the other, to build optimal strategies for achieving desired outcomes. The tools developed in these mathematical areas apply to many areas of engineering and science including aviation, power networks, climate change, and social behavior of networks.
In his lecture “Reaction-Diffusion Models: Dynamics, Control, and Numerics,” Zuazua described a class of equations that are ubiquitous in a variety of fields including combustion and population dynamics. The control of these processes has many applications, in which the aim is to drive a system to a given final configuration in finite time, subject to the structural and energetic constraints of the process.
In particular, Zuazua discussed his recent work on the Fisher-KPP equation that models the wave of advance of advantageous genes in the context of population dynamics and the and Allen-Cahn equation that describes phase separations in multi-component alloy systems. In some cases, constrained controllability for large times can be achieved, but there is a minimal waiting time for this property to hold, while in others we have negative results showing the existence of threshold effects, indicating that some targets can never be achieved.
Math Kangaroo
Math Kangaroo is an international mathematics competition for students in grades 1-12. This multiple-choice test takes place every year on the third Thursday in March. Instead of focusing on knowledge of formulas, the competition focuses on logical puzzles.
This is the largest mathematical competition ever, with more than 6 million students participating in recent years. The competition was established in France in 1991 and was modeled after a competition that had been run in Australia since 1978. The competition was named “Math Kangaroo” to pay tribute to the Australian precursor. The competition reached the United States in 1998, when Maria Omelanczuk first organized it in Chicago. There were only 32 participants the first year, but the competition has been growing exponentially since then. In 2019, there were 31,837 participants in 43 states and territories.
The idea to organize this competition in Pittsburgh was suggested by Joanna Hajlasz back in 2006, and in 2007, Zuzana Swigonova organized the first Math Kangaroo with eight members of the Fox Chapel School District. Since 2008, Piotr Hajlasz and David Swigon have been organizing the competition at the University of Pittsburgh with between 100 and 200 participants each year. In 2009, our competition was featured in the Pittsburgh Post-Gazette.
One of the prominent past participants of the competition at the University of Pittsburgh is Andrew Gu. He is a two-time gold medal winner at the International Mathematical Olympiad and is currently studying at MIT.
The Fox Chapel School District and the University of Pittsburgh were the first sites for the Math Kangaroo competition in Pennsylvania. Currently, there are 18 sites across the state, and in 2019 Pennsylvania had the ninth largest participant count out of all U.S. states.
We believe that the Math Kangaroo competition promotes mathematics by focusing on interesting logical problems and we hope to keep organizing the competition in the years to come
Recent Workshops at the Pitt Mathematical Research Center
Time Filters and Predictive Accuracy
Date: May 29 - 30, 2019
The problem of numerical solution of complicated, coupled systems of evolution equations arises in nearly every application of scientific and technological importance and has spurred the development of much of modern numerical analysis. This has proven to be an area where appetite for better algorithms and greater computational resources expands to match both. Current practice often involves using either splitting methods or different time discretizations for different terms representing different physical effects. The resulting implicit-explicit (IMEX) combinations of methods are beyond the powerful theory of linear multistep methods and must be analyzed method by method until a systematic theory develops. These combinations lead to new computational artifacts for which novel time filters and stabilizations have developed. This workshop promoted the direct interaction between experts from different communities and linked rigorous numerical analysis and analysis of PDEs with current problems of impact. For more information, click here.
Local and Nonlocal Trends is Analysis and Geometry
Date: October 11 - 13, 2019
This workshop brought together established senior mathematicians, young researchers, and graduate students working on local and nonlocal differential equations and applications, particularly to geometry. The extremely fruitful interplay between geometry and analysis is as old as the two subjects, and in recent years nonlocal techniques have been developed that promise further applications in Geometric Analysis. There were fifteen talks by speakers from Europe and the Americas and a poster session. Funding was provided from the NSF (proposal number DMS-1931340) and the MRC. For more information, click here.