# By the Numb3rs Fall 2010

## LETTER FROM THE CHAIR

Dear Alumni and Friends,

Welcome to the third and first electronic issue of By the Numb3rs. I’d like to thank everyone who responded to the survey–we are grateful for your feedback and happy to be responding with what you want.

In this issue, we’re pleased to feature a profile of alumni Tim Adamo, who is pursuing his doctorate in mathematics at Oxford University in England.

We are also pleased to announce that Professor Thomas Hales has been recognized both inside and outside the University–with a Chancellor’s Award for Distinguished Research and a Fulkerson Prize. We’ve been fortunate to receive two grants from the National Science Foundation. And we also have new faculty members Jeff Wheeler and Konstantine Zelatore to introduce you to.

As always, please keep in touch. We love hearing from alumni and learning about the exciting things you’re working on. Visit our website, www.mathematics.pitt.edu, for information on staying in touch and the latest information on the department.

class

Sincerely,

Ivan Yotov

Chair,

Department of Mathematics

Events

### Michalik Lecture on January 24, 2011 Features Roger Penrose

We are pleased to announce that the 2011 Michalik Lecture will feature noted mathematician Roger Penrose. The title of his talk will be "Can we see through the Big Bang, into another World?" Penrose has a remarkable resume and will certainly have a stimulating and thought-provoking presentation. Highlights of his background include:

- Earning his Ph.D. at Cambridge (St John's College) in 1958, and writing a thesis on "tensor methods in algebraic geometry" under algebraist and geometer John A. Todd.
- He devised and popularised the Penrose triangle in the 1950s, describing it as "impossibility in its purest form" and exchanged material with the artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it.
- In 1965 at Cambridge, he proved that singularities (such as black holes) could be formed from the gravitational collapse of immense, dying stars.
- His 1971 invention of spin networks, which later came to form the geometry of spacetime in loop quantum gravity.
- The 1974 discovery of Penrose tilings, which are formed from two tiles that can only tile the plane nonperiodically, and are the first tilings to exhibit fivefold rotational symmetry.
- In 2004 Penrose released
*The Road to Reality: A Complete Guide to the Laws of the Universe*, a 1,099-page book aimed at giving a comprehensive guide to the laws of physics.

His awards for his contributions to science are just as prestigious:

- He was elected a Fellow of the Royal Society of London in 1972.
- In 1975, Stephen Hawking and Penrose were jointly awarded the Eddington Medal of the Royal Astronomical Society.
- In 1985, he was awarded the Royal Society Royal Medal.
- Along with Stephen Hawking, he was awarded the prestigious Wolf Foundation Prize for Physics in 1988.
- In 1990 Penrose was awarded the Albert Einstein Medal for outstanding work related to the work of Albert Einstein by the Albert Einstein Society.
- From 1992 to 1995 he served as President of the International Society on General Relativity and Gravitation.
- In 1994, Penrose was knighted for services to science.
- In 1998, he was elected Foreign Associate of the United States National Academy of Sciences. In 2000 he was appointed to the Order of Merit.

The Michalik Lecture Series is a way of continuing to recognize former student and faculty member Edmund R. Michalik’s long history with the University of Pittsburgh and the Department of Mathematics. From receiving his M.S. in Mathematics in 1940 throughout his career until 1980 he volunteered his time and taught as an Adjunct Professor in the Department of Mathematics. His dedication to both mathematics and the University was exemplary.

##

FEATURED ALUMNI

### Tim Adamo

Oxford University is one the preeminent academic institutions in the world – and where 2009 Department of Mathematics graduate Tim Adamo is taking what he learned at the University of Pittsburgh and applying it in the PhD program.

Adamo, who also majored in psychology and minored in physics, had the opportunity to work with people across several departments during his time at Pitt, people who have had a significant impact on his work.

“I was fortunate to work with Ted Newman in Physics and Bard Ermentrout, and Alexander Matros in Economics,” Adamo said. “I was also lucky enough to be influenced by a wide variety of faculty; just a few who I would consider particularly important in terms of how they influenced the way I think now are: Tom Hales, Anna Vainchtein, Bill Troy, Piotr Hajlasz in Mathematics; Vladimir Savinov and Dan Boyanovsky in Physics and Jack Ochs in Economics.”

Combining his interest in math and physics, Adamo is a member of the mathematical physics research group at Oxford, where he works in two areas -- classical general relativity and twistor theory. General relativity is Einstein's theory of gravity and Twistor theory is an approach to studying space-time rooted in complex geometry.

“With general relativity, I'm interested in how we can use complex and differential geometry to learn things about the physics encoded by the curvature of space-time, especially in asymptotic scenarios -- which are very far away from the gravitating source,” Adamo explained. “In addition to allowing us to learn things about general relativity, twistor theory also shows some promise for being an alternative root to a unified theory of physics (i.e., uniting general relativity with quantum field theory). I am particularly interested in twistor actions for gauge theories and for gravity; these constructions allow us to calculate things like scattering amplitudes for physical processes (the sort of stuff that the measure at particle colliders like the LHC) using twistor theory. My work is focused on extending twistor Yang-Mills theory from the action-based perspective, and on trying to find a fully non-linear twistor action for graviton scattering processes.”

Working with diverse groups of people is something that Adamo mastered during his time at Pitt – a skill that has certainly prepared him well for his work at Oxford.

“The people at Oxford, both the professors and students, are working on a very wide variety of topics, and it can be hard to understand what other people are talking about when you're trying to become an expert in your own area at the same time. At Pitt, I was able to take a broad array of coursework which now makes it easier for me to speak intelligently with faculty members and other students who are not in my own (small) area of expertise,” Adamo said. “And I still maintain a connection to Pitt with my collaborations with Ted Newman in the Physics department on research projects in general relativity.”

After completing his work at Oxford, Adamo hopes to continue working in academia, and influence the next generation of mathematicians. He is certainly off to an impressive start, working as a teaching assistant last fall at Oxford for a course in Special Relativity and Electromagnetism.

*Photo Curtesy of Chris Chirdon

## FACULTY UPDATES

### Recent Additions to Our Faculty

### Meet Jeff Wheeler

The Department of Mathematics is pleased to introduce our newest faculty member, Jeff Wheeler. Wheeler earned his Ph.D. from the University of Memphis in May 2008. The primary result of Jeff's dissertation involved extending a Combinatorial Number-Theoretic conjecture of Paul Erdos and Hans Heilbronn to finite groups (the original conjecture was established in 1995). His research won first place in the Math and Computer Science division of the University of Memphis graduate research fair. In addition, four of the top five co-authors with Paul Erdos (Andras Sarkozy, Ralph Faudree, Richard Schelp, and Cecil Rousseau) were at Memphis Jeff's final year, and two of which were on his committee (Sarkozy and Rousseau). Jeff was also fortunate to have the renowned Combinatorist Bela Bollobas on his committee.

Jeff's first two papers appeared this year in the number theory journal Acta Arithmetica. His paper with Paul Balister has earned Wheeler an Erdos number of three, and being Paul's student gives him the distinction of being an academic nephew of Andrew Wiles. Jeff also comes to Pitt with a rich and successful teaching history from his time lecturing at Belmont Technical College (St. Clairsville, OH), Miami University (Oxford, Ohio), the University of Tennessee-Knoxville, the University of Memphis, Rhodes College (Memphis), Duquesne University, and Carnegie Mellon University.

Jeff is a Wheeling, West Virginia native who is happy to again live in a region that is not flat. In addition to teaching and doing math, Jeff enjoys hiking - especially in the mountains - and drinking and brewing good beer. He and his wife Jamie both earned their bachelor's degrees from Miami University and their master's degrees from the University of Tennessee. Moving to Pittsburgh has allowed Jamie to continue her eight year career with FedEx. After doing finance for many years, Jamie now solves customers' logistic concerns. She has won FedEx's highest award - the Corporate Five Star Award - from founder and CEO Fred Smith. Jamie and Jeff live in Marshall Township, north of the city, with their soon-to-be four year-old daughter, Anna, and their 18 month-old son, Jackson.

### Meet Konstantine Zelator

Konstantine Zelator is a native of Athens, Greece and obtained a diploma (5-year degree) in civil engineering from the National Technical University of Athens, Greece in 1978; a master’s of science degree in mathematics in 1982 from Brown University in Providence, Rhode Island.

Between 1984-2010 Zelator has been very active both in teaching and research. He has published 21 papers in traditional, refereed print journals. He has also published 23 papers in the electronic publication arXiv.org, owned and operated by the Cornell University Library. He is currently working on another six papers which are in various stages of development.

Zelator has worked as a faculty member at quite a few colleges and universities, which include the University of Pittsburgh, Rhode Island College, University of Toledo, University of Northern Colorado, Antioch College/University, Carnegie Mellon University, Heidelberg College and Penn State University.

Zelator published a sci-fi book in 2003 entitled Atlantis Revisited (Dorrance Publishing). In October 2001 he founded his own publishing entity, Brainstorm Fantasia Inc. Recently he published through Brainstorm Fantasia 2 math books After Calculus Algebra: Relations, Numbers, Functions, equations and A Trigonometric Primer: From elementary to Advanced Trigonometry.

Konstantine Zelator became a naturalized US citizen in 1991 and holds dual citizenship with US and Greece.

### Professor Stuart Hastings Retires

The Department of Mathematics is sorry to announce the retirement of Professor Stuart Hastings, after an illustrious 23 year career at the University. Professor Hastings received his Ph.D. in 1964, under the direction of Norman Levinson at MIT. After time at Case Western Reserve University and SUNY Buffalo, he came to Pitt in 1987, as departmental chair. He stayed in this position for eight years, at the end of which he was happy to turn the administration over to his successor, Professor Chadam, and direct his full attention to teaching and research.

Some of his most enjoyable teaching moments have been in recent years, where he taught mostly upper level classes for math majors, particularly linear algebra and differential equations.

“We have had some excellent students in the new century, and the great majority of students now, whether they are particularly skilled in math or not, have been fun to work with,” Hastings said. “I’m approaching retirement with mixed feelings -- looking forward to the increased freedom but the probably decreased association with the student age group. I hope to not lose all such contact, however, I’m anticipating teaching the honors version of ordinary differential equations in the spring term, 2011.”

Hastings graduate teaching has also been rewarding over the years. On the border between teaching and research comes advising of graduate students. His Ph.D. students here at Pitt have been, and continue to be, a source of significant pride.

“ I am so pleased that two of them were awarded Andrew Mellon Fellowships by the University, and I continue to be in contact with a number of former students, from the Pitt years and before, about interesting research issues.” Hastings added.

Hastings research has been mostly in differential equations, and he has enjoyed collaborations and discussions over many years with Professors Ermentrout, McLeod and Troy, as well as more recent work with them and with Professor Chen. In addition, he has enjoyed the collegiality of the math department over the years, and the discussions about math, teaching, and life with faculty, staff and students remain a pleasure.

Moving beyond the world of differential equations, Hastings enjoyed additional collaborations. In conjunction with James Greenberg, who was later Head of the math department at CMU, he developed what became known as the Greenberg-Hastings cellular automaton, and he was pleased to see in a recent Google search that this model is continuing to be used by researchers around the world. Another excursion outside of differential equations resulted in a collaboration with two younger mathematicians at Pitt, Professors Borisov and Dickinson. This was a project in geometry which grew out discussions at departmental teas about his new hobby of woodworking.

“I have no ambition to make fine furniture, but I do hope to continue making toys for my grandchildren,” Hastings adds. “I actually know very little geometry, and so in this paper, published last month, I provided some of the questions and my collaborators provided interesting, and sometimes unexpected, answers. “

Professor Hastings will still be frequenting the department -- this fall he will be working with a Ph.D student as she completes her thesis, and finishing a graduate level book on differential equations with Professor Mcleod.

## NEW GRANTS

### Juan Manfredi’s award from the National Science Foundation is on Analysis of the p-Laplacian

In many problems in physics and engineering the relevant energies are proportional to the square of the velocity. The resulting equations are linear and model very well small variations from equilibrium. But more substantial variations are better modeled by considering non-quadratic energies. In this proposal we study some aspects of the mathematical theory of the equations that result from the minimization of energies (or other quantities in physics and engineering) that are given by power laws.

Manfredi explores the connections between p-harmonic functions and stochastic games. It may shine new light into some optimization problems that can be formulated in spaces quite more general than Euclidean space (graphs, trees, length spaces). In addition, Manfredi will use the formulation of Tug-of-War games in simple graphs to mentor several freshman students who used computer simulation to run these games, and are exposed to mathematical thinking early in their undergraduate career.

### Anna Vainchtein receives an award from the National Science Foundation to study “Kinetics of Lattice Phase Transitions”

Anna Vainchtein received an award from the National Science Foundation to study “Kinetics of Lattice Phase Transitions”. This proposal is concerned with physically-motivated modeling of materials undergoing martensitic phase transition, a diffusionless deformation of crystal lattice from the high-symmetry parent austenite phase to the low-symmetry martensite phase which can exist in several symmetry-related twin variants. This project has been funded for 3 years.

### Jon Rubin receives an award from the Nation Science Foundation to study the use of mathematical modeling and analysis to investigate how the brain generates rhythms that drive respiration, locomotion, and other rhythmic processes

The topic of this project is the use of mathematical modeling and analysis to investigate how the brain generates rhythms that drive respiration, locomotion, and other rhythmic processes. The work will involve various techniques from dynamical systems theory, which allows us to study solutions to complicated systems of differential equations, and will break new ground in the analysis of how intrinsic neuronal properties interact with the architecture of connections among neurons to generate particular activity patterns. The results will lead to biological predictions about how the respiratory system can adapt to extreme conditions, such as oxygen deprivation, and how it may be possible to restore locomotor rhythms after spinal cord injury.

## AWARDS

### Thomas Hales and Sam Ferguson Awarded the Fulkerson Prize for Outstanding Work in Discrete Mathematics

The innovative work of Professor Thomas Hales, along with that of his collaborator Sam Ferguson, was awarded the 2009 Fulkerson Prize for two papers in the area of discrete geometryπ–"A proof of the Kepler Conjecture" and "Sphere Packings, V. Pentahedral Prisms"

### Professor Gartside Receives Teaching Excellance Award

Prof. Paul Gartside is the winner of the 2010 Tina and David Bellet Teaching Excellence Award. The Bellet teaching awards were established in 1998 by School of Arts and Sciences alumnus David Bellet and his wife, Tina, to recognize outstanding and innovative undergraduate teaching in Arts and Sciences.

More>

### Thomas Hales Awarded 2010 Chancellor’s Award for Distinguished Research

The work of Thomas Hales was also recently recognized by the University with a Chancellor’s Award for Distinguished Research. At the awards ceremony, Chancellor Mark Nordenberg praised the Mellon Professor of Mathematics and senior scholar Thomas Hales for his seminal contributions to a broad range of mathematics areas, including discrete geometry, algebra and formal theorem proving.

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