Donaldson gives 2014 Alfred Brauer Lectures

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Sir Professor Simon Kirwan Donaldson, who recently became a permanent member of the Simons Center at Stony Brook, gives the Alfred Brauer Lectures in Mathematics this week, titled “Canonical Kähler metric and algebraic geometry.” The first of these three lectures was held yesterday afternoon, followed by a reception, with the remaining lectures today and tomorrow.

Professor Donaldson became internationally famous with his 1983 D. Phil. thesis “The Yang-Mills equations over Kähler manifolds,” which proved stunning new results about distinguishing differentiable structures on four-manifolds. This seminal work revolutionized the approach to geometry in dimension four, and led to his receiving the Fields Medal in 1986 (before he reached the age of 30). Through articles, books, and over 40 thesis students, he has influenced complex and symplectic geometry, in particular with recent work on Kähler metrics on manifolds, the topic of his Brauer Lectures.

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Professor Donaldson (left) speaks with Professor Varchenko (right) at the reception following the first of his three lectures.

Besides his Fields Medal, Donaldson has among other honors won or shared the Crafoord Prize, Polya Prize, King Faisal Prize, and Shaw Prize. A Fellow of the Royal Society since 1986, he is also a Foreign Associate Member of the US National Academy of Sciences and the French Académie des Sciences.

The Alfred Brauer Fund was established by the Department of Mathematics in 1984 on the occasion of Dr. Brauer’s ninetieth birthday , and the Alfred Brauer Lectures began in 1985. The most recent Brauer Lecturers have been Peter Sarnak, János Kollár, Andrew Majda, Jeff Cheeger, Shing-Tung Yau, Percy Deift, Charles Fefferman, Claire Voisin, Alex Eskin, Gérard Laumon, Alexander Lubotzky, and Vaughan Jones.

A special thank you to Jon Wahl (pictured left below with Donaldson on right) for once again organizing this year’s Brauer Lectures.

Wahl and Donaldson

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Triangle Lectures in Combinatorics return to Chapel Hill

The Triangle Lectures in Combinatorics is a series of combinatorial workshops held each semester on a Saturday in the Research Triangle region of North Carolina, funded by the National Security Agency and the National Science Foundation. The workshop this spring will be hosted by the University of North Carolina, Chapel Hill in Chapel Hill, North Carolina on February 22, 2014. It will include four one hour invited talks as well as coffee breaks and ample time for discussions throughout the day. There will also be two related seminar talks on Friday afternoon just prior to the meeting.

More information about the conference can be found at its web site, http://www.math.ncsu.edu/TLC/.

Thank you to Prof. Richard Rimanyi for being the department member on the Spring 2014 TLC Organizing Committee.

Chris Sogge lectures in PDE mini-school

DSC_0173November 21st and 22nd, the Department’s PDE Group held the second of three NSF supported graduate mini-schools in Partial Differential Equations for this academic year (information about the first mini-school is also available).

The main speaker was Chris Sogge of Johns Hopkins University, who spoke about pointwise bounds for eigenfunctions of the Laplacian on Riemannian manifolds.  Fortunately, we had a great turn out for all the lectures as we drew a large audience of our own graduate students and undergraduates who have been working with Hans Christianson and Jason Metcalfe studying aspects of semi-classical analysis.  A special thank you to Jason Metcalfe for arranging most of the details regarding the speaker and attendees, as well as to Elaine Bullock and Sunny Oakley from the math department staff for all the administrative support.

Chris’ first lecture on Thursday, November 21st outlined some of the aspects of spectral analysis and its connection in particular to the geodesic flow and the wave equation on a given manifold.  He also outlined where some of the difficulties of extending the result to manifolds with boundary might arise.  He focused on spectral cluster estimates in particular the first day.  Then, on Friday, he was able to take the machinery he had introduced and walk the audience through the ideas of some very recent work he has done separately with Matt Blair of the University of New Mexico (who spent part of a sabbatical at UNC recently) and Steve Zelditch of Northwestern.  The key arguments are to improve the pointwise bounds for spectral clusters if possible and to apply the Von Neumann ergodic theorem in order to relate the notion of properties of self focal points on the manifold to when one can improve a pointwise estimate on a spectral cluster.

In addition, there were two supporting lectures by Chris’ graduate students Hongtan Sun and Min Xue.  Hongtan spoke Thursday about dispersive estimates for the wave equation on backgrounds with hyperbolic trapped orbits.  Min spoke Friday about Strichartz estimates for Klein-Gordon equations in asymptotically Euclidean settings.  In addition, we had graduate student Yuanlong Chen of University of Washington and postdoctoral fellow Peng Shao at the Institute for Advanced Study in attendance for the lectures.

All lecture notes and talk slides are available online at the mini-school web site.  Congratulations to all involved for a second successful PDE mini-school.  We look forward to the third.

Kevin Zumbrun lectures in UNC PDE mini-school

DSC_0160This past week we held the first of three NSF supported graduate mini-schools in Partial Differential Equations (October 2-4, 2013) for this academic year.  The main speaker was Kevin Zumbrun of Indiana University, who spoke about stability of periodic waves in systems of hyperbolic conservation laws.  Fortunately, we had a great turn out for all the lectures as we drew a large audience from both the pure and applied faculty, neighboring universities, other departments and a host of our graduate students.  A special thank you to the Elaine Bullock and Sunny Oakley from the math department staff for setting up the snacks and coffee for everyone each afternoon.

DSC_0162 Kevin’s first lecture discussed the existence of periodic solutions and, motivated by ideas of Whitham, a modified approach towards studying their modulation and stability within equations related to fluid flow.  In the second lecture, he discussed spectral stability and various analytic and numerical methods for computing the Floquet spectrum for related periodic problems.  Finally, he discussed the rigorous and demanding perturbation theory involved in studying these equations on long or global time scales.

In addition, there were three supporting lectures by Kevin’s graduate students Blake Barker and Soyeun Jung of Indiana and a postdoc Fang Yu of Penn State.  Blake spoke Wednesday about numerically assisted proofs of spectral stability and rigorous bounds on numerical computations using interval arithmetic, and Soyeun spoke Thursday about pointwise bounds for linearized operators arising as perturbations of periodic solutions in reaction-diffusion equations.  The final supporting talk of the mini-school was given by Fang Yu, who spoke about some Nash-Moser techniques for studying stability of shock-like solutions in 3d Euler flows.

Lastly,DSC_0165 the mini-school was nicely complemented by a related talk in the Applied Math Seminar by Tom Beale from Duke (which was kindly re-scheduled to a later time so as to allow everyone to attend both it and the mini-school).  In a fitting end to the week, Tom aptly spoke about efficient numerical methods for studying fluid flows in 2 and 3 dimension.

More details about the workshop in general and all the talk slides can be found at http://www.unc.edu/~marzuola/Mini-Schools.

Congratulations and thank yous to Profs. Hans Christianson and Jeremy Marzuola for the NSF grant (also with department alumna Prof. Anna Mazzucato [Ph.D., 2000] of Penn State) that supported this effort in addition to the summer 2012 conference in honor of Michael Taylor, and to the entire UNC PDE group for putting these mini-schools together.

The second PDE mini-school will occur November 20-21, featuring lectures from Chris Sogge on eigenfunctions of the Laplacian on manifolds.

Ergodic Theory Workshop

Prof. Idris Assani organized and hosted the 12th Ergodic Theory Workshop, March 21-23, 2013. Amidst an excellent three days of mathematical presentations, the workshop also well met explicit goals including the fostering of collaborations within and outside UNC Chapel Hill and increasing the participation of women and young researchers. In particular, this workshop brought in participants from across the USA, and from Austria, England, France, Italy, Poland, Senegal, Ukraine, and Uruguay. The keynote address to open the workshop was given in the department’s colloquium by Prof. Amie Wilkinson from the University of Chicago.

Prof. Assani with the Ergodic Theory Workshop participants in front of Phillips Hall

Preliminary feedback from the workshop shows that, once again, it has been a great success. Comments so far include

  • “I am filled with admiration for you and what you’ve done. That after all of these years the workshop remains fresh, informal and so inclusive is incredible.”
  • “I enjoyed meeting and talking with old friends, and making some new friends. I thought the meeting was well run and the broad mix of junior and senior speakers, of both genders, was excellent.”

Congratulations to Idris for another successful workshop.

Vaughan Jones gives Brauer Lectures

The 2013 Brauer Lectures were given earlier this week by Vaughan Jones, Professor of Mathematics at Vanderbilt University and Emeritus Professor at Berkeley. Jones’ three lectures on “Von Neumann Algebras” opened Monday, March 4th with an introductory lecture for a general mathematical audience, followed by more detailed explanations in subsequent lectures on Tuesday and Wednesday about how the subject has developed.

Vaughan Jones is famous for his surprising discovery of the so-called Jones polynomial, a fundamental invariant in knot theory that arose from work in the apparently unrelated subject of Von Neumann algebras. This work has revolutionized the ancient subject of knots, and has led as well to new developments in physics and biology. It was no surprise when Jones was awarded the Fields Medal in 1990 at the International Congress of Mathematicians in Kyoto. A native of New Zealand, Jones received his Docteurès Sciences in Mathematics under André Haefliger at the University of Geneva in 1979. He came to the US in 1980, holding positions at UCLA and Penn before becoming Professor of Mathematics at the University of California at Berkeley in 1985. He has been Professor at Vanderbilt since 2011. Besides his Fields Medal, Jones has won the New Zealand Government Science Medal and the Onsager Medal. His honors include election as Fellow of the Royal Society and U.S. National Academy of Sciences, and honorary membership in the London Mathematical Society. Long active on scientific advisory and editorial boards, he was in 2004 elected vice-president of the American Mathematical Society.

Alfred Brauer (1894–1985) had a profound impact on the Mathematics Department at UNC. Born in Germany, he held a position at the University of Berlin until the advent of the Nazis during the 1930s. He fled the country in 1939, accepting Hermann Weyl’s invitation to the Institute for Advanced Study in Princeton. He came to North Carolina in 1942, teaching here until his retirement in 1966. Alfred Brauer was honored by the University with the award of a Kenan professorship in 1959, the Tanner Award for excellence in undergraduate teaching in 1965, and an honorary doctor of legal letters degree in 1972.

To honor the memory of Alfred Brauer and to recognize his many contributions to the Mathematics Department at UNC, the Alfred Brauer Fund was established by the Department of Mathematics in 1984 on the occasion of his ninetieth birthday and the Alfred Brauer Lectures were begun in 1985. The most recent Brauer Lecturers have been Peter Sarnak, János Kollár, Andrew Majda, Jeff Cheeger, Shing-Tung Yau, Percy Deift, Charles Fefferman, Claire Voisin, Alex Eskin, Gérard Laumon, and Alexander Lubotzky.

From L to R: Department Chair Rich McLaughlin, Brauer Lecturer Vaughan Jones (sporting an appropriately local t-shirt), and Brauer Lectures organizer Jon Wahl

2011-12 Recap: Celebrating Warren Wogen’s career

Prof. Warren Wogen retired at the end of the 2010-11 academic year. During his decades of service to the Department, it appears that he held almost every administrative post or task at one time or another, and served in every position with excellence. Now holding the title of Emeritus Professor of Mathematics, we belatedly gathered in Spring 2012 to celebrate his long career in the Department.

It isn’t necessarily that we’re quite that slow at planning things; rather, Warren caught us off guard by deciding to outright retire rather than take a “phased retirement”. The perhaps-too-true-not-to-tell joke is that he made this decision after we asked him to be a go-to mentor on all things regarding the Department Chair and Director of Graduate Studies positions for his phased retirement service duties. Only he truly knows whether that prospective headache drove him to simply jump into full retirement instead! Either way, his long commitment to the well being of the Department deserved special recognition.

In what will hopefully become a new Department tradition for all retirements, we chose to honor Warren with a special visitor of his choosing to speak in our Colloquium. On March 15, Prof. Stephan Garcia of Pomona College gave the special retirement colloquium on the subject of “Hidden Symmetries in Everyday Operators”. It was a wonderful presentation with broad appeal (the photograph below, taken in the dark, doesn’t do it justice), including pointers to Warren’s own research work.

We additionally gathered for a traditional retirement dinner honoring Warren. After an evening of good food, a number of excellent stories were shared by his colleagues about Warren across the years. We will miss seeing his good-natured dedication on display day-to-day; but we hope that he will enjoy his emeritus status and that we will see him frequently in the Department. Congratulations to Warren.