Latest PDE mini-school held this week

Continuing their successful mini-schools from the past two years, the UNC PDE group held their latest mini-school this week. Each two-to-three day school features a series of lectures by a principal invited speaker. This week’s principal speaker was Patrick Gérard, giving a series of three talks on “Long time estimates of solutions to Hamiltonian nonlinear PDEs”. A particular hallmark of the mini-schools is that the principal speakers are asked to make the lectures accessible to graduate students and to provide an indication of some open problems in the research area. This workshop is supported by the National Science Foundation under grant number DMS-1501020 Professors Hans Christianson and Jason Metcalfe.

Congratulations to Hans and Jason for continuing these excellent workshops.

New grants to department faculty

The past year has been another successful year for Carolina Mathematics faculty obtaining grants to support the activities of the department. In addition to the many awards that continue from previous periods, new grants over the past 12 months include the following awards:

Congratulations to everyone involved.

PDE/Analysis Mini-Schools Continue for 2015

minischools2015Congratulations to Professors Hans Christianson and Jason Metcalfe for their new grant from the National Science Foundation to support the continuation of the UNC PDE mini-schools into 2017. Continuing from the success of their previous mini-schools, each 2-3 day school will feature a series of 3-5 lectures by a principal speaker. The talks are tailored to an audience of graduate students and are intended to introduce the audience to a modern and important class of research problems. Three to five complementary talks will be given by additional invited participants, often the principal speaker’s graduate students, postdocs, or young collaborators.

The first UNC PDE/Analysis mini-school of 2015 starts this week with 5 lectures by Gunther Uhlmann (University of Washington), beginning at a graduate student level and introducing a current research topic. The title of this week’s lectures is “Inverse Problems: Seeing the Unseen.” There will be several satellite talks by Uhlmann’s students and postdocs. The full schedule is available online.

The second mini-school of 2015 will be held April 8-10, with Alex Ionescu (Princeton) on “Water Wave Models in 2D and 3D: Regularity and Formation of Singularities.” The third mini-school will be this summer, with Steve Zelditch (Northwestern) on “Planck’s Constant, Time, and Stationary States in Quantum Mechanics.”

Congratulations again to Hans and Jason for continuing to bring these great events to Chapel Hill.

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.

Faculty deliver invited lectures at conferences and summer schools – Part 2

Continuing our previous discussion about lectures given by Carolina Mathematics faculty at workshops and conferences this summer, today we highlight those activities from the second half of Summer 2013.

Joe Cima will be giving a one hour invited address at the conference “Invariant Subspaces of the Shift Operator” sponsored by the Canadian government at the Centre de Recherches Mathematiques in Montreal. He will also give a shorter talk at the CBMS conference at Clemson University.

Both Hans Christianson and Jeremy Marzuola spoke at the Joint International Meeting of the American Mathematical Society and the Romanian Mathematical Society, held in Alba Iulia, Romania.

Chris Jones has had a particularly eventful past month, first as a co-organizer of the INDAM Workshop on “Mathematical Paradigms of Climate Science” in Rome, Italy, a plenary lecture given at the First Annual CliMathNet Conference, held in Exeter, UK, and finally as an organizer of the Idealab on Tipping Points in the Climate System held at the Institute for Computational and Experimental Research in Mathematics at Brown University.

Peter Mucha gave an invited talk on “Time-dependent generalizations of hub and authority scores” at the Workshop on Time-Dependent and Multiplex Networks at the University of Oxford.

Karl Petersen will speak in the special session on Symbolic Dynamics at the Mathematical Congress of the Americas in Guanajuato, Mexico.

Alexander Varchenko will present a series of three lectures on “Bethe algebras and geometric Langlands correspondence” at the GEOQUANT 2013 ESI School and Conference on Geometry and Quantization in Vienna, Austria.

Jon Wahl was one of the 9 invited speakers at the conference “A Singular Life“, honoring and marking the retirement of Eduard Looijenga with “a celebration of his achievements and influence in Dutch and International mathematics” in Utrecht, The Netherlands.

Congratulations to all.

Faculty deliver invited lectures at conferences and summer schools

Summer for Carolina Mathematics includes a variety of courses taught in our summer sessions, many faculty busy working on their sponsored research, and an enhanced opportunity to travel to workshops and conferences to give lectures and meet with fellow mathematicians for collaborative activities.

Ivan Cherednik gave an invited lecture last month in the representation theory seminar at the Institut de Mathématiques de Jussieu-Paris Rive Gauche. He is giving a similar lecture as one of four invited speakers on June 24th at the Institute Henri Poincaré.

Hans Christianson will speak later this month at the conference on “Quantum chaos, resonances and semi-classical measures” in Roscoff, France.

Jingfang Huang was a plenary speaker last week at The 1st Chongqing Workshop on Computational and Applied Mathematics.

Chris Jones gave one of the plenary lectures at the First Central Region Conference on Numerical Analysis and Dynamical Systems, held last month at the University of Kansas. He then gave a public lecture colloquium on ”Climate Change: the Science and the Math” at the University of Missouri and an invited lecture at a conference on “Topological Methods in Differential Equations and Nonautonomous Flows” in Florence, Italy. This week, he is one of the keynote speakers at the “Workshop on slow-fast dynamics: theory, numerics, application to life and earth sciences” in Barcelona.

Robert Lipshitz spoke last month at the “Low Dimensional Topology” workshop at the Simons Center for Geometry and Physics.

Jeremy Marzuola is presently giving a topics course at the Karlsruhe Institute of Technology on Nonlinear Waves this summer, with 8 lectures spread over 7 weeks on nonlinear bound states and their stability properties in the context of the Schrodinger equation. He will then speak later this month at the conference on “Quantum chaos, resonances and semi-classical measures” in Roscoff, France.

Laura Miller was an invited session plenary speaker at the symposium on “Microscale Interactions in Aquatic Environments” held at Les Houches Physics School in March. In recognition of her excellent interdisciplinary teaching, Miller has also been tapped to teach the mathematics “bridge” course this summer to the first cohort of incoming Chancellor’s Science Scholars.

Peter Mucha gave five lectures as one of the four keynote speakers at the Summer School on Network Science held last month at the Interdisciplinary Mathematics Institute at the University of South Carolina.

Karl Petersen gave an invited seminar talk last month at Ohio State. This week, he is attending the Automata Theory and Symbolic Dynamics Workshop at the University of British Columbia, where graduate student Kathleen Carroll will be talking about their joint work on symbolic dynamics (as part of her master’s project).

Lev Rozansky was an invited speaker at the conference on “Quantum Topology and Hyperbolic Geometry” held in Nha Trang, Vietnam last month.

Michael Taylor was an invited speaker at the “Analysis, Complex Geometry, and Mathematical Physics” conference at Columbia University last month.

Alexander Varchenko is one of the plenary speakers next week at the 21st International Conference on Integrable Systems and Quantum Symmetries in Prague. Later this month, he is also an invited speaker at the “Experimental and Theoretical Methods in Algebra, Geometry and Topology” conference in Romania.

Jon Wahl gave a mini-course series of 4 invited lectures at the conference “Geometry and Topology of Complex Singularities” in April 15-19, at CIRM, Luminy, near Marseille.

The above only covers the first half of this summer. We will come back to this topic again next month to discuss the faculty presentations scheduled for the second half of the summer. In the meantime, best wishes for pleasant travels to all involved.