Science Expo 2015

The annual Science Expo at UNC this past Saturday once again included a strong showing from Carolina Mathematics. The day started a little slowly, with the local public school district in Saturday school making up the many weather closings this past winter. But the event finished with a great turnout.

Special thanks go out to all of the graduate students from the department who make our participation in this event as big as it is, to Jeremy Marzuola for being the faculty organizer of our department participation in the Science Expo, and to graduate student Claudia Falcon for the many pictures shown below (click on them for higher resolution originals).

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Recent Grants to the Department

Carolina Mathematics faculty continue to bring in a wide variety of sponsored research grants to support the work of the Department. In addition to the many continuing active awards from previous periods, newly awarded grants over the past 9 months include the following:

Congratulations to all involved.

Summer 2014 faculty presentations

While the Department remains very busy with summer classes, summer is also a time for many faculty and students to focus on research and to travel to collaborate and present their work in nationally and internationally recognized venues.

Idris Assani co-directed a summer school on Ergodic Theory and Dynamical Systems in M’bour, Senegal, June 4-14.

Joe Cima gave an invited talk at the Seventh Conference on Function Spaces at Southern Illinois University Edwardsville, May 20-24.

Ellen Eischen gave invited talks in the conference p-adic Variation in Number Theory at Boston University, June 2-6, and in the Caltech Number Theory Seminar. She has also been invited to participate in the Algebraische Zahlentheorie workshop at the Mathematisches Forschungsinstitut Oberwolfach, Germany, and the Connections for Women: New Geometric Methods in Number Theory and Automorphic Forms workshop at MSRI.

Jingfang Huang co-organized the workshop Mathematics in Action: Modeling and analysis in molecular biology and electrophysiology in Suzhou, China, June 2-5. Huang will also give an invited talk at the Beijing Computational Science Research Center (CSRC).

Shrawan Kumar is giving a invited series of four lectures at the University of Pisa, Italy on “The saturated tensor product problem,” June 24-27.

Jeremy Marzuola co-organized a week-long workshop in May on Dynamics in Geometric Dispersive Equations and the Effects of Trapping, Scattering and Weak Turbulence at the Banff International Research Station for Mathematical Innovation and Discovery. Marzuola was also an invited speaker at the Stability of Solitary Waves Workshop at the Centro di Ricerca Matematica Ennio De Giorgi in Pisa, Italy. He then visited the Hausdorff Research Institute for Mathematics in Bonn, Germany to speak in a workshop and participate in their trimester on harmonic analysis and PDEs.

Jason Metcalfe spoke at the same Banff workshop in May on Dynamics in Geometric Dispersive Equations and the Effects of Trapping, Scattering and Weak Turbulence and gave a pair of invited seminar talks at Zhejiang University in Hangzhou, China.

Laura Miller and a number of her group members are off to Osaka, Japan for the Joint Annual Meeting of the Japanese Society for Mathematical Biology and the Society for Mathematical Biology, July 28 to August 1, where Miller will give one of the invited plenary talks.

Karl Petersen’s passport has been busy, between a conference on Ergodic Theory and Dynamical Systems in Torun, Poland, and talks that he gave in Tartu, Estonia and Rouen, France. Petersen will also give a mini-courses lecture series at the 4th Pingree Park Dynamics Workshop: Foundations and Frontiers in Symbolic Dynamics, July 14-17 in Colorado.

In similarly country-hopping travel style, Justin Sawon has given talks at the Lorentz Center in Leiden, Netherlands, and at the University of Utrecht, Netherlands, and has others scheduled at the University of Waterloo, Canada, and as an invited speaker at the 9th Pacific Rim Conference on Complex Geometry, July 27 to August 1, in Gunsan, South Korea.

Sasha Varchenko will be one of the invited speakers at New Trends in Quantum Integrability, an International Conference on New Trends in Quantum Groups and Integrable Systems, August 18-22, at University of Surrey, UK.

Carolina Mathematics will also be well represented at the the 2014 SIAM Annual Meeting, held this year in Chicago. Greg Forest will speak in a session on Nonlinear Fluids. Jeremy Marzuola and Laura Miller are both speaking in a session organized by Miller on Plant and Protist Biomechanics. Sorin Mitran is presenting in a session on Mesoscale and Nonlocal Models of Materials with Microstructure. And new faculty arrival Katie Newhall is speaking on “Dynamics of Ferromagnets” in a session on Applications in Nonlinear Dynamics with Chaos, Stochasticity, and Multiple Scales.

Mathematics at the 2014 UNC Science Expo

Last weekend, the Department of Mathematics had another great showing at the annual UNC Science Expo. The department hosted a variety of booths and activities outside (on a prototypically gorgeous Carolina spring day), as well as special demonstrations in the Joint Applied Math and Marine Sciences Fluids Lab.

The corn starch walk is always a particular favorite, appearing in the University Gazette’s special photo gallery of the Science Expo.

Thank you to Jeremy Marzuola for organizing the department’s participation in this important campus-wide event. Our pictures of the event were taken by Marzuola, department chair Rich McLaughlin, and graduate student Claudia Falcon.

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Marzuola wins NSF CAREER award

CrystalcuspProfessor Jeremy Marzuola has been named a recipient of a Faculty Early Career Development “CAREER” award from the National Science Foundation (NSF).

As the NSF describes, “The Faculty Early Career Development (CAREER) Program is a Foundation-wide activity that offers the National Science Foundation’s most prestigious awards in support of junior faculty who exemplify the role of teacher-scholars through outstanding research, excellent education and the integration of education and research within the context of the mission of their organizations.”

Titled Nonlinear PDE Models in Mathematical Physics and Experiment, Marzuola’s CAREER award provides him with $440,000 of research support over five years, allowing him to explore the mathematics of a variety of physical model systems, including but not limited to crystal surface evolution (as in the image here, from a recent paper by Marzuola and Jon Weare).

Marzuola is the fourth Carolina Mathematics faculty member to win a CAREER award while a member of the Department, joining Peter Mucha in 2007, Jason Metcalfe in 2011, and Laura Miller in 2012. Additionally, Rich McLaughlin won a CAREER award at Utah in 1997 and brought the grant with him when he moved to Carolina, making Marzuola our fifth overall recipient of this prestigious award affiliated with the Department.

Congratulations to Jeremy on this outstanding recognition.

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.